rustyfi-lang 0.1.1

//! The primitive registry. Shaped so the ~300 vminst instructions can be
//! ported one `prims!` line at a time; primitives are registered under their
//! real v0.0.6 names so later stdlib loading finds them.
//!
//! `document`, `+p` and `\emph` are not natives: they live in the
//! `stdja-mini` stdlib package
//! (`lib-rustyfi/dist/packages/stdja-mini.satyh`), loaded through
//! `rustyfi-loader` and typechecked/evaluated like any other `.satyh`
//! library. See that file's header comment for the primitives it is built
//! from.

use crate::eval::{available_fields, eval_error, DecoEntry, EvalError, Interp};
use crate::quoted::{BText, IText, MathElem};
use crate::value::{BaseEnv, DocumentValue, Env, TextInfo, Value};
use rustyfi_backend::char_script;
use rustyfi_backend::{
    break_into_lines, break_opportunities, chop_page, default_math_variant_char, fit_cell,
    graphics_bbox, linear_transform_graphics, linear_transform_path, measure_block,
    natural_metrics, path_bbox, place_block_at, placed_line_extent, shift_graphics, shift_path,
    Annot, AnnotAction, BreakKind, Cell, Closing, Color, Context, Dash, DecoId, DocExtras, DocInfo,
    FontKey, GraphicsElem, GraphicsFnId, HookId, HorzBox, HorzStringInfo, HyphenLang, ImageId,
    ImageResource, InlineMarkKind, Language, Length, ListMarkKind, MathCharClass, MathConstants,
    MathCorner, MathGlyph, MathKind, MathScriptLevel, NamedDest, OutlineEntry, Paddings, Page,
    PageGeometry, PaperSize, Path, PathSeg, Point, PrePath, PureHorzBox, Script, ScriptFont,
    Subpath, TabularBox, VertBox, VertVariantPolicy, FORCED_BREAK_PENALTY, MIN_FIRST_ASCENDER,
    NO_BREAK_PENALTY,
};
// Only the `load-pdf-image` importer builds these, and it is compiled out
// without the `pdf-image` feature.
#[cfg(feature = "pdf-image")]
use rustyfi_backend::{ImportedObjects, ObjRepr, PdfPageResource};
use rustyfi_syntax::RustyfiVersion;
use std::collections::BTreeMap;
#[cfg(feature = "pdf-image")]
use std::collections::BTreeSet;
use std::rc::Rc;
use std::sync::Arc;
// UAX #15 normalization / UAX #29 grapheme segmentation, for
// `normalize-string-to-nf{c,d}`/`split-grapheme-cluster`.
use unicode_normalization::UnicodeNormalization;
use unicode_segmentation::UnicodeSegmentation;

/// Font keys agreed with this port's base-14 metrics provider.
const FONT_REGULAR: FontKey = FontKey(0);
const FONT_BOLD: FontKey = FontKey(1);
const FONT_OBLIQUE: FontKey = FontKey(2);

/// Which target version(s) a `PrimDef` row is registered under. Mirrors
/// `RustyfiVersion`'s two-variant shape today; `#[non_exhaustive]` for the
/// same reason `RustyfiVersion` is (a future third generation gets a new
/// arm here, not a redesign) — every `match` on this type needs a wildcard.
#[non_exhaustive]
#[derive(Clone, Copy, Debug, PartialEq, Eq)]
pub enum VersionSpan {
    /// Registered under every version this port implements. The default
    /// for every `prims!` line that omits a tag.
    Both,
    V0_0Only,
    V0_1Only,
}

impl VersionSpan {
    /// Whether a `PrimDef`/type-table row tagged `self` should be visible
    /// under `version`. `Both` always allows; `V0_0Only`/`V0_1Only` allow
    /// exactly their own version — no partial/future-version fallback (a
    /// third generation gets its own new `VersionSpan` arm, not silent
    /// inclusion under an existing one).
    pub fn allows(self, version: RustyfiVersion) -> bool {
        match (self, version) {
            (VersionSpan::Both, _) => true,
            (VersionSpan::V0_0Only, RustyfiVersion::V0_0) => true,
            (VersionSpan::V0_1Only, RustyfiVersion::V0_1) => true,
            _ => false,
        }
    }
}

pub struct PrimDef {
    pub name: &'static str,
    pub arity: usize,
    pub run: fn(&mut Interp, Vec<Value>) -> Result<Value, EvalError>,
    pub version: VersionSpan,
}

impl std::fmt::Debug for PrimDef {
    fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
        write!(
            f,
            "PrimDef({}/{}, {:?})",
            self.name, self.arity, self.version
        )
    }
}

macro_rules! prims {
    ($($($tag:ident)? $name:literal ($arity:literal) => $f:path;)*) => {
        static PRIM_DEFS: &[PrimDef] = &[
            $(PrimDef {
                name: $name,
                arity: $arity,
                run: $f,
                version: prims!(@span $($tag)?),
            },)*
        ];
    };
    (@span) => { VersionSpan::Both };
    (@span v006) => { VersionSpan::V0_0Only };
    (@span v01) => { VersionSpan::V0_1Only };
}

/// Generate the `_v006`/`_v01` `PrimDef`-shaped pair for a primitive body
/// that needs to know the generation of the code that CALLED it.
///
/// The graphics-callback family (the primitives below, and the deco family
/// behind them) needs this: those bodies decide whether a callback returns `graphics
/// list` (0.0.6) or one `graphics` collection (0.1). Do NOT read
/// `interp.version` for that — it is a single whole-program field naming the
/// ENTRY document's generation, while a spliced 0.0.6 package calls these
/// primitives with its OWN convention.
///
/// Registering the body twice fixes it at compile time: `compile.rs`'s
/// `Ast::VersionScope` arm folds a primitive reference against the innermost
/// enclosing scope's version, so a call inside a 0.0.6 dependency picks the
/// `_v006` row and one in the 0.1 entry picks `_v01`, with nothing threaded
/// through the interpreter. The two rows share one type-table entry per
/// version (`prim_types::primitive_type_with_version`).
macro_rules! version_forked_prims {
    ($($v006:ident, $v01:ident => $body:path;)*) => {$(
        fn $v006(interp: &mut Interp, args: Vec<Value>) -> Result<Value, EvalError> {
            $body(interp, RustyfiVersion::V0_0, args)
        }
        fn $v01(interp: &mut Interp, args: Vec<Value>) -> Result<Value, EvalError> {
            $body(interp, RustyfiVersion::V0_1, args)
        }
    )*};
}

version_forked_prims! {
    prim_inline_graphics_v006, prim_inline_graphics_v01 => prim_inline_graphics;
    prim_inline_graphics_outer_v006, prim_inline_graphics_outer_v01
        => prim_inline_graphics_outer;
    prim_tabular_v006, prim_tabular_v01 => prim_tabular;
    prim_inline_frame_outer_v006, prim_inline_frame_outer_v01 => prim_inline_frame_outer;
    prim_inline_frame_inner_v006, prim_inline_frame_inner_v01 => prim_inline_frame_inner;
    prim_inline_frame_breakable_v006, prim_inline_frame_breakable_v01
        => prim_inline_frame_breakable;
    prim_block_frame_breakable_v006, prim_block_frame_breakable_v01
        => prim_block_frame_breakable;
}

prims! {
    "read-inline" (2) => prim_read_inline;
    "read-block" (2) => prim_read_block;
    // v0.0.6 (vminst.ml `BackendLineBreaking`): `bool -> bool -> context ->
    // inline-boxes -> block-boxes` — the two leading bools select whether
    // the paragraph's top/bottom edge is breakable across a page boundary.
    "line-break" (4) => prim_line_break;
    // `page -> (pbinfo -> page-content-scheme) -> (pbinfo -> page-parts) ->
    // block-boxes -> document` (vminst.ml:1024, `BackendPageBreaking`) —
    // v0.0.6's `page` ADT argument. 0.1's `page` ADT is gone; the v01 arm's
    // first argument becomes a plain `length * length` instead, same arity
    // and same `page_break_core` backing loop.
    v006 "page-break" (4) => prim_page_break_v006;
    v01  "page-break" (4) => prim_page_break_v01;

    // `page-break-multicolumn` (vminst.ml:1065
    // `BackendPageBreakingMultiColumn`) / `page-break-two-column`
    // (vminst.ml:1041 `BackendPageBreakingTwoColumn`): same v006/v01 fork
    // shape as `page-break` above.
    v006 "page-break-multicolumn" (7) => prim_page_break_multicolumn_v006;
    v01  "page-break-multicolumn" (7) => prim_page_break_multicolumn_v01;
    v006 "page-break-two-column" (6) => prim_page_break_two_column_v006;
    v01  "page-break-two-column" (6) => prim_page_break_two_column_v01;

    // ---- int arithmetic (vminst.ml: Plus/Minus/Times/Divides/Mod) --------
    "+" (2) => prim_int_add;
    "-" (2) => prim_int_sub;
    "*" (2) => prim_int_mul;
    "/" (2) => prim_int_div;
    "mod" (2) => prim_int_mod;

    // ---- int comparisons (vminst.ml: EqualTo/GreaterThan/LessThan; the "<>"/">="/"<=" trio comes from primitives.cppo.ml's `general_table`,
    // defined there as `LogicalNot (EqualTo ..)` / `LogicalNot (LessThan ..)`
    // / `LogicalNot (GreaterThan ..)`, typed `int -> int -> bool`) ----------
    "==" (2) => prim_int_eq;
    "<>" (2) => prim_int_ne;
    "<" (2) => prim_int_lt;
    ">" (2) => prim_int_gt;
    "<=" (2) => prim_int_le;
    ">=" (2) => prim_int_ge;

    // ---- 0.1 bitwise ops (dev-0-1-0 vminst.ml: PrimitiveBitShiftLeft :2495, PrimitiveBitShiftRight :2477, PrimitiveBand :2527,
    // PrimitiveBor :2541, PrimitiveBxor :2513, PrimitiveBnot :2556).
    // 0.0.6 upstream has none of these; `<<`/`>>` lex as ordinary
    // BinopLt/BinopGt opsymbol runs under BOTH versions (lexer.rs:634-653)
    // and simply stay unbound names under 0.0.6. --
    v01 "<<" (2) => prim_bit_shift_left;
    v01 ">>" (2) => prim_bit_shift_right;
    v01 "band" (2) => prim_band;
    v01 "bor" (2) => prim_bor;
    v01 "bxor" (2) => prim_bxor;
    v01 "bnot" (1) => prim_bnot;

    // ---- bool (vminst.ml: LogicalAnd/LogicalOr/LogicalNot) ----------------
    // NOTE: registered here as strict 2-arg primitives (both arguments are
    // evaluated before the call, since primitive application is call-by-
    // value). Real SATySFi short-circuits "&&"/"||" via elaboration
    // (build-in `if`); that desugaring lives in the (out-of-scope) elaborator.
    "&&" (2) => prim_bool_and;
    "||" (2) => prim_bool_or;
    "not" (1) => prim_bool_not;

    // ---- float (vminst.ml: FloatPlus/FloatMinus/FloatTimes/FloatDivides, PrimitiveFloat, PrimitiveRound) ---------------------------------------
    "+." (2) => prim_float_add;
    "-." (2) => prim_float_sub;
    "*." (2) => prim_float_mul;
    "/." (2) => prim_float_div;
    "float" (1) => prim_float_of_int;
    "round" (1) => prim_round;

    // ---- 0.1 float comparisons (saphe-split@b836d512 vminst.ml:2679-2740:
    // PrimitiveFloatGreaterThan/-LessThan/-GreaterThanOrEqualTo/
    // -LessThanOrEqualTo, named ">."/"<."/">=."/"<=."). Confirmed absent
    // from 0.0.6 upstream (0 hits in either its v0.0.6 tag or dev-0-1-0's
    // vminst.ml/primitives.cppo.ml) — genuinely v01-only, unlike "+."/"-."/
    // "*."/"/." above; float.satyg's `abs`/`max`/`min` need `>=.`/`<=.`.
    // All four lex as ordinary BinopGt/BinopLt opsymbol runs under both
    // versions (lexer.rs:634-653), same as the bitwise "<<"/">>" above.
    v01 ">." (2) => prim_float_gt;
    v01 "<." (2) => prim_float_lt;
    v01 ">=." (2) => prim_float_ge;
    v01 "<=." (2) => prim_float_le;

    // ---- length arithmetic (vminst.ml: LengthPlus/LengthMinus/LengthTimes/ LengthDivides/LengthLessThan/LengthGreaterThan) -----------------------
    "+'" (2) => prim_length_add;
    "-'" (2) => prim_length_sub;
    "*'" (2) => prim_length_scale;
    "/'" (2) => prim_length_div;
    "<'" (2) => prim_length_lt;
    ">'" (2) => prim_length_gt;

    // ---- string (vminst.ml: Concat, PrimitiveArabic, PrimitiveSame) -------
    "^" (2) => prim_string_concat;
    "arabic" (1) => prim_arabic;
    "string-same" (2) => prim_string_same;

    // ---- list cons ----------------------------------------------------------
    // Upstream makes `::` syntax (`UTListCons`/`ListCons`), not a primitive.
    // This port's elaborator flattens every binary operator into
    // `Apply(Apply(Var(op_text), lhs), rhs)` (see `elaborate.rs`'s
    // operator-precedence fold), so `::` needs an env-bound primitive like
    // `+`/`^`.
    "::" (2) => prim_list_cons;

    // ---- mutable-cell dereference (evaluator.cppo.ml `Dereference`) --------
    // Upstream's "!" *constructs* a `Dereference` AST node that a later pass
    // reduces (primitives.cppo.ml: `lambda1 (fun v1 -> Dereference(v1))`);
    // this port has no such two-step split, so "!" is an ordinary strict
    // primitive that dereferences directly — structural deviation only.
    "!" (1) => prim_deref;

    // ---- string, continued (vminst.ml: PrimitiveStringLength/StringSub/ StringExplode; low-priority additions verified against vminst.ml) ----
    "string-length" (1) => prim_string_length;
    "string-sub" (3) => prim_string_sub;
    "string-explode" (1) => prim_string_explode;
    "regexp-of-string" (1) => prim_regexp_of_string;
    "string-match" (2) => prim_string_match;
    "split-on-regexp" (2) => prim_split_on_regexp;

    // ---- text embedding (vminst.ml:1707 PrimitiveEmbed: string -> inline- text; the interp body wraps the string as a one-element quoted text) --
    "embed-string" (1) => prim_embed_string;

    // ---- context ops -----------------------------------------------------
    //
    // vminst.ml:1434 `PrimitiveSetFontSize`: `~% (tLN @-> tCTX @-> tCTX)`.
    "set-font-size" (2) => prim_set_font_size;
    // vminst.ml:1449 `PrimitiveGetFontSize`: `~% (tCTX @-> tLN)`.
    "get-font-size" (1) => prim_get_font_size;
    // vminst.ml:1633 `PrimitiveSetLeading`: `~% (tLN @-> tCTX @-> tCTX)`,
    // sets `ctx.leading` — the baseline-to-baseline distance, which is
    // exactly our existing `Context::leading` field. (There is *also* a
    // `set-min-gap-of-lines`, vminst.ml:1291-1292, which sets a *different*
    // field, `min_gap_of_lines` — the minimum extra gap between two lines'
    // bounding boxes, on top of `leading`. We don't model that separate
    // field, so `set-leading` is the one that matches "baseline distance"
    // and an existing Context field.)
    "set-leading" (2) => prim_set_leading;
    // vminst.ml:1396 `PrimitiveSetParagraphMargin`:
    // `~% (tLN @-> tLN @-> tCTX @-> tCTX)`. Sets the new `paragraph_top`/
    // `paragraph_bottom` fields (see context.rs); not wired into any
    // box-producing primitive yet (a future `+p` would consult them).
    "set-paragraph-margin" (3) => prim_set_paragraph_margin;
    // vminst.ml:1648 `PrimitiveGetTextWidth`: `~% (tCTX @-> tLN)`.
    "get-text-width" (1) => prim_get_text_width;
    // vminst.ml:1247 `PrimitiveGetInitialContext`:
    // `~% (tLN @-> tICMD tMATH @-> tCTX)` — a paragraph width and the
    // *default math command* (the handler used for bare `${...}` math
    // embedded directly in inline text). FAITHFUL: the second argument is
    // interned via `Interp::register_math_command` and installed as
    // `Context::math_command`, consulted by `read_inline`'s `EmbedMath` arm.
    "get-initial-context" (2) => prim_get_initial_context;
    // LOCAL, non-upstream primitive: `set-font-key : int -> context ->
    // context`, sets `Context::font` directly to `FontKey(n)`. v0.0.6 has no
    // primitive shaped like this at all — real font switching there goes
    // through `set-font : script -> (string * float * float) -> context ->
    // context` (choosing a font *by name* per script, vminst.ml's
    // `PrimitiveSetFont`), which is far richer than this port's
    // base-14-metrics-by-`FontKey` model can support. `set-font-key` is the
    // minimal faithful-enough stand-in the `stdja-mini` stdlib package
    // (lib-rustyfi/dist/packages/stdja-mini.satyh) needs to implement
    // `\emph`/`\bold` by switching to the oblique/bold base-14 face
    // (`FONT_OBLIQUE`/`FONT_BOLD` above) without inventing a whole font-name
    // resolution layer. Out-of-range keys are accepted as-is (there is no
    // registry to validate against yet); an unknown `FontKey` simply fails
    // later, when a font metrics lookup for it comes up empty.
    "set-font-key" (2) => prim_set_font_key;

    // ---- box combinators (vminst.ml `HorzConcat`/`VertConcat`/ `BackendVertSkip`/`BackendFixedEmpty`/`BackendOuterEmpty`) ----------
    //
    // vminst.ml:803 `HorzConcat`: `~% (tIB @-> tIB @-> tIB)`.
    "++" (2) => prim_inline_concat;
    // vminst.ml:818 `VertConcat`: `~% (tBB @-> tBB @-> tBB)`.
    "+++" (2) => prim_block_concat;
    // vminst.ml:1757 `BackendFixedEmpty`: `~% (tLN @-> tIB)` — a fixed-width
    // box with no stretch/shrink (`PureHorzBox::FixedEmpty`, hbox.rs).
    "inline-skip" (1) => prim_inline_skip;
    // vminst.ml:1771 `BackendOuterEmpty`: `~% (tLN @-> tLN @-> tLN @-> tIB)`,
    // params `(widnat, widshrink, widstretch)` in that order — exactly the
    // (natural, shrinkable, stretchable) field order `PureHorzBox::OuterEmpty`
    // already uses, so this is a direct wrap, no new box variant needed.
    "inline-glue" (3) => prim_inline_glue;
    // vminst.ml:1171 `BackendVertSkip`: `~% (tLN @-> tBB)`, builds
    // `VertFixedBreakable(len)` — our existing `VertBox::Skip(len)`.
    "block-skip" (1) => prim_block_skip;

    // ---- the reflow marker-box
    // constructors. No vminst.ml entry — these are NEW primitives (not an
    // upstream port), the minimal hook that is unavoidable since
    // list/emphasis structure is 100% interpreted `.satyh` with no existing
    // Rust interception point. Both take a plain `int` tag (there is no
    // surface syntax to pass a Rust enum literal from `.satyh` source) —
    // see `prim_list_mark`/`prim_inline_mark`'s doc comments for the exact
    // tag encoding. Registered for `Both` versions (harmless/unused under
    // 0.0.6 today; the 0.0.6 `itemize.satyh` may be wired to them later). ----
    "list-mark" (1) => prim_list_mark;
    "inline-mark" (1) => prim_inline_mark;

    // `|>` (reverse application) is NOT a primitive: it is elaborated
    // directly to `Apply(f, x)` (see `elaborate.rs`'s `climb`).

    // ---- float trig / log / exp / rounding (vminst.ml 2729-2880) ----------
    "sin" (1) => prim_sin;
    "asin" (1) => prim_asin;
    "cos" (1) => prim_cos;
    "acos" (1) => prim_acos;
    "tan" (1) => prim_tan;
    "atan" (1) => prim_atan;
    "atan2" (2) => prim_atan2;
    "log" (1) => prim_log;
    "exp" (1) => prim_exp;
    // vminst.ml:2865/2880 `PrimitiveCeil`/`PrimitiveFloor`: both `float ->
    // float` (NOT `int` — easy to mistype; contrast `round`, above, which
    // does return `int`).
    "ceil" (1) => prim_ceil;
    "floor" (1) => prim_floor;
    // vminst.ml:2319 `PrimitiveShowFloat`: `float -> string`, OCaml's
    // `string_of_float`.
    "show-float" (1) => prim_show_float;

    // ---- byte-indexed string ops (vminst.ml 2056-2196) ---------------------
    // vminst.ml:2159 `PrimitiveStringByteLength`: counts UTF-8 BYTES, unlike
    // `string-length`'s Unicode-scalar-value count above.
    "string-byte-length" (1) => prim_string_byte_length;
    // vminst.ml:2123 `PrimitiveStringSubBytes`: byte-indexed `string-sub`.
    "string-sub-bytes" (3) => prim_string_sub_bytes;
    // vminst.ml:2196 `PrimitiveStringUnexplode`: inverse of `string-explode`.
    "string-unexplode" (1) => prim_string_unexplode;

    // ---- 0.1 Unicode string prims (dev-0-1-0 vminst.ml :2050/:2066/:2082),
    // via the `unicode-normalization`/`unicode-segmentation` crates. --------
    v01 "normalize-string-to-nfc" (1) => prim_normalize_string_to_nfc;
    v01 "normalize-string-to-nfd" (1) => prim_normalize_string_to_nfd;
    v01 "split-grapheme-cluster" (1) => prim_split_grapheme_cluster;

    // ---- diagnostics (vminst.ml 2056, 3133) --------------------------------
    // vminst.ml:2056 `PrimitiveDisplayMessage`: `string -> unit`. Upstream
    // prints to stdout (`print_endline`); see `prim_display_message`'s doc
    // comment for why this port deliberately prints to stderr instead.
    "display-message" (1) => prim_display_message;
    // vminst.ml:3133 `AbortWithMessage`: `string -> 'a` — raises a dynamic
    // error carrying the message verbatim.
    "abort-with-message" (1) => prim_abort_with_message;
    // ---- images (raster images). Mirrors v0.0.6 vminstdef.yaml:540/:554. -
    "load-image"          (1) => prim_load_image;         // string -> image
    "use-image-by-width"  (2) => prim_use_image_by_width; // image -> length -> inline-boxes
    // `load-pdf-image : string -> int -> image` (v0.0.6 vminstdef.yaml:525;
    // dev-0-1-0 `PrimitiveLoadPdfImage` — same name/type/body across both
    // versions).
    "load-pdf-image" (2) => prim_load_pdf_image;
    // `read-file : string -> list string` (dev-0-1-0 vminst.ml :3073) —
    // REAL, `load-image`'s cwd-relative-path precedent
    // (`prim_load_image`'s doc comment above): job-directory resolution
    // isn't plumbed into `Interp` at all yet, so this resolves against the
    // process cwd instead of upstream's job directory — documented
    // deviation, see `prim_read_file`'s own doc comment.
    v01 "read-file" (1) => prim_read_file;
    // `register-document-information : document-information-dictionary ->
    // unit` (dev-0-1-0 vminst.ml :2978) — REAL:
    // stores into `Interp::doc_info` (last-write-wins), drained into
    // `DocExtras::doc_info`, emitted as the PDF `/Info` dictionary by both
    // writers.
    v01 "register-document-information" (1) => prim_register_document_information;
    // ==== graphics primitives ====
    // Paths, fill/stroke, and the `inline-graphics` on-page sink. Argument
    // order transcribed from `tools/gencode/vminst.ml`: `start-path` :713,
    // `line-to` :727, `terminate-path` :759, `close-with-line` :773,
    // `fill` :2398, `stroke` :2381, `inline-graphics` :1872.
    "start-path" (1) => prim_start_path;
    "line-to" (2) => prim_line_to;
    "terminate-path" (1) => prim_terminate_path;
    "close-with-line" (1) => prim_close_with_line;
    "fill" (2) => prim_fill;
    "stroke" (3) => prim_stroke;
    // These three take a graphics-producing CALLBACK whose result shape
    // forks (`graphics list` vs one `graphics` collection) — see
    // `version_forked_prims!`'s doc comment.
    v006 "inline-graphics" (4) => prim_inline_graphics_v006;
    v01  "inline-graphics" (4) => prim_inline_graphics_v01;
    // `tabular : (cell list) list -> (length list -> length list ->
    // graphics list) -> inline-boxes` (vminst.ml:539);
    v006 "tabular" (2) => prim_tabular_v006;
    v01  "tabular" (2) => prim_tabular_v01;
    // `inline-graphics-outer : length -> length -> (length -> point ->
    // graphics list) -> inline-boxes` (vminst.ml:1891
    // `BackendInlineGraphicsOuter`).
    v006 "inline-graphics-outer" (3) => prim_inline_graphics_outer_v006;
    v01  "inline-graphics-outer" (3) => prim_inline_graphics_outer_v01;
    // ---- gr.satyh prims — see tools/gencode/vminst.ml for exact
    // signatures: `bezier-to` :742, `close-with-bezier` :787, `shift-path`
    // :663, `linear-transform-path` :678, `shift-graphics` :2451,
    // `linear-transform-graphics` :2432, `get-graphics-bbox` :2466,
    // `get-path-bbox` :696, `dashed-stroke` :2414, `draw-text` :2363.
    "bezier-to" (4) => prim_bezier_to;
    "close-with-bezier" (3) => prim_close_with_bezier;
    "shift-path" (2) => prim_shift_path;
    "linear-transform-path" (5) => prim_linear_transform_path;
    "shift-graphics" (2) => prim_shift_graphics;
    "linear-transform-graphics" (5) => prim_linear_transform_graphics;
    // `get-graphics-bbox`: v0.0.6 = un-optioned pair (vminst.ml:2466); v0.1
    // wraps `option` (dev-0-1-0 vminst.ml:2301).
    v006 "get-graphics-bbox" (1) => prim_get_graphics_bbox_v006;
    v01  "get-graphics-bbox" (1) => prim_get_graphics_bbox_v01;
    "get-path-bbox" (1) => prim_get_path_bbox;
    "dashed-stroke" (4) => prim_dashed_stroke;
    "draw-text" (2) => prim_draw_text;
    // ---- 0.1 graphics-collection prims (dev-0-1-0 vminst.ml :3105/:3119).
    // `graphics` is a collection under 0.1 — these two build/wrap it; the 6
    // hidden callback-result retypes that make a `graphics`-producing
    // callback return ONE collection instead of `list graphics` live at
    // their existing (untagged `Both`) rows below, coerced per-version by
    // `coerce_graphics_result`.
    v01 "unite-graphics" (1) => prim_unite_graphics;
    v01 "clip-graphics-by-path" (2) => prim_clip_graphics_by_path;

    // ==== `pervasives.satyh` prims. Argument order transcribed from
    // `tools/gencode/vminst.ml`: `get-natural-metrics` :2020,
    // `inline-frame-outer` :1787, `set-manual-rising` :1661,
    // `script-guard` :1908, `discretionary` :1969. ====
    "get-natural-metrics" (1) => prim_get_natural_metrics;
    // A `deco`'s result shape forks the same way, and its closure fires
    // LONG after (a post-page-break pass), so the generation must be
    // captured here — see `version_forked_prims!`/`DecoEntry`.
    v006 "inline-frame-outer" (3) => prim_inline_frame_outer_v006;
    v01  "inline-frame-outer" (3) => prim_inline_frame_outer_v01;
    // vminst.ml:1807 `BackendInnerFrame`: same `tPADS @-> tDECO @-> tIB @->
    // tIB` as `inline-frame-outer`.
    v006 "inline-frame-inner" (3) => prim_inline_frame_inner_v006;
    v01  "inline-frame-inner" (3) => prim_inline_frame_inner_v01;
    "set-manual-rising" (2) => prim_set_manual_rising;
    "script-guard" (2) => prim_script_guard;
    "discretionary" (4) => prim_discretionary;

    // `get-axis-height` (vminst.ml:1739 `PrimitiveGetAxisHeight`) —
    // STAND-IN, see body; REMOVED in 0.1 (superseded by
    // `get-math-axis-height-ratio`).
    v006 "get-axis-height" (1) => prim_get_axis_height;

    // ==== page-break-hook callback seam + cross-reference fixpoint ====
    "hook-page-break" (1) => prim_hook_page_break;
    "hook-page-break-block" (1) => prim_hook_page_break_block;
    "register-cross-reference" (2) => prim_register_cross_reference;
    "get-cross-reference" (1) => prim_get_cross_reference;
    "probe-cross-reference" (1) => prim_probe_cross_reference;

    // ==== `annot.satyh`'s prim surface (link annotations + the frame/
    // script stand-ins it needs to type-check) ====
    "get-leftmost-script" (1) => prim_get_leftmost_script;
    "get-rightmost-script" (1) => prim_get_rightmost_script;
    v006 "inline-frame-breakable" (3) => prim_inline_frame_breakable_v006;
    v01  "inline-frame-breakable" (3) => prim_inline_frame_breakable_v01;
    "register-destination" (2) => prim_register_destination;
    "register-link-to-uri" (6) => prim_register_link_to_uri;
    "register-link-to-location" (6) => prim_register_link_to_location;

    // ==== the faithful `Value::Math` primitive layer `math.satyh` is built
    // out of. 19 fork into v006/v01 pairs (v006 = zero behavior change; v01
    // consumes/produces `Value::MathBoxes`); 5 more are REMOVED in 0.1
    // outright (v006-tagged, untouched bodies). ====
    v006 "math-char" (2) => prim_math_char_v006;
    v01  "math-char" (3) => prim_math_char_v01;
    v006 "math-big-char" (2) => prim_math_big_char_v006;
    v01  "math-big-char" (3) => prim_math_big_char_v01;
    v006 "math-char-with-kern" (4) => prim_math_char_with_kern_v006;
    v01  "math-char-with-kern" (5) => prim_math_char_with_kern_v01;
    v006 "math-big-char-with-kern" (4) => prim_math_big_char_with_kern_v006;
    v01  "math-big-char-with-kern" (5) => prim_math_big_char_with_kern_v01;
    v006 "math-concat" (2) => prim_math_concat_v006;
    v01  "math-concat" (2) => prim_math_concat_v01;
    v006 "math-group" (3) => prim_math_group_v006;
    v01  "math-group" (3) => prim_math_group_v01;
    v006 "math-sup" (2) => prim_math_sup_v006;
    v01  "math-sup" (3) => prim_math_sup_v01;
    v006 "math-sub" (2) => prim_math_sub_v006;
    v01  "math-sub" (3) => prim_math_sub_v01;
    v006 "math-frac" (2) => prim_math_frac_v006;
    v01  "math-frac" (3) => prim_math_frac_v01;
    v006 "math-radical" (2) => prim_math_radical_v006;
    v01  "math-radical" (3) => prim_math_radical_v01;
    v006 "math-lower" (2) => prim_math_lower_v006;
    v01  "math-lower" (3) => prim_math_lower_v01;
    v006 "math-upper" (2) => prim_math_upper_v006;
    v01  "math-upper" (3) => prim_math_upper_v01;
    // REMOVED in 0.1 outright — v006-tagged, untouched bodies.
    v006 "math-pull-in-scripts" (3) => prim_math_pull_in_scripts;
    v006 "math-color" (2) => prim_math_color;
    v006 "math-char-class" (2) => prim_math_char_class;
    v006 "math-variant-char" (2) => prim_math_variant_char;
    // ==== the `set-math-variant-char`/`get-left-math-class`/
    // `get-right-math-class` trio: no bundled `.satyh` consumer needed yet,
    // built on `Context::math_variant_char_map` + `VariantCharPending`.
    // Forked v006/v01. ====
    v006 "set-math-variant-char" (4) => prim_set_math_variant_char_v006;
    v01  "set-math-variant-char" (3) => prim_set_math_variant_char_v01;
    v006 "get-left-math-class" (2) => prim_get_left_math_class_v006;
    v01  "get-left-math-class" (1) => prim_get_left_math_class_v01;
    v006 "get-right-math-class" (2) => prim_get_right_math_class_v006;
    v01  "get-right-math-class" (1) => prim_get_right_math_class_v01;
    v006 "math-paren" (3) => prim_math_paren_v006;
    v01  "math-paren" (4) => prim_math_paren_v01;
    v006 "math-paren-with-middle" (4) => prim_math_paren_with_middle_v006;
    v01  "math-paren-with-middle" (5) => prim_math_paren_with_middle_v01;
    // REMOVED in 0.1 outright.
    v006 "text-in-math" (2) => prim_text_in_math;
    "convert-string-for-math" (3) => prim_convert_string_for_math;
    v006 "embed-math" (2) => prim_embed_math_v006;
    v01  "embed-math" (2) => prim_embed_math_v01;
    "set-math-command" (2) => prim_set_math_command;
    // `set-math-font` forks in its argument, not its effect: 0.0.6 takes the
    // math face's ABBREV (`string`), saphe-split takes the opaque `font`
    // handle (`tFONTKEY`). Both end at the same `Context::math_font`.
    v006 "set-math-font" (2) => prim_set_math_font_v006;
    v01  "set-math-font" (2) => prim_set_math_font_v01;
    // LOCAL, non-upstream, V0_1-only — the port's spelling for upstream's
    // internal `LoadSingleFont{path}` node; see `prim_load_single_font`.
    v01  "load-single-font" (1) => prim_load_single_font;
    v006 "space-between-maths" (3) => prim_space_between_maths_v006;
    v01  "space-between-maths" (3) => prim_space_between_maths_v01;
    // ==== NEW in 0.1 — `math-text`/`math-boxes` split + `read-math` + the
    // hidden `val math`-without-scripts wrapper prim. ====
    v01 "read-math" (2) => prim_read_math;
    v01 "stringify-math" (2) => prim_stringify_math;
    v01 "set-math-char" (4) => prim_set_math_char;
    v01 "set-math-char-class" (2) => prim_set_math_char_class;
    v01 "get-math-char-class" (1) => prim_get_math_char_class;
    v01 "embed-inline-to-math" (2) => prim_embed_inline_to_math;
    v01 "get-math-axis-height-ratio" (1) => prim_get_math_axis_height_ratio;
    v01 "%math-attach-scripts" (4) => prim_math_attach_scripts;

    // ==== hyphenation/unidata loader + setter stand-ins, V0_1-only
    // (genuinely absent from 0.0.6 upstream). FAITHFUL types
    // (`prim_types.rs`); ACCEPT-AND-RETURN bodies, not hard-error
    // stand-ins like `stringify-math` above — std-ja evaluates `val
    // unidata = load-unicode-char-database …` at module LOAD time, so an
    // erroring stand-in would break every consumer at load, not just at
    // use. ====
    v01 "load-hyphenation-dictionary" (1) => prim_load_hyphenation_dictionary;
    v01 "load-unicode-char-database"  (3) => prim_load_unicode_char_database;
    v01 "set-hyphenation-dictionary"  (2) => prim_set_hyphenation_dictionary;
    v01 "set-unicode-char-database"   (2) => prim_set_unicode_char_database;

    "raise-inline" (2) => prim_raise_inline;
    "embed-block-breakable" (2) => prim_embed_block_breakable;
    "unite-path" (2) => prim_unite_path;
    "set-min-gap-of-lines" (2) => prim_set_min_gap_of_lines;

    // ==== context-setter + box-combinator prims `code.satyh`/
    // `itemize.satyh` need. Argument order from `tools/gencode/vminst.ml`:
    // `set-text-color` :1603, `get-text-color` :1618, `set-hyphen-penalty`
    // :1692, `set-space-ratio` :1309, `split-into-lines` :2269,
    // `block-frame-breakable` :1090, `embed-block-top` :1145, `set-font`
    // :1463; `set-code-text-command`/`get-natural-length` have no
    // vminst.ml entry. ====
    "set-text-color" (2) => prim_set_text_color;
    "get-text-color" (1) => prim_get_text_color;
    "set-hyphen-penalty" (2) => prim_set_hyphen_penalty;
    // `set-hyphen-min : int -> int -> context -> context` (left_hyphen_min,
    // right_hyphen_min).
    "set-hyphen-min" (3) => prim_set_hyphen_min;
    "set-space-ratio" (4) => prim_set_space_ratio;
    "set-space-ratio-between-scripts" (6) => prim_set_space_ratio_between_scripts;
    "split-into-lines" (1) => prim_split_into_lines;
    v006 "block-frame-breakable" (4) => prim_block_frame_breakable_v006;
    v01  "block-frame-breakable" (4) => prim_block_frame_breakable_v01;
    "embed-block-top" (3) => prim_embed_block_top;
    // `set-font` forks in its SECOND argument's head only: 0.0.6's
    // `string * float * float` vs saphe-split's `font * float * float`.
    v006 "set-font" (3) => prim_set_font_v006;
    v01  "set-font" (3) => prim_set_font_v01;
    // `get-font` (vminstdef.yaml:1350) forks in its RESULT's head, for the
    // same reason and along the same seam.
    v006 "get-font" (2) => prim_get_font_v006;
    v01  "get-font" (2) => prim_get_font_v01;
    "set-code-text-command" (2) => prim_set_code_text_command;
    "get-natural-length" (1) => prim_get_natural_length;

    // ==== `set-dominant-wide-script`/`set-dominant-narrow-script`/
    // `set-language` are FAITHFUL stores with real getter round-trips
    // below; `register-outline` is likewise FAITHFUL (drives real PDF
    // `/Outlines` bookmarks). Only `set-every-word-break` remains a
    // STAND-IN (accepted and dropped). ====
    "set-dominant-wide-script" (2) => prim_set_dominant_wide_script;
    "set-dominant-narrow-script" (2) => prim_set_dominant_narrow_script;
    "set-language" (3) => prim_set_language;
    "get-dominant-wide-script" (1) => prim_get_dominant_wide_script;
    "get-dominant-narrow-script" (1) => prim_get_dominant_narrow_script;
    "get-language" (2) => prim_get_language;
    "set-every-word-break" (3) => prim_set_every_word_break;
    "register-outline" (1) => prim_register_outline;
    "extract-string" (1) => prim_extract_string;

    // ==== proof.satyh/footnote-scheme.satyh prims: `embed-block-bottom`
    // :1185, `line-stack-bottom` :1229 (both `tools/gencode/vminst.ml`),
    // `add-footnote` :1130. ====
    "embed-block-bottom" (3) => prim_embed_block_bottom;
    "line-stack-bottom" (1) => prim_line_stack_bottom;
    "line-stack-top" (1) => prim_line_stack_top;
    "add-footnote" (1) => prim_add_footnote;

    // ==== three PURE text-info prims — `get-initial-text-info` :953,
    // `deepen-indent` :921, `break` :935 (tools/gencode/vminst.ml,
    // text-mode). The text/html backends are OUT of scope for this PDF
    // port, so all three live in the single shared env (upstream keys
    // prims per mode).
    //
    // `get-initial-text-info` forks: v0.0.6 (vminst.ml:953) is `unit ->
    // text-info`; v0.1 (dev-0-1-0 vminst.ml:904-925) threads a text-mode
    // default math command + math-scripts stringifier into `tctxsub`. The
    // v01 body ACCEPTS AND DROPS both (STAND-IN, same degenerate policy as
    // `stringify-math`) — both bodies return `TextInfo{indent: 0}`. ====
    v006 "get-initial-text-info" (1) => prim_get_initial_text_info_v006;
    v01  "get-initial-text-info" (2) => prim_get_initial_text_info_v01;
    "deepen-indent" (2) => prim_deepen_indent;
    "break" (1) => prim_break;
}

/// The base environment v0.0.6 `document` programs start in. Back-compat
/// wrapper over `base_env_with_version(V0_0)`.
pub fn base_env() -> BaseEnv {
    base_env_with_version(RustyfiVersion::V0_0)
}

/// The base environment for a given target version — filters `PRIM_DEFS` by
/// `VersionSpan::allows`, so e.g. a `V0_1` env binds `prim_page_break_v01`
/// under the name `"page-break"`, never `prim_page_break_v006`. The five
/// bare-constant `env.define`s below (`inline-fil`/`inline-nil`/`block-nil`/
/// `omit-skip-after`/`clear-page`) live outside `PrimDef`/`VersionSpan` and
/// stay unconditional — all five exist in 0.1 upstream too (audited against
/// `dev-0-1-0:src/frontend/primitives.cppo.ml`); `tests/v01_prims_scalar.rs`'s
/// `bare_constants_bound_under_v01` proves it.
pub fn base_env_with_version(version: RustyfiVersion) -> BaseEnv {
    let mut env = BaseEnv::new();
    for def in PRIM_DEFS {
        if !def.version.allows(version) {
            continue;
        }
        env.define(
            def.name,
            Value::Prim {
                def,
                applied: Vec::new(),
            },
        );
    }
    env.define(
        "inline-fil",
        Value::InlineBoxes(vec![HorzBox::Pure(PureHorzBox::OuterFil)]),
    );
    // `inline-nil`/`block-nil`: no vminst.ml entry — v0.0.6 gets the empty
    // list for free from literal `{}`/`<>` syntax, which this port's syntax
    // layer doesn't produce standalone; these constants are the equivalent
    // value bound to a name.
    env.define("inline-nil", Value::InlineBoxes(Vec::new()));
    env.define("block-nil", Value::BlockBoxes(Vec::new()));
    // `omit-skip-after : inline-boxes` (`primitives.cppo.ml:567`) — a bare
    // CONSTANT marking `HorzOmitSkipAfter`, a line-breaking hint to drop the
    // interword glue that would otherwise follow (used at the tail of
    // `math.satyh`'s `\eqn`/`\math-list`/`\align`). STAND-IN: this port's
    // line-breaker has no such marker box, so it's the empty `inline-boxes`
    // list — never consulted, since none of those wrappers is called by
    // the file itself.
    env.define("omit-skip-after", Value::InlineBoxes(Vec::new()));
    // `clear-page : block-boxes` (`primitives.cppo.ml:569`) — a single-
    // element list carrying `VertBox::ClearPage`, which `chop_page`
    // (rustyfi-backend) treats as "end this page here". FAITHFUL.
    env.define("clear-page", Value::BlockBoxes(vec![VertBox::ClearPage]));
    // `here : string` — upstream `here` is a LEXER keyword expanding at lex
    // time to the source file's directory (`Filename.dirname`). This port
    // has no such lexer entry (`here` lexes as a plain `Token::Var`), so
    // it's a V0_1-only nullary CONSTANT bound to the empty string. Never
    // dereferenced as a real path: its consumers (`unidata.satyh`/
    // `hyph-english.satyh`) feed `here ^ …` into the `load-*` stand-ins
    // above, which drop the path unread.
    if version == RustyfiVersion::V0_1 {
        env.define("here", Value::Str(String::new()));
    }
    env
}

// ---- argument extractors ------------------------------------------------------

fn as_context(v: Value) -> Result<Context, EvalError> {
    match v {
        Value::Context(c) => Ok(*c),
        other => eval_error(format!("expected a context, got {}", other.type_name())),
    }
}

fn as_text_info(v: Value) -> Result<TextInfo, EvalError> {
    match v {
        Value::TextInfo(t) => Ok(t),
        other => eval_error(format!("expected a text-info, got {}", other.type_name())),
    }
}

fn as_hyphenation(v: Value) -> Result<HyphenLang, EvalError> {
    match v {
        Value::Hyphenation(tag) => Ok(tag),
        other => eval_error(format!("expected a hyphenation, got {}", other.type_name())),
    }
}

fn as_inline_text(v: Value) -> Result<(Rc<Vec<IText>>, Env), EvalError> {
    match v {
        Value::InlineText { elems, env } => Ok((elems, env)),
        other => eval_error(format!("expected inline-text, got {}", other.type_name())),
    }
}

fn as_block_text(v: Value) -> Result<(Rc<Vec<BText>>, Env), EvalError> {
    match v {
        Value::BlockText { elems, env } => Ok((elems, env)),
        other => eval_error(format!("expected block-text, got {}", other.type_name())),
    }
}

fn as_inline_boxes(v: Value) -> Result<Vec<HorzBox>, EvalError> {
    match v {
        Value::InlineBoxes(b) => Ok(b),
        other => eval_error(format!("expected inline-boxes, got {}", other.type_name())),
    }
}

fn as_block_boxes(v: Value) -> Result<Vec<VertBox>, EvalError> {
    match v {
        Value::BlockBoxes(b) => Ok(b),
        other => eval_error(format!("expected block-boxes, got {}", other.type_name())),
    }
}

fn as_int(v: Value) -> Result<i64, EvalError> {
    match v {
        Value::Int(n) => Ok(n),
        other => eval_error(format!("expected int, got {}", other.type_name())),
    }
}

fn as_float(v: Value) -> Result<f64, EvalError> {
    match v {
        Value::Float(x) => Ok(x),
        other => eval_error(format!("expected float, got {}", other.type_name())),
    }
}

fn as_bool(v: Value) -> Result<bool, EvalError> {
    match v {
        Value::Bool(b) => Ok(b),
        other => eval_error(format!("expected bool, got {}", other.type_name())),
    }
}

fn as_str(v: Value) -> Result<String, EvalError> {
    match v {
        Value::Str(s) => Ok(s),
        other => eval_error(format!("expected string, got {}", other.type_name())),
    }
}

// `regexp-of-string : string -> regexp` — the port models a `regexp` as its
// underlying pattern string, so this is the identity on the string.
fn prim_regexp_of_string(_interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
    let s = as_str(args.pop().unwrap())?;
    Ok(Value::Str(s))
}

// `string-match : regexp -> string -> bool` — whether `input` matches the
// pattern in full (anchored). Only the character-class subset `satysfi-base`'s
// `char.satyg` uses (`[…]`, with `a-z` ranges and an optional leading `^`
// negation) is modeled; any other pattern is compared literally.
fn prim_string_match(_interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
    let input = as_str(args.pop().unwrap())?;
    let pattern = as_str(args.pop().unwrap())?;
    Ok(Value::Bool(regexp_full_match(&pattern, &input)))
}

fn regexp_full_match(pattern: &str, input: &str) -> bool {
    let p: Vec<char> = pattern.chars().collect();
    if p.len() >= 2 && p[0] == '[' && p[p.len() - 1] == ']' {
        // A character class matches exactly one character.
        let mut chars = input.chars();
        match (chars.next(), chars.next()) {
            (Some(c), None) => char_in_class(&p[1..p.len() - 1], c),
            _ => false,
        }
    } else {
        input == pattern
    }
}

// `split-on-regexp : regexp -> string -> (int * string) list` — split `input`
// at every character matching the (single-character) pattern, pairing each
// resulting segment with its starting code-point offset. Handles the pattern
// forms base uses: a `[…]` class, an escaped literal (`\.`), or a bare
// literal character; anything else never matches (one segment = the whole
// string).
fn prim_split_on_regexp(_interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
    let input = as_str(args.pop().unwrap())?;
    let pattern = as_str(args.pop().unwrap())?;
    let is_delim = single_char_matcher(&pattern);
    let mut segments: Vec<Value> = Vec::new();
    let mut seg_start = 0usize;
    let mut cur = String::new();
    for (idx, c) in input.chars().enumerate() {
        if is_delim(c) {
            segments.push(Value::Tuple(vec![
                Value::Int(seg_start as i64),
                Value::Str(std::mem::take(&mut cur)),
            ]));
            seg_start = idx + 1;
        } else {
            cur.push(c);
        }
    }
    segments.push(Value::Tuple(vec![
        Value::Int(seg_start as i64),
        Value::Str(cur),
    ]));
    Ok(Value::List(segments))
}

/// A predicate matching one character against a `regexp` pattern's single-char
/// forms (a `[…]` class, an escaped literal `\X`, or a bare literal char).
fn single_char_matcher(pattern: &str) -> Box<dyn Fn(char) -> bool> {
    let p: Vec<char> = pattern.chars().collect();
    if p.len() >= 2 && p[0] == '[' && p[p.len() - 1] == ']' {
        let cls: Vec<char> = p[1..p.len() - 1].to_vec();
        Box::new(move |c| char_in_class(&cls, c))
    } else if p.len() == 2 && p[0] == '\\' {
        let lit = p[1];
        Box::new(move |c| c == lit)
    } else if p.len() == 1 {
        let lit = p[0];
        Box::new(move |c| c == lit)
    } else {
        Box::new(|_| false)
    }
}

fn char_in_class(cls: &[char], c: char) -> bool {
    let (neg, cls) = match cls.first() {
        Some('^') => (true, &cls[1..]),
        _ => (false, cls),
    };
    let mut i = 0;
    let mut found = false;
    while i < cls.len() {
        if i + 2 < cls.len() && cls[i + 1] == '-' {
            if cls[i] <= c && c <= cls[i + 2] {
                found = true;
            }
            i += 3;
        } else {
            if cls[i] == c {
                found = true;
            }
            i += 1;
        }
    }
    found ^ neg
}

fn as_length(v: Value) -> Result<Length, EvalError> {
    match v {
        Value::Length(l) => Ok(l),
        other => eval_error(format!("expected length, got {}", other.type_name())),
    }
}

fn as_list(v: Value) -> Result<Vec<Value>, EvalError> {
    match v {
        Value::List(items) => Ok(items),
        other => eval_error(format!("expected list, got {}", other.type_name())),
    }
}

fn as_image(v: Value) -> Result<ImageId, EvalError> {
    match v {
        Value::Image(id) => Ok(id),
        other => eval_error(format!("expected image, got {}", other.type_name())),
    }
}

// ---- graphics argument extractors ------------------------------------------

/// `point` = `Value::Tuple([Length, Length])` (mirrors `evalUtil.ml:228`'s
/// point extraction).
fn as_point(v: Value) -> Result<Point, EvalError> {
    match v {
        Value::Tuple(vs) if vs.len() == 2 => {
            let mut it = vs.into_iter();
            let x = as_length(it.next().unwrap())?;
            let y = as_length(it.next().unwrap())?;
            Ok((x, y))
        }
        other => eval_error(format!(
            "expected a point (length * length), got {}",
            other.type_name()
        )),
    }
}

/// `color` = `Value::Ctor("Gray"|"RGB"|"CMYK", ..)` (mirrors
/// `evalUtil.ml:124`'s `get_color` exactly — a wrong shape here would
/// surface only at draw time).
fn as_color(v: Value) -> Result<Color, EvalError> {
    match v {
        Value::Ctor(name, payload) => match (name.as_str(), payload.map(|b| *b)) {
            ("Gray", Some(p)) => Ok(Color::Gray(as_float(p)?)),
            ("RGB", Some(Value::Tuple(vs))) if vs.len() == 3 => {
                let mut it = vs.into_iter();
                let r = as_float(it.next().unwrap())?;
                let g = as_float(it.next().unwrap())?;
                let b = as_float(it.next().unwrap())?;
                Ok(Color::Rgb(r, g, b))
            }
            ("CMYK", Some(Value::Tuple(vs))) if vs.len() == 4 => {
                let mut it = vs.into_iter();
                let c = as_float(it.next().unwrap())?;
                let m = as_float(it.next().unwrap())?;
                let y = as_float(it.next().unwrap())?;
                let k = as_float(it.next().unwrap())?;
                Ok(Color::Cmyk(c, m, y, k))
            }
            (other, _) => eval_error(format!(
                "expected a color (Gray/RGB/CMYK), got variant '{other}'"
            )),
        },
        other => eval_error(format!("expected a color, got {}", other.type_name())),
    }
}

/// `script` = nullary `Value::Ctor` (prim_types.rs `script_decl`); mirrors
/// upstream `get_script` (evalUtil.ml:235-241).
fn as_script(v: Value) -> Result<Script, EvalError> {
    match v {
        Value::Ctor(name, None) => match name.as_str() {
            "HanIdeographic" => Ok(Script::HanIdeographic),
            "Kana" => Ok(Script::Kana),
            "Latin" => Ok(Script::Latin),
            "OtherScript" => Ok(Script::OtherScript),
            other => eval_error(format!("expected a script, got variant '{other}'")),
        },
        other => eval_error(format!("expected a script, got {}", other.type_name())),
    }
}

/// Inverse of [`as_script`] (upstream `make_script_value`, evalUtil.ml:244).
fn make_script_value(s: Script) -> Value {
    let name = match s {
        Script::HanIdeographic => "HanIdeographic",
        Script::Kana => "Kana",
        Script::Latin => "Latin",
        Script::OtherScript => "OtherScript",
    };
    Value::Ctor(name.to_string(), None)
}

/// `language` = nullary `Value::Ctor` (prim_types.rs `language_decl`);
/// mirrors upstream `get_language_system` (evalUtil.ml:262).
fn as_language(v: Value) -> Result<Language, EvalError> {
    match v {
        Value::Ctor(name, None) => match name.as_str() {
            "Japanese" => Ok(Language::Japanese),
            "English" => Ok(Language::English),
            "NoLanguageSystem" => Ok(Language::NoLanguageSystem),
            other => eval_error(format!("expected a language, got variant '{other}'")),
        },
        other => eval_error(format!("expected a language, got {}", other.type_name())),
    }
}

/// Inverse of [`as_language`] (upstream `make_language_system_value`).
fn make_language_value(l: Language) -> Value {
    let name = match l {
        Language::Japanese => "Japanese",
        Language::English => "English",
        Language::NoLanguageSystem => "NoLanguageSystem",
    };
    Value::Ctor(name.to_string(), None)
}

/// `page` = `Value::Ctor("A4Paper"|.., None | Some(Tuple[Length;2]))`
/// — `page-break`'s first argument, mapped to the backend's
/// `PaperSize`.
fn as_page(v: Value) -> Result<PaperSize, EvalError> {
    match v {
        Value::Ctor(name, payload) => match (name.as_str(), payload.map(|b| *b)) {
            ("A0Paper", None) => Ok(PaperSize::A0),
            ("A1Paper", None) => Ok(PaperSize::A1),
            ("A2Paper", None) => Ok(PaperSize::A2),
            ("A3Paper", None) => Ok(PaperSize::A3),
            ("A4Paper", None) => Ok(PaperSize::A4),
            ("A5Paper", None) => Ok(PaperSize::A5),
            ("USLetter", None) => Ok(PaperSize::USLetter),
            ("USLegal", None) => Ok(PaperSize::USLegal),
            ("UserDefinedPaper", Some(Value::Tuple(vs))) if vs.len() == 2 => {
                let mut it = vs.into_iter();
                let w = as_length(it.next().unwrap())?;
                let h = as_length(it.next().unwrap())?;
                Ok(PaperSize::UserDefined(w, h))
            }
            (other, _) => eval_error(format!(
                "expected a page (A4Paper/.../UserDefinedPaper), got variant '{other}'"
            )),
        },
        other => eval_error(format!("expected a page, got {}", other.type_name())),
    }
}

/// v0.1's `page-break`'s first argument: a plain `(length * length)` tuple
/// — the `page` ADT (`as_page` above) no longer exists upstream in 0.1.
/// Maps straight into `PaperSize::UserDefined`, the exact same backend
/// value `as_page`'s own `UserDefinedPaper` arm produces: the retype drops
/// the ADT wrapper without changing what geometry `page-break` can
/// express, so only the source `Value` shape differs.
fn as_page_v01(v: Value) -> Result<PaperSize, EvalError> {
    match v {
        Value::Tuple(vs) if vs.len() == 2 => {
            let mut it = vs.into_iter();
            let w = as_length(it.next().unwrap())?;
            let h = as_length(it.next().unwrap())?;
            Ok(PaperSize::UserDefined(w, h))
        }
        other => eval_error(format!(
            "expected a page as (length * length), got {}",
            other.type_name()
        )),
    }
}

/// `paddings` = `Value::Tuple([Length; 4])` in `(paddingL, paddingR,
/// paddingT, paddingB)` order (mirrors `evalUtil.ml`'s `get_paddings`).
/// `inline-frame-outer`'s first argument.
fn as_paddings(v: Value) -> Result<(Length, Length, Length, Length), EvalError> {
    match v {
        Value::Tuple(vs) if vs.len() == 4 => {
            let mut it = vs.into_iter();
            let l = as_length(it.next().unwrap())?;
            let r = as_length(it.next().unwrap())?;
            let t = as_length(it.next().unwrap())?;
            let b = as_length(it.next().unwrap())?;
            Ok((l, r, t, b))
        }
        other => eval_error(format!(
            "expected paddings (length * length * length * length), got {}",
            other.type_name()
        )),
    }
}

/// `cell` = `Value::Ctor("NormalCell"|"EmptyCell"|"MultiCell", ..)` (mirrors
/// `evalUtil.ml:102`'s `get_cell`) — `tabular`'s grid entries;
fn as_cell(v: Value) -> Result<Cell, EvalError> {
    match v {
        Value::Ctor(name, payload) => match (name.as_str(), payload.map(|b| *b)) {
            ("NormalCell", Some(Value::Tuple(vs))) if vs.len() == 2 => {
                let mut it = vs.into_iter();
                let (l, r, t, b) = as_paddings(it.next().unwrap())?;
                let ib = as_inline_boxes(it.next().unwrap())?;
                Ok(Cell::Normal(Paddings { l, r, t, b }, ib))
            }
            ("EmptyCell", None) => Ok(Cell::Empty),
            ("MultiCell", Some(Value::Tuple(vs))) if vs.len() == 4 => {
                let mut it = vs.into_iter();
                let numrow = as_int(it.next().unwrap())?;
                let numcol = as_int(it.next().unwrap())?;
                let (l, r, t, b) = as_paddings(it.next().unwrap())?;
                let ib = as_inline_boxes(it.next().unwrap())?;
                Ok(Cell::Multi(
                    numrow.max(0) as usize,
                    numcol.max(0) as usize,
                    Paddings { l, r, t, b },
                    ib,
                ))
            }
            (other, _) => eval_error(format!(
                "expected a cell (NormalCell/EmptyCell/MultiCell), got variant '{other}'"
            )),
        },
        other => eval_error(format!("expected a cell, got {}", other.type_name())),
    }
}

/// `(cell list) list` — `tabular`'s first argument.
fn as_cell_grid(v: Value) -> Result<Vec<Vec<Cell>>, EvalError> {
    as_list(v)?
        .into_iter()
        .map(|row| -> Result<Vec<Cell>, EvalError> {
            as_list(row)?.into_iter().map(as_cell).collect()
        })
        .collect()
}

fn as_prepath(v: Value) -> Result<PrePath, EvalError> {
    match v {
        Value::PrePath(p) => Ok(p),
        other => eval_error(format!("expected pre-path, got {}", other.type_name())),
    }
}

fn as_path(v: Value) -> Result<Path, EvalError> {
    match v {
        Value::Path(p) => Ok(p),
        other => eval_error(format!("expected path, got {}", other.type_name())),
    }
}

fn as_graphics(v: Value) -> Result<GraphicsElem, EvalError> {
    match v {
        Value::Graphics(g) => Ok(g),
        other => eval_error(format!("expected graphics, got {}", other.type_name())),
    }
}

/// `dash` = `length * length * length` (mirrors `evalUtil.ml`'s `get_tuple3
/// get_length`) — `dashed-stroke`'s 2nd argument, `(d1, d2, d0)` = on-length,
/// off-length, phase.
fn as_dash(v: Value) -> Result<Dash, EvalError> {
    match v {
        Value::Tuple(vs) if vs.len() == 3 => {
            let mut it = vs.into_iter();
            let d1 = as_length(it.next().unwrap())?;
            let d2 = as_length(it.next().unwrap())?;
            let d0 = as_length(it.next().unwrap())?;
            Ok((d1, d2, d0))
        }
        other => eval_error(format!(
            "expected a dash pattern (length * length * length), got {}",
            other.type_name()
        )),
    }
}

/// The inverse of `as_point` (mirrors `evalUtil.ml:228`'s point
/// construction) — used by `inline-graphics` to build the `(0pt, 0pt)`
/// origin its callback is (eagerly) invoked with; see that primitive's doc
/// comment for the shift-covariance caveat this stands in for.
fn make_point_value(pt: Point) -> Value {
    Value::Tuple(vec![Value::Length(pt.0), Value::Length(pt.1)])
}

/// `length list` construction (mirrors `evalUtil.ml:709`) — builds the
/// box-local grid-line coordinates `tabular`'s rule callback is (eagerly)
/// invoked with; see `prim_tabular`'s doc comment.
fn make_length_list(lens: &[Length]) -> Value {
    Value::List(lens.iter().map(|l| Value::Length(*l)).collect())
}

// ---- primitive-body macros ----------------------------------------------------
//
// The arithmetic, comparison, boolean, and unary-conversion primitives all
// share one strict-call shape: the (already-evaluated) operands are popped
// right-to-left through a type extractor, then the result is re-wrapped as a
// `Value`. These macros capture that shape so each primitive is a single line.
// The vminst.ml citations for each stay on the `prims!` registration table
// above; per-primitive notes ride along on the invocations below.

/// A strict binary primitive. Pops `b` then `a` (i.e. rightmost argument
/// first, matching application order) through the given extractor(s) and wraps
/// `body` as `Value::$ctor`. Accepts either one extractor for both operands or
/// a `(as_a, as_b)` pair when the operands have different types.
macro_rules! binop_prim {
    ($name:ident, ($as_a:path, $as_b:path), $ctor:ident, |$a:ident, $b:ident| $body:expr) => {
        fn $name(_interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
            let $b = $as_b(args.pop().unwrap())?;
            let $a = $as_a(args.pop().unwrap())?;
            Ok(Value::$ctor($body))
        }
    };
    ($name:ident, $as:path, $ctor:ident, |$a:ident, $b:ident| $body:expr) => {
        binop_prim!($name, ($as, $as), $ctor, |$a, $b| $body);
    };
}

/// A strict binary comparison: like `binop_prim!` but always wraps as
/// `Value::Bool`.
macro_rules! cmp_prim {
    ($name:ident, $as:path, |$a:ident, $b:ident| $body:expr) => {
        binop_prim!($name, ($as, $as), Bool, |$a, $b| $body);
    };
}

/// A strict unary primitive: pops one operand through `as` and wraps `body`
/// as `Value::$ctor`.
macro_rules! unop_prim {
    ($name:ident, $as:path, $ctor:ident, |$a:ident| $body:expr) => {
        fn $name(_interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
            let $a = $as(args.pop().unwrap())?;
            Ok(Value::$ctor($body))
        }
    };
}

/// A strict binary primitive with a fallible body: `body` is the function's
/// tail expression and must itself yield `Result<Value, EvalError>`, so it can
/// guard cases like division by zero.
macro_rules! binop_prim_try {
    ($name:ident, $as:path, |$a:ident, $b:ident| $body:expr) => {
        fn $name(_interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
            let $b = $as(args.pop().unwrap())?;
            let $a = $as(args.pop().unwrap())?;
            $body
        }
    };
}

// ---- text conversion ----------------------------------------------------------

/// Convert quoted inline text to boxes under `ctx` (the core of
/// `read-inline`): words become measured `InnerString`s, whitespace becomes
/// glue, embedded commands are applied to `ctx` and their arguments.
pub fn read_inline(
    interp: &mut Interp,
    ctx: &Context,
    elems: &[IText],
    env: &Env,
) -> Result<Vec<HorzBox>, EvalError> {
    let mut out = Vec::new();
    for elem in elems {
        match elem {
            IText::Text(text) => text_to_boxes(interp, ctx, text, &mut out)?,
            // `ImInputHorzEmbeddedCodeText` (`evaluator.cppo.ml:768-779`): hand
            // the literal to the context's code-text command if one is
            // installed, else set it as ordinary text
            // (`DefaultCodeTextCommand`).
            IText::CodeText(text) => match ctx.code_text_command {
                Some(id) => {
                    let cmd = interp.math_commands[id.0].clone();
                    let v = interp.apply(cmd, Value::Context(Box::new(ctx.clone())))?;
                    let v = interp.apply(v, Value::Str(text.clone()))?;
                    out.extend(as_inline_boxes(v)?);
                }
                None => text_to_boxes(interp, ctx, text, &mut out)?,
            },
            IText::Cmd { cmd, args } => {
                // Resolved at compile time (`crate::quoted`); running it can
                // still raise the same "unbound inline command" error for the
                // defensive case the compiler could not resolve.
                let cmd = cmd.run(env, interp)?;
                let mut v = interp.apply(cmd, Value::Context(Box::new(ctx.clone())))?;
                for arg in args {
                    let mut opt_vals = Vec::with_capacity(arg.opts.len());
                    for (label, e) in &arg.opts {
                        opt_vals.push((label.clone(), e.run(env, interp)?));
                    }
                    let arg_v = arg.arg.run(env, interp)?;
                    v = interp.apply_with_opts(v, opt_vals, arg_v)?;
                }
                out.extend(as_inline_boxes(v)?);
            }
            IText::Embed { expr, span } => {
                let v = expr.run(env, interp)?;
                match v {
                    Value::InlineText {
                        elems: sub_elems,
                        env: cap_env,
                    } => {
                        out.extend(read_inline(interp, ctx, &sub_elems, &cap_env)?);
                    }
                    other => {
                        return Err(EvalError {
                            span: Some(*span),
                            msg: format!(
                                "expected inline-text in '#…;' embed, got {}",
                                other.type_name()
                            ),
                        });
                    }
                }
            }
            IText::EmbedMath { elems, .. } => {
                // Upstream: a bare `${…}` in inline text evaluates by
                // applying the context's installed `[math] inline-cmd` to
                // (ctx, the math value) — `apply(cmd, ctx)` then
                // `apply(_, math)`, exactly like `IText::Cmd` above.
                let installed = ctx
                    .math_command
                    .and_then(|id| interp.math_commands.get(id.0).cloned());
                match installed {
                    Some(cmd) => {
                        let v = interp.apply(cmd, Value::Context(Box::new(ctx.clone())))?;
                        let v = interp.apply(
                            v,
                            Value::MathText {
                                elems: Rc::clone(elems),
                                env: env.clone(),
                            },
                        )?;
                        out.extend(as_inline_boxes(v)?);
                    }
                    None => {
                        // No installed command (contexts built by
                        // `Context::initial` directly, i.e. unit tests):
                        // reflect + lay out through the faithful engine so
                        // `\cmd`/`#var` still evaluate — the same machinery
                        // `+math(${…})` uses via `as_math`. This fallback
                        // dispatches on `interp.version`
                        // — the installed-command path above is version-
                        // blind already (an ordinary `[math-text] inline-
                        // cmd` applied to `(ctx, math-text)`).
                        let mut atoms = Vec::new();
                        if interp.version.math_is_split() {
                            for e in elems.iter() {
                                reflect_math_elem_v01(interp, ctx, e, env, &mut atoms)?;
                            }
                        } else {
                            for e in elems.iter() {
                                reflect_math_elem(interp, e, env, &mut atoms)?;
                            }
                        }
                        out.push(HorzBox::Pure(layout_math_value(interp, ctx, &atoms)?));
                    }
                }
            }
        }
    }
    // Space inline `\code(…)`/`${…}` boxes against adjacent CJK prose the way
    // SATySFi does (the text-run glue in `text_to_boxes` can't see these
    // cross-element boundaries). Idempotent — a boundary already carrying glue
    // is skipped.
    Ok(insert_box_interscript_glue(out, ctx))
}

/// Convert quoted block text to vertical boxes (the core of `read-block`).
fn read_block(
    interp: &mut Interp,
    ctx: &Context,
    elems: &[BText],
    env: &Env,
) -> Result<Vec<VertBox>, EvalError> {
    let mut out = Vec::new();
    for elem in elems {
        match elem {
            BText::Cmd { cmd, args } => {
                let cmd = cmd.run(env, interp)?;
                let mut v = interp.apply(cmd, Value::Context(Box::new(ctx.clone())))?;
                for arg in args {
                    let mut opt_vals = Vec::with_capacity(arg.opts.len());
                    for (label, e) in &arg.opts {
                        opt_vals.push((label.clone(), e.run(env, interp)?));
                    }
                    let arg_v = arg.arg.run(env, interp)?;
                    v = interp.apply_with_opts(v, opt_vals, arg_v)?;
                }
                out.extend(as_block_boxes(v)?);
            }
            BText::Embed { expr, span } => {
                let v = expr.run(env, interp)?;
                match v {
                    Value::BlockText {
                        elems: sub_elems,
                        env: cap_env,
                    } => {
                        out.extend(read_block(interp, ctx, &sub_elems, &cap_env)?);
                    }
                    other => {
                        return Err(EvalError {
                            span: Some(*span),
                            msg: format!(
                                "expected block-text in '#…;' embed, got {}",
                                other.type_name()
                            ),
                        });
                    }
                }
            }
        }
    }
    Ok(out)
}

/// UAX#14 byte offsets in `text` that are a real, content-driven break
/// candidate: every `break_opportunities` boundary except the one always
/// reported at `text.len()` (the segmenter's "always break at the end of
/// text" convention — an artifact of segmenting this one run in isolation,
/// not a signal about what follows it in the paragraph, since
/// `text_to_boxes` is called once per `IText::Text` leaf and more content
/// may follow via a sibling `Cmd`, `Embed`, or `EmbedMath`).
fn uax14_boundaries(text: &str) -> Vec<Option<BreakKind>> {
    let mut boundary = vec![None; text.len() + 1];
    for (offset, kind) in break_opportunities(text) {
        if offset < text.len() {
            boundary[offset] = Some(kind);
        }
    }
    boundary
}

/// This run's `(font, size, rising)` for `script` (see `Context::font_scheme`'s
/// doc comment): `Latin` reads `ctx.font` itself (NOT `font_scheme[Latin].font`)
/// so `set-font-key`/`\bold`/`\emph` keep working unchanged, while still
/// picking up `font_scheme[Latin]`'s ratio/rising (written in lockstep by
/// `set-font Latin ..`).
///
/// `OtherScript` first goes through `normalize_script` (`horzBox.ml:472`):
/// upstream's `CommonNarrow`/`Inherited` resolve to `ctx.dominant_narrow_script`
/// rather than to a scheme slot of their own; this port's `char_script` has no
/// separate Common bucket, so everything outside Latin-1..Latin-Ext-B and the
/// CJK ranges lands in `OtherScript` and gets the same treatment — the only
/// WIDE Common chars (`U+3000` fullwidth forms) already fall in
/// `char_script`'s `HanIdeographic` range, so this costs nothing there.
///
/// Real effect, not a niceness: without `set-dominant-narrow-script Kana`, a
/// document's `□`/`✓` both resolve to a Latin face with NEITHER glyph, degrade
/// to the same `.notdef` glyph id and `ToUnicode` entry, and one of the two
/// simply vanishes from the extracted text — enumitem's three missing `✓`,
/// each overprinted onto a `□` by the document's own `ooalign`.
///
/// Defaults to `OtherScript` (`Context::initial`, matching upstream), so a
/// document that never calls the primitive is unaffected and the recursion is
/// one step deep at most.
fn script_font(ctx: &Context, script: Script) -> ScriptFont {
    if script == Script::OtherScript && ctx.dominant_narrow_script != Script::OtherScript {
        return script_font(ctx, ctx.dominant_narrow_script);
    }
    if script == Script::Latin {
        ScriptFont {
            font: ctx.font,
            ..ctx.font_scheme[Script::Latin as usize]
        }
    } else {
        ctx.font_scheme[script as usize]
    }
}

/// Measure `text` (already known to be one script run) at `size` under
/// `font`, falling back per-glyph to `fallback_font` (`ctx.font`) when
/// `font` has no glyph for a character — the "CJK per-glyph metrics path
/// stubbed" case: a character within a script-run's bucket
/// that its assigned font happens to lack (e.g. a fullwidth-form character
/// absent from a narrow CJK face) still measures via the Latin default
/// rather than failing the whole run. Errors (both fonts lack the glyph)
/// name the offending character and font key.
///
/// **Known limitation** (documented, not fixed): the
/// measurement here can fall back per-glyph, but `PureHorzBox::InnerString`
/// carries one `HorzStringInfo::font` for its WHOLE text run — so if a
/// fallback glyph is actually used, the PDF writer's `emit_box` still tries
/// to look it up in `font`'s face at render time and fails there instead.
/// Splitting a run into sub-boxes at the source-font-only/fallback boundary
/// (a faithful fix) is future work; every stdja default face configuration
/// covers its script's whole repertoire, so this path is not expected to
/// trigger in practice.
fn measure_run(
    interp: &Interp,
    font: FontKey,
    fallback_font: FontKey,
    text: &str,
    size: Length,
) -> Result<Length, EvalError> {
    let mut width = Length::ZERO;
    for c in text.chars() {
        // A character absent from BOTH the run font and the fallback degrades
        // to a `.notdef`-style box (half-em advance) rather than aborting the
        // whole document — the way real typesetters render an uncovered glyph.
        // (satysfi-base's `enumitem`/the SATySFi Book use a few glyphs — `□`,
        // `〚` — that the bundled Latin face lacks; a faithful per-glyph
        // font-fallback via run-splitting is the documented follow-up.) This
        // only ever changes behavior for a glyph that would otherwise be a
        // hard error, so covered-glyph documents are byte-identical.
        let advance = interp
            .metrics
            .advance(font, c, size)
            .or_else(|| interp.metrics.advance(fallback_font, c, size))
            .unwrap_or(size * 0.5);
        width += advance;
    }
    Ok(width)
}

/// Build one `InnerString` box for `text`, measured through [`measure_run`]
/// with `sf`'s font/size/rising — the single construction site shared by
/// `text_to_boxes`'s `flush_word` for both the plain (no-hyphenation) path
/// and each hyphenated fragment / hyphen glyph. Factored out so both paths
/// measure/build identically — this is part of what makes the width-identity
/// argument hold: `measure_run` is purely additive per char (no
/// kerning/ligatures), so concatenating the fragments this produces
/// reconstructs exactly the box a single un-split call would have produced.
fn make_inner_string_pure_box(
    interp: &Interp,
    ctx: &Context,
    sf: ScriptFont,
    size: Length,
    rising: Length,
    text: String,
) -> Result<PureHorzBox, EvalError> {
    let width = measure_run(interp, sf.font, ctx.font, &text, size)?;
    // SATySFi measures a run's height/depth from the ACTUAL per-glyph bounding
    // boxes (fontInfo.ml `get_metrics_of_word`), not the font-level
    // ascender/descender — so a no-descender run (CJK, digits, TOC dots) is
    // shorter and packs tighter at block boundaries.
    let (height, depth) = interp.metrics.run_vextent(sf.font, &text, size);
    Ok(PureHorzBox::InnerString {
        info: HorzStringInfo {
            font: sf.font,
            size,
            rising,
            color: ctx.text_color,
        },
        height,
        depth,
        text,
        width,
    })
}

/// Whether two adjacent runs' scripts form a Latin↔CJK boundary that gets
/// SATySFi's default inter-script glue (`primitives.ml:517-524`: entries for
/// `(Latin, Kana)`, `(Kana, Latin)`, `(Latin, Han)`, `(Han, Latin)` only —
/// NOT Kana↔Han, and not same-script).
fn is_latin_cjk_boundary(a: Script, b: Script) -> bool {
    let is_cjk = |s| matches!(s, Script::HanIdeographic | Script::Kana);
    (a == Script::Latin && is_cjk(b)) || (is_cjk(a) && b == Script::Latin)
}

/// Upstream `is_open_punctuation` (`charBasis.ml:133`: `OP | QU | JLOP`) —
/// opening brackets and quotes. Consulted for the LEFT edge of a script
/// boundary only.
fn is_open_punct(c: char) -> bool {
    matches!(
        c,
        '(' | '['
            | '{'
            | '"'
            | '\''
            | '（'
            | '「'
            | '『'
            | '【'
            | '〔'
            | '〈'
            | '《'
            | '［'
            | '｛'
            | '〖'
            | '〘'
            | '〚'
            | '“'
            | '‘'
    )
}

/// Upstream `is_close_punctuation` (`charBasis.ml:139`: `CL | CP | QU | NS |
/// JLCP | JLNS | JLCM | JLFS`) — closing brackets, quotes, and the kuten/touten
/// family. Consulted for the RIGHT edge of a script boundary only.
///
/// Two families the port used to list are NOT in that set, and their absence is
/// upstream's own, not an oversight:
/// - `!` `?` `！` `？` are line-break class `EX` (`LineBreak.txt:2566,2582` for
///   the fullwidth pair), which appears in no arm of `is_close_punctuation`;
/// - `,` `.` `;` `:` are `IS`, likewise absent.
///
/// Their FULLWIDTH cousins are a different matter and stay: `，`/`．` are
/// overridden to `JLCM`/`JLFS` (`lineBreakDataMap.ml:95-96`) and `：`/`；` are
/// `NS` (`LineBreak.txt:2580`).
///
/// Listing the six suppressed the 0.24em inter-script glue — and, since that
/// glue is the boundary's only break candidate, the break opportunity with it —
/// before every sentence-final mark that is not a kuten.
fn is_close_punct(c: char) -> bool {
    matches!(
        c,
        ')' | ']'
            | '}'
            | '"'
            | '\''
            | '）'
            | '」'
            | '』'
            | '】'
            | '〕'
            | '〉'
            | '》'
            | '］'
            | '｝'
            | '〗'
            | '〙'
            | '〛'
            | '”'
            | '’'
            | '、'
            | '。'
            | '，'
            | '．'
            | '・'
            | '：'
            | '；'
    )
}

/// Whether SATySFi's default inter-script glue is suppressed between a
/// left-hand character `l` and a right-hand `r`.
///
/// `pure_space_between_scripts` (`convertText.ml:31`) drops the glue when
/// `is_open_punctuation lbc1 || is_close_punctuation lbc2` — the LEFT edge being
/// OPENING punctuation, or the RIGHT edge being CLOSING punctuation. The aki
/// that would otherwise sit there is supplied by the separate JLreq
/// class-spacing layer.
///
/// The port used to test one symmetric "is punctuation" predicate against BOTH
/// edges, which suppressed far more than upstream: `、` before a Latin/math run
/// is a *closing* mark on the LEFT, which upstream does not suppress. Since this
/// glue is also the only break opportunity at such a boundary, suppressing it
/// left the breaker with nowhere to break — latexcmds ran
/// `…、${dropcolor}` 32pt past the margin because there was no legal break
/// between the touten and the math box.
fn interscript_glue_suppressed(l: char, r: char) -> bool {
    is_open_punct(l) || is_close_punct(r)
}

/// JLreq character classes SATySFi's inter-CJK spacing distinguishes
/// (`charBasis.ml:116-122`). Only the classes that actually change spacing are
/// modelled; every other CJK character is `None` ("ordinary").
#[derive(Clone, Copy, PartialEq, Eq)]
enum JlClass {
    /// cl-01, fullwidth OPEN punctuation — carries a leading half-width kern.
    Open,
    /// cl-02, fullwidth CLOSE punctuation — trailing half-width kern.
    Close,
    /// cl-06, kuten (fullwidth full stop) — trailing half-width kern.
    FullStop,
    /// cl-07, touten (fullwidth comma) — trailing half-width kern.
    Comma,
    /// cl-05, nakaten (fullwidth middle dot) — quarter-width kern BOTH sides.
    MiddleDot,
}

fn jl_class(c: char) -> Option<JlClass> {
    match c {
        '（' | '「' | '『' | '【' | '〔' | '〈' | '《' | '［' | '｛' | '〖' | '〘' | '〚' => {
            Some(JlClass::Open)
        }
        '）' | '」' | '』' | '】' | '〕' | '〉' | '》' | '］' | '｝' | '〗' | '〙' | '〛' => {
            Some(JlClass::Close)
        }
        '。' | '．' => Some(JlClass::FullStop),
        '、' | '，' => Some(JlClass::Comma),
        '・' | '：' | '；' => Some(JlClass::MiddleDot),
        _ => None,
    }
}

/// `ideographic_single`'s TRAILING kern for `c` (`convertText.ml:266-283`), as a
/// negative ratio of `font_size`: JLCP/JLFS/JLCM are `[glyph; hwkern]`, JLMD is
/// `[qwkern; glyph; qwkern]`.
///
/// A kern belongs to the CHARACTER, not to the boundary — `ideographic_single`
/// runs per chunk and never consults its neighbours. Hence one char per
/// function, even though the only caller today is the pair-shaped
/// [`cjk_pair_space`]: at a CJK↔Latin boundary the CJK side still carries its own
/// kern upstream, and this port does not yet emit it there (see the
/// `PreventBreak` arm of `text_to_boxes` for what that costs and what unblocking
/// it needs).
fn cjk_trailing_kern(c: char) -> f64 {
    match jl_class(c) {
        Some(JlClass::Close) | Some(JlClass::FullStop) | Some(JlClass::Comma) => -0.5,
        Some(JlClass::MiddleDot) => -0.25,
        _ => 0.0,
    }
}

/// `ideographic_single`'s LEADING kern for `c` — JLOP is `[hwkern; glyph]`,
/// JLMD `[qwkern; glyph; qwkern]`. See [`cjk_trailing_kern`].
fn cjk_leading_kern(c: char) -> f64 {
    match jl_class(c) {
        Some(JlClass::Open) => -0.5,
        Some(JlClass::MiddleDot) => -0.25,
        _ => 0.0,
    }
}

/// The glue SATySFi puts between two directly adjacent CJK characters, as an
/// absolute `(natural, shrink, stretch)` — `space_between_chunks`
/// (`convertText.ml:220`) with `ideographic_single`'s compensating kerns
/// (`convertText.ml:266`) folded in.
///
/// Upstream renders CJK punctuation at its full em and kerns it back:
/// `。`/`、`/`）` carry a trailing −0.5em kern, `（` a leading one, `・` −0.25em
/// on both sides. `pure_space_between_classes` (`convertText.ml:194`) then adds
/// a half-width space back — natural 0.5em, stretch 0.25em, shrink 0.25em
/// unless the pair is "hard" (after a full stop). Net natural width is
/// unchanged, but each punctuation mark contributes **0.25em of stretch** — ten
/// times the 0.025em `adjacent_stretch` between ordinary characters, and the
/// bulk of a Japanese line's elasticity. Two punctuation marks in a row
/// (`」、`, `」。`) get NO space back, so the pair sets 0.5em tighter.
///
/// **Which font size each part scales against is not uniform, and that is the
/// point of taking three sizes rather than one.** Upstream applies the kerns
/// (`halfwidth_kern`/`quarterwidth_kern`, `convertText.ml:110-118`) and all
/// four `pure_halfwidth_space_*` sizes to `get_corrected_font_size ctx script`
/// (`convertText.ml:76-79`) — the font size TIMES the script's own ratio, 0.88
/// for stdja's CJK face, so a half-width kern at 12pt is −5.28pt and not −6pt.
/// Only `adjacent_space` (`:101-106`) takes the RAW `ctx.font_size`. Scaling
/// everything by the raw size made every JLreq class space 13.6% too elastic
/// (0.25 × 12 = 3pt of stretch where upstream has 0.25 × 10.56 = 2.64pt);
/// since punctuation carries ten times the stretch of an ordinary
/// inter-character gap, that error set the stretch budget of a whole Japanese
/// line and so its justified glyph positions.
///
/// `size_a`/`size_b` are the corrected sizes of the LEFT and RIGHT characters,
/// upstream's `size1`/`size2` (`convertText.ml:196-198`); the `hwsoftM`/
/// `hwhardM` arms take `Length::max` of the two, exactly as `sizeM` does. They
/// differ only when the two characters resolve to different `font_scheme` slots
/// (`Kana` vs `HanIdeographic`) carrying different ratios.
fn cjk_pair_space(
    a: char,
    size_a: Length,
    b: char,
    size_b: Length,
    raw_size: Length,
    adjacent_stretch: f64,
) -> (Length, Length, Length) {
    use JlClass::*;
    let (ca, cb) = (jl_class(a), jl_class(b));
    // Kerns from `ideographic_single`, each a NEGATIVE ratio of its OWN
    // character's corrected size. Between two CJK characters the pair's kern is
    // exactly `a`'s trailing plus `b`'s leading one, which is what makes the
    // pair form equivalent to upstream's per-character one here.
    let kern = size_a * cjk_trailing_kern(a) + size_b * cjk_leading_kern(b);
    let size_m = Length::max(size_a, size_b);
    // `pure_space_between_classes`, in its own match order. The third component
    // of each arm is the size that arm's space scales against.
    let hwsoft = |s: Length| (s * 0.5, s * 0.25, s * 0.25);
    let hwhard = |s: Length| (s * 0.5, Length::ZERO, s * 0.25);
    let cls = match (ca, cb) {
        (Some(Close), Some(Open)) | (Some(Comma), Some(Open)) => Some(hwsoft(size_m)),
        (Some(FullStop), Some(Open)) => Some(hwhard(size_m)),
        (_, Some(Open)) => Some(hwsoft(size_b)),
        (Some(Close), Some(Comma)) | (Some(Close), Some(FullStop)) => None,
        (Some(Close), _) | (Some(Comma), _) => Some(hwsoft(size_a)),
        (Some(FullStop), _) => Some(hwhard(size_a)),
        _ => None,
    };
    match cls {
        Some((n, sh, st)) => (kern + n, sh, st),
        // No class space: `adjacent_space` (natural 0, shrink 0, stretch
        // `adjacent_stretch` × the RAW size), plus whatever kern the pair
        // carries.
        None => (kern, Length::ZERO, raw_size * adjacent_stretch),
    }
}

/// A box's LEADING glyph for inter-script spacing, or `None` for
/// glue/discretionary/skip/image (a "transparent" separator — an inter-script
/// space is never inserted adjacent to one) and for math (reported as a Latin
/// `'x'`, matching SATySFi where a `${…}` chunk spaces against CJK like Western
/// text). The char lets the caller apply the `is_interscript_punct` guard.
fn box_leading_char(b: &HorzBox) -> Option<char> {
    match b {
        HorzBox::Pure(PureHorzBox::InnerString { text, .. }) => text.chars().next(),
        HorzBox::Pure(PureHorzBox::Math { .. }) => Some('x'),
        _ => None,
    }
}

/// A box's TRAILING glyph (see `box_leading_char`).
fn box_trailing_char(b: &HorzBox) -> Option<char> {
    match b {
        HorzBox::Pure(PureHorzBox::InnerString { text, .. }) => text.chars().last(),
        HorzBox::Pure(PureHorzBox::Math { .. }) => Some('x'),
        _ => None,
    }
}

/// Insert SATySFi's inter-script glue (`default_script_space_map`) between two
/// DIRECTLY-adjacent boxes whose touching edges are Latin↔CJK — the boundary
/// that `text_to_boxes` can't see because it spans separate inline elements: a
/// `\code(…)`/`${…}` box against surrounding CJK prose ("cellfmt 型", "𝑛 番目").
/// A boundary already carrying a glue/discretionary reads as `None` on one edge
/// and is skipped, so this is idempotent and never doubles the text-run glue.
/// The Latin↔CJK inter-script space, `pure_space_between_scripts`
/// (`convertText.ml:29-50`).
///
/// **RIGID — natural `0.24 * font_size`, no shrink, no stretch** — and that is
/// upstream's behaviour, not a simplification. `default_script_space_map`
/// (`primitives.cppo.ml:488`) really does carry the triple
/// `(0.24, 0.08, 0.16)`, but `pure_space_between_scripts` spends it like this:
///
/// ```ocaml
/// Some(LBAtom((natural (size *% r0), size *% r1, size *% r2), EvHorzEmpty))
/// ```
///
/// `LBAtom`'s first field is `metrics = length_info * length * length`, i.e.
/// *(width info, HEIGHT, DEPTH)* (`lineBreakBox.ml:7`), and `natural wid`
/// builds `{natural = wid; shrinkable = zero; stretchable = zero}`
/// (`lineBreakBox.ml:54-59`). So `r1` and `r2` land in the height and depth
/// slots; only `r0` reaches the width. Contrast the sibling
/// `pure_halfwidth_space_soft` (`convertText.ml:83-85`), which builds its
/// elasticity with `make_width_info` and passes `Length.zero, Length.zero` for
/// height and depth — the correct shape, right next door. The commented-out
/// predecessor at `convertText.ml:58` has the same misplacement, so v0.0.6 has
/// never had an elastic inter-script space.
///
/// The stray height (`0.08 * size`) and depth (`0.16 * size`) are swallowed by
/// `get_total_metrics`'s `max hacc h` / `min dacc d` (`lineBreak.ml:55-59`) —
/// a 0.96pt height never exceeds a real glyph's and a POSITIVE depth never
/// wins a `min` against a descender — so rigidity is the only observable
/// consequence, and it is the one that matters: this glue sits at every
/// Japanese/Latin junction, and giving it 0.16em of stretch let the port soak
/// up justification slack that upstream is forced to push into the
/// inter-character `adjacent_space` inside the CJK runs themselves.
///
/// Still a break point: upstream wraps this box in `discretionary_if_breakable`
/// (`convertText.ml:228`) exactly as it does the elastic glues, and an
/// `OuterEmpty` with zero shrink and stretch is still `is_glue()` — which is
/// also why a ratio of 0.0 emits a zero-width box rather than nothing.
///
/// The ratio comes from `ctx.script_space_map`, so
/// `set-space-ratio-between-scripts` reaches it (slydifi's arctic theme zeroes
/// all four Latin↔CJK directions).
fn interscript_glue(ctx: &Context, left: Script, right: Script) -> PureHorzBox {
    PureHorzBox::OuterEmpty {
        natural: ctx.font_size * ctx.script_space_map[left as usize][right as usize],
        shrinkable: Length::ZERO,
        stretchable: Length::ZERO,
    }
}

fn insert_box_interscript_glue(boxes: Vec<HorzBox>, ctx: &Context) -> Vec<HorzBox> {
    if boxes.len() < 2 {
        return boxes;
    }
    let mut out: Vec<HorzBox> = Vec::with_capacity(boxes.len());
    for b in boxes {
        if let (Some(pc), Some(cc)) = (out.last().and_then(box_trailing_char), box_leading_char(&b))
        {
            let (ls, rs) = (char_script(pc), char_script(cc));
            if is_latin_cjk_boundary(ls, rs) && !interscript_glue_suppressed(pc, cc) {
                out.push(HorzBox::Pure(interscript_glue(ctx, ls, rs)));
            }
        }
        out.push(b);
    }
    out
}

fn text_to_boxes(
    interp: &mut Interp,
    ctx: &Context,
    text: &str,
    out: &mut Vec<HorzBox>,
) -> Result<(), EvalError> {
    // Interword glue is upstream's
    // `context_main.space_natural`/`space_shrink`/`space_stretch`
    // (`set-space-ratio`), each a ratio of `font_size` — NOT a measured
    // glyph-advance of the space character and NOT a fraction of the natural
    // width. `ctx.space_*` always carries a value (defaults 0.33/0.08/0.16,
    // matching `Context::initial`'s own upstream-faithful defaults), so this
    // is a plain formula, no fallback needed.
    let space_width = ctx.font_size * ctx.space_natural;
    let boundary = uax14_boundaries(text);
    let mut word = String::new();
    let flush_word =
        |word: &mut String, script: Script, out: &mut Vec<HorzBox>| -> Result<(), EvalError> {
            if word.is_empty() {
                return Ok(());
            }
            let sf = script_font(ctx, script);
            let size = ctx.font_size * sf.ratio;
            // The script-font's own baseline raise (a ratio of font_size) PLUS the
            // manual raise from `set-manual-rising` (`ctx.manual_rising`, an
            // absolute Length). Both feed `HorzStringInfo.rising`, which every
            // render path adds to the baseline before `Tj`. `manual_rising`
            // defaults to `Length::ZERO` (`Context::initial`), so a document that
            // never calls `set-manual-rising` is byte-identical. Real effect: the
            // `\SATySFi`/`\LaTeX`/`\TeX` logo kerning.
            let rising = ctx.font_size * sf.rising + ctx.manual_rising;

            // Knuth-Liang hyphenation opt-in injection: fires ONLY when a
            // dictionary has been installed (`ctx.hyphen_dictionary ==
            // Some(tag)`) and the run's script is Latin. With `hyphen_dictionary
            // == None` (the `Context::initial` default), `breaks` is always
            // empty and the code below falls straight through to the
            // single-`InnerString` path.
            let breaks = match ctx.hyphen_dictionary {
                Some(tag) if script == Script::Latin => {
                    // An explicit soft hyphen (U+00AD) authored in the word
                    // takes priority over dictionary-derived breaks (matches the
                    // `hyphenation` crate's own `Standard::hyphenate` priority
                    // rule). Only reachable here with a soft hyphen still
                    // embedded in `word` because the tokenizer above
                    // (`text_to_boxes`'s per-char loop) defers to this branch
                    // instead of splitting on it as an ordinary UAX#14 boundary
                    // — gated on this same `Some(tag) && Latin` condition, so
                    // `hyphen_dictionary == None` never reaches
                    // `strip_soft_hyphens` and reproduces exactly today's
                    // split-at-soft-hyphen behavior.
                    let (clean, shy_breaks) = crate::hyphenation::strip_soft_hyphens(word);
                    if !shy_breaks.is_empty() {
                        *word = clean;
                        shy_breaks
                    } else {
                        crate::hyphenation::hyphenate_word(
                            tag,
                            word,
                            ctx.left_hyphen_min.max(0) as usize,
                            ctx.right_hyphen_min.max(0) as usize,
                        )
                    }
                }
                _ => Vec::new(),
            };

            if breaks.is_empty() {
                out.push(HorzBox::Pure(make_inner_string_pure_box(
                    interp,
                    ctx,
                    sf,
                    size,
                    rising,
                    std::mem::take(word),
                )?));
                return Ok(());
            }

            // Width-identity invariant (also see
            // `make_inner_string_pure_box`'s doc comment): `measure_run` is
            // purely additive per char (no
            // kerning/ligatures), so splitting `word` into fragments here and
            // rejoining them via empty-slot `Discretionary`s (taken only at a
            // chosen line break) reproduces the exact width/height/depth of the
            // un-split box when no break is actually taken — only words the DP
            // *does* break render differently, which is the intended new
            // behavior, confined to documents that opt in.
            let chars: Vec<char> = word.chars().collect();
            let penalty = ctx.hyphen_badness.clamp(i32::MIN as i64, i32::MAX as i64) as i32;
            let mut prev = 0usize;
            for &b in &breaks {
                let fragment: String = chars[prev..b].iter().collect();
                out.push(HorzBox::Pure(make_inner_string_pure_box(
                    interp, ctx, sf, size, rising, fragment,
                )?));
                let hyphen_box =
                    make_inner_string_pure_box(interp, ctx, sf, size, rising, "-".to_string())?;
                out.push(HorzBox::Pure(PureHorzBox::Discretionary {
                    penalty,
                    pre_break: vec![hyphen_box],
                    post_break: Vec::new(),
                    no_break: Vec::new(),
                }));
                prev = b;
            }
            let tail: String = chars[prev..].iter().collect();
            out.push(HorzBox::Pure(make_inner_string_pure_box(
                interp, ctx, sf, size, rising, tail,
            )?));
            word.clear();
            Ok(())
        };
    // `Some(s)` exactly when `word` is non-empty — the script of the run
    // currently being accumulated (a run also breaks on a script
    // change, not just on whitespace/UAX#14, see `char_script`).
    let mut word_script: Option<Script> = None;
    // The script of the immediately-preceding *typeset* character (persists
    // across the UAX#14 discretionary flushing that resets `word_script`), so
    // an inter-script boundary can be detected even between two single-char
    // CJK/Latin runs. Reset by an explicit space (no auto inter-script glue is
    // added adjacent to a real space). See the `is_latin_cjk_boundary` insert.
    let mut prev_script: Option<Script> = None;
    // The preceding typeset char itself, for the `is_interscript_punct` guard.
    let mut prev_char: Option<char> = None;
    for (i, c) in text.char_indices() {
        // Whitespace normalization around CJK — upstream's rewrite table
        // (`lineBreakDataMap.ml:143-157`, applied before any box is built):
        //
        //   CJK + (SP|BR) + Latin -> deleted      Latin + (SP|BR) + CJK -> deleted
        //   CJK + BR      + CJK   -> deleted      CJK   + SP      + CJK -> KEPT
        //   any remaining (SP|BR) touching CJK -> deleted; a leftover BR -> space
        //
        // Every space/line break adjacent to CJK is dropped EXCEPT a single
        // literal space between two CJK characters — the Latin/CJK boundary's
        // spacing is supplied by the inter-script glue below (0.24em), not by
        // the author's whitespace, so keeping it both double-counted that
        // boundary and turned every source line break into a space (the port
        // set `あります。 1 つは`/`これは 指定した` where SATySFi sets both
        // tight — figbox `manual.saty:116-120`). Deleting is a plain
        // `continue`: the characters either side still space against each
        // other through the inter-script rule, as if the whitespace had never
        // been written.
        if c == ' ' || c == '\n' {
            let is_cjk_script = |s| matches!(s, Script::HanIdeographic | Script::Kana);
            let prev_cjk = prev_script.is_some_and(is_cjk_script);
            let rest = &text[i + c.len_utf8()..];
            // Whether more whitespace follows: upstream's rules only ever match
            // ONE space between the two CJK characters (a longer run falls
            // through to the delete-everything rules), so a run collapses away.
            let run_continues = rest
                .chars()
                .next()
                .is_some_and(|ch| matches!(ch, ' ' | '\n'));
            let next_cjk = rest
                .chars()
                .find(|ch| !matches!(ch, ' ' | '\n'))
                .is_some_and(|ch| is_cjk_script(char_script(ch)));
            if prev_cjk || next_cjk {
                let keep = c == ' ' && !run_continues && prev_cjk && next_cjk;
                if !keep {
                    continue;
                }
            }
        }
        if c == ' ' || c == '\n' {
            if let Some(s) = word_script.take() {
                flush_word(&mut word, s, out)?;
            }
            prev_script = None;
            prev_char = None;
            // Avoid piling up doubled glue at text-run boundaries — but ONLY
            // for elastic (prose) spaces. A RIGID space (shrink == stretch == 0,
            // i.e. `code.satyh`'s `set-space-ratio (charwid/fs) 0. 0.`) is a
            // fixed-width verbatim column: SATySFi never collapses consecutive
            // ones, so the aligned source in a `+code` block keeps its spacing
            // (`| How       | I`, not the collapsed `| How | I`). Collapsing them
            // shortened code lines and let the port pack code blocks too tight.
            let rigid_space = ctx.space_shrink == 0.0 && ctx.space_stretch == 0.0;
            if rigid_space
                || !matches!(
                    out.last(),
                    Some(HorzBox::Pure(PureHorzBox::OuterEmpty { .. }))
                )
            {
                out.push(HorzBox::Pure(PureHorzBox::OuterEmpty {
                    natural: space_width,
                    // Upstream derives shrink/stretch directly as a ratio
                    // of `font_size` (`ctx.space_shrink`/`space_stretch`),
                    // NOT as a fraction of `space_width` — the previous
                    // `space_width * 0.25`/`* 0.5` was a port-invented
                    // approximation.
                    shrinkable: ctx.font_size * ctx.space_shrink,
                    stretchable: ctx.font_size * ctx.space_stretch,
                }));
            }
            continue;
        }
        let script = char_script(c);
        // Inter-script glue (`primitives.ml:517-524` `default_script_space_map`,
        // applied in `convertText.ml` `pure_space_between_scripts`): SATySFi's
        // default context inserts a `0.24 * size` space between a Latin run and
        // an adjacent CJK (Kana/Han) run — the space visible as "2 つ" /
        // "+easytable は" that the port otherwise packs tight ("2つ"). Emitted
        // at the boundary using `prev_script` (a CJK char resets `word_script`
        // via its UAX#14 discretionary, so this can't rely on `word_script`
        // alone). The glue is also an `is_break_point`, matching upstream (the
        // boundary is a legal break). See [`interscript_glue`] for why it is
        // RIGID even though `default_script_space_map` carries a triple.
        if let (Some(prev), Some(pc)) = (prev_script, prev_char) {
            if is_latin_cjk_boundary(prev, script) && !interscript_glue_suppressed(pc, c) {
                if let Some(s) = word_script.take() {
                    if !word.is_empty() {
                        flush_word(&mut word, s, out)?;
                    }
                }
                out.push(HorzBox::Pure(interscript_glue(ctx, prev, script)));
            }
        }
        if let Some(cur) = word_script {
            if cur != script {
                flush_word(&mut word, cur, out)?;
            }
        }
        word_script = Some(script);
        prev_script = Some(script);
        prev_char = Some(c);
        word.push(c);
        // Only non-ASCII text gets UAX#14 discretionaries: plain ASCII stays
        // on exactly today's space/newline-only splitter, so existing Latin
        // fixtures wrap identically (a real, tested divergence otherwise —
        // UAX#14 allows a break after a hyphen, which would fragment e.g.
        // "SATySFi-in-Rust" into three `InnerString`s instead of one,
        // changing the PDF content stream even though the zero-width
        // discretionaries between them render no differently when unchosen).
        // CJK and other non-ASCII scripts have no such existing behavior to
        // preserve, and are exactly where UAX#14 breaking is the whole point
        // (no interword glue at all otherwise, see `is_break_point`'s doc).
        // A soft hyphen (U+00AD) inside a run that the Knuth-Liang injection
        // above will consume (dictionary installed, Latin script) must NOT
        // be split here as an ordinary UAX#14 break-after point — doing so
        // would flush/fragment the word right at the soft hyphen before
        // `flush_word`'s hyphenation branch ever sees the whole word,
        // pre-empting `strip_soft_hyphens`'s explicit-break handling.
        // Instead let it accumulate into `word` like any other Latin letter.
        // Gated on the exact same `Some(_) && Latin` condition as that
        // branch, so `hyphen_dictionary == None` (or a non-Latin run)
        // reproduces exactly today's split-at-soft-hyphen behavior.
        let is_gated_soft_hyphen =
            c == '\u{ad}' && script == Script::Latin && ctx.hyphen_dictionary.is_some();
        // UAX#14 break opportunities apply to ALL text, ASCII included — that
        // is simply what upstream's line-break engine does (it runs over the
        // whole run with no script gate). Do NOT narrow this to non-ASCII, or
        // to the explicit hyphen — both approximations leave a load-bearing
        // gap:
        //
        //   - `+fig-center` (54.7pt, unbreakable) made the candidate widths jump
        //     clean over the feasible window — 400.32pt (ratio 2.72, dropped) to
        //     455.00pt (overfull) with nothing between — so the breaker fell back
        //     to a degenerate one-character line.
        //   - a `+code` line `…?:(drop) ?:(dropcolor)` ran 80pt past the column
        //     and clean off the paper, because the only break the port allowed
        //     was at a space, and breaking there left a rigid line 7.7pt short
        //     (dropped). UAX#14 grants a break between `:` and `(` — offset 2 of
        //     `?:(drop)…` — which is exactly where SATySFi breaks it.
        //
        // Cost: an ASCII run is now split into one `InnerString` per break
        // opportunity. Widths are unaffected (`measure_run` is purely additive,
        // see `make_inner_string_pure_box`), so this only changes how the text
        // is CHUNKED, not where any glyph lands.
        if !is_gated_soft_hyphen {
            let after = i + c.len_utf8();
            // The inter-chunk spacing between two DIRECTLY ADJACENT CJK
            // characters: `cjk_pair_space` folds `pure_space_between_classes` /
            // `adjacent_space` (`convertText.ml:101/194`) together with
            // `ideographic_single`'s compensating kerns (`convertText.ml:266`).
            //
            // The elastic part is the give a Japanese line justifies with.
            // Without it a CJK line's only give was whatever incidental Latin
            // spaces it happened to contain — a handful of points across a whole
            // line — so the breaker could neither fill to the column nor accept a
            // break that needed a hair of stretch.
            //
            // Only between two CJK characters: a CJK/Latin boundary is
            // `pure_space_between_scripts`'s job (the inter-script glue
            // above), and upstream falls through to `adjacent_space` only
            // once that has returned `None` (`space_between_chunks`,
            // `convertText.ml:220`).
            let is_cjk = |s| matches!(s, Script::HanIdeographic | Script::Kana);
            let next_char = text[after..].chars().next();
            let next_is_cjk = next_char.is_some_and(|nc| is_cjk(char_script(nc)));
            let pair = if is_cjk(script) && next_is_cjk {
                let nc = next_char.expect("checked");
                // `get_corrected_font_size` per SIDE (`convertText.ml:76-79`):
                // font size times the script's own `font_scheme` ratio. The
                // kerns and the JLreq class spaces scale against these; only
                // `adjacent_space` takes the raw size. See `cjk_pair_space`.
                let size_a = ctx.font_size * script_font(ctx, script).ratio;
                let size_b = ctx.font_size * script_font(ctx, char_script(nc)).ratio;
                Some(cjk_pair_space(
                    c,
                    size_a,
                    nc,
                    size_b,
                    ctx.font_size,
                    ctx.adjacent_stretch,
                ))
            } else {
                None
            };
            // `discretionary_if_breakable alw badns lphb`
            // (`convertText.ml:183-190`) — the ONE decision upstream makes at a
            // chunk boundary. The spacing is computed the same way either way;
            // only its container depends on whether UAX#14 grants a break:
            //
            //   AllowBreak    -> LBDiscretionary(badns, id, [glue], [], [])
            //   PreventBreak  -> LBPure(glue)
            //
            // The port used to emit the `AllowBreak` arm and *nothing* for
            // `PreventBreak`, so at every prohibited boundary — and in Japanese
            // prose that is one boundary in several, since LB13 forbids a break
            // before `、`/`。`/`」`/`）` and LB14 after `（`/`「` — a CJK line
            // carried give only at the subset of its boundaries that happened to
            // be breakable. A line with no give has to FILL its measure with
            // characters, which is part of why the port packs more per line than
            // SATySFi.
            match boundary[after] {
                Some(kind) => {
                    flush_word(&mut word, script, out)?;
                    word_script = None;
                    let mut no_break = Vec::new();
                    if let Some((n, sh, st)) = pair {
                        // The kern part is RIGID and must never be a break point,
                        // so it rides as a `FixedEmpty` rather than as glue.
                        if n != Length::ZERO {
                            no_break.push(PureHorzBox::FixedEmpty { width: n });
                        }
                        no_break.push(PureHorzBox::OuterEmpty {
                            natural: Length::ZERO,
                            shrinkable: sh,
                            stretchable: st,
                        });
                    }
                    out.push(HorzBox::Pure(PureHorzBox::Discretionary {
                        penalty: match kind {
                            BreakKind::Allowed => 0,
                            BreakKind::Mandatory => FORCED_BREAK_PENALTY,
                        },
                        pre_break: Vec::new(),
                        post_break: Vec::new(),
                        no_break,
                    }));
                }
                // The `PreventBreak` arm: `LBPure(glue)`, spelled as a
                // `Discretionary` whose every break slot is empty and whose
                // penalty is `NO_BREAK_PENALTY` (a bare `OuterEmpty` IS a
                // breakpoint in this box model, so a pure elastic box has no
                // other spelling).
                //
                // Only the ELASTIC half, deliberately — the one place this
                // port knowingly diverges from `discretionary_if_breakable`.
                // Landing the RIGID half too was written and MEASURED: it makes
                // the kern model ASYMMETRIC, since `cjk_pair_space`'s kern is a
                // property of the PAIR while upstream's is a property of the
                // CHARACTER, and the two agree only when BOTH neighbours are
                // CJK — `生成・変換` would get the nakaten's kern on both sides
                // while `（例：textbox` gets only its leading one (the trailing
                // side faces Latin, unreached by `cjk_pair_space`) — figbox's
                // largest intra-line divergence from upstream (mean |dx| on
                // that line 2.5pt -> 6.5pt).
                //
                // Completing it needs the per-character kerns at CJK<->Latin
                // boundaries and run edges too, which needs the source-
                // whitespace rewrite applied BEFORE `uax14_boundaries` rather
                // than during this loop (upstream's own order). Without that a
                // `。` before a deleted source newline gets its trailing kern
                // while the class space that pays it back is skipped (the
                // lookahead sees the newline, not the character after it), and
                // the layout-fidelity gate fails 12 ways. So the natural-width
                // bug the rigid half would fix — `」。`/`」、` a half-em too
                // wide, `末・雲` a quarter — stays exactly as open as before.
                None => {
                    if let Some((_, sh, st)) = pair {
                        if sh != Length::ZERO || st != Length::ZERO {
                            flush_word(&mut word, script, out)?;
                            word_script = None;
                            out.push(HorzBox::Pure(PureHorzBox::Discretionary {
                                penalty: NO_BREAK_PENALTY,
                                pre_break: Vec::new(),
                                post_break: Vec::new(),
                                no_break: vec![PureHorzBox::OuterEmpty {
                                    natural: Length::ZERO,
                                    shrinkable: sh,
                                    stretchable: st,
                                }],
                            }));
                        }
                    }
                }
            }
        }
    }
    match word_script {
        Some(s) => flush_word(&mut word, s, out),
        None => Ok(()),
    }
}

// ---- math conversion ----------------------
//
// Walks the already-elaborated `MathElem` tree straight into one
// `PureHorzBox::Math`, fixed-constant shift/scale (no MATH table).

/// Superscript/subscript size ratio, used ONLY as `MathC`'s fallback when
/// the current math font has no OpenType MATH table (`script_percent_scale_down
/// / 100`). Not read anywhere outside `MathC` — every layout site goes
/// through `MathC::script_scale`/`sup_shift_clamped`/etc. so a MATH-table
/// font gets the real per-font ratio instead.
const SCRIPT_SCALE: f64 = 0.7;
/// Superscript raise, as a fraction of `ctx.font_size` — `MathC`'s
/// no-MATH-table fallback (`superscript_shift_up` clamped per
/// `math.ml:527`). Not read outside `MathC`.
const SUP_SHIFT: f64 = 0.5;
/// Cramped-style superscript raise fallback — the no-MATH-table fallback
/// `sup_shift_clamped` uses in place of `SuperscriptShiftUpCramped` when there
/// is no real MATH table to read. Deliberately set EQUAL to `SUP_SHIFT`: every
/// checked-in fixture font has no MATH table, so cramped and uncramped
/// superscripts get the identical fallback shift there. Only a real MATH
/// font (host-installed, test-guarded) makes cramped/uncramped diverge.
const SUP_SHIFT_CRAMPED: f64 = SUP_SHIFT;
/// Subscript drop, as a fraction of `ctx.font_size` — `MathC`'s
/// no-MATH-table fallback (`subscript_shift_down` per
/// `math.ml:545`). Not read outside `MathC`.
const SUB_SHIFT: f64 = 0.25;
/// `MathC::frac_numer_shift`'s no-MATH-table fallback: a flat,
/// content-independent numerator raise, as a fraction of the fraction's own
/// LOCAL size (mirrors `sup_shift_clamped`'s None-branch style, which
/// also ignores ink extent with no MATH table). Not read outside `MathC`.
const FRAC_NUMER_SHIFT_FALLBACK: f64 = 0.33;
/// `MathC::frac_denom_shift`'s no-MATH-table fallback (mirrors
/// `FRAC_NUMER_SHIFT_FALLBACK`; applied as a downward, i.e. negative, shift
/// by the caller). Not read outside `MathC`.
const FRAC_DENOM_SHIFT_FALLBACK: f64 = 0.33;

/// MATH-table resolver: one query of `interp.metrics.math_constants(font)`
/// per laid-out math run, memoized here so every shift/scale/kern site in
/// that run reads the SAME `Option` instead of re-querying — and so a font
/// with no MATH table (every `Base14Metrics` call, and any TTF that lacks
/// one) transparently falls back to the flat pre-MATH-table constants
/// above. Fields are ratios of
/// the font size; callers multiply by whichever size is in scope
/// (`ctx.font_size` for the shift magnitudes — matching the pre-existing
/// "shift doesn't shrink with nesting" behavior these constants always had
/// — or the atom's own local `size` for glyph-relative queries like
/// `script_scale`/kerning).
struct MathC {
    c: Option<MathConstants>,
    /// `ctx.math_cramped` at the point this `MathC` was built — whether the
    /// current math sub-formula is laid out cramped. Consulted only by
    /// `sup_shift`/`sup_shift_clamped`, the sole positioning formula cramped
    /// changes in this port's feature set.
    cramped: bool,
}

impl MathC {
    fn of(interp: &Interp, ctx: &Context) -> Self {
        Self {
            c: interp.metrics.math_constants(ctx.math_font),
            cramped: ctx.math_cramped,
        }
    }

    /// Flat, unclamped superscript raise (`math.ml:527`'s `h_supstd` alone,
    /// no `math.ml:524-533` clamp) — the shape `layout_math_atom`'s callers
    /// need when no base/script ink extent is at hand yet.
    fn sup_shift(&self, s: Length) -> Length {
        match self.c {
            None => {
                s * if self.cramped {
                    SUP_SHIFT_CRAMPED
                } else {
                    SUP_SHIFT
                }
            }
            Some(c) => {
                s * if self.cramped {
                    c.superscript_shift_up_cramped
                } else {
                    c.superscript_shift_up
                }
            }
        }
    }

    /// Flat, unclamped subscript drop (mirrors `sup_shift`).
    fn sub_shift(&self, s: Length) -> Length {
        self.c
            .map(|c| s * c.subscript_shift_down)
            .unwrap_or(s * SUB_SHIFT)
    }

    /// `script_percent_scale_down / 100`, or the fixed `SCRIPT_SCALE`
    /// fallback. Nesting-level scale gap: upstream
    /// switches to `script_script_percent_scale_down` one level deeper;
    /// this port applies `script_scale_down` uniformly at every depth.
    fn script_scale(&self) -> f64 {
        self.c.map(|c| c.script_scale_down).unwrap_or(SCRIPT_SCALE)
    }

    /// `math.ml`'s `h_bar` (axis height): the vertical center math content
    /// (fraction bars, `get-axis-height`) aligns to. Falls back to a fixed
    /// `0.25` ratio with no MATH table.
    fn axis(&self, s: Length) -> Length {
        self.c.map(|c| s * c.axis_height).unwrap_or(s * 0.25)
    }

    /// `math.ml:524-533` `superscript_baseline_height`, clamped: the
    /// MAGNITUDE of the upward shift a superscript needs given the base's
    /// own ink height (`h_base`, a positive extent above ITS baseline) and
    /// the superscript's own ink depth (`d_sup`, a positive extent below
    /// ITS baseline — i.e. `MathGlyph.height`/`.depth`, not upstream's
    /// signed `Length.negate`d fields). Falls back to the flat `sup_shift`
    /// (ignoring `h_base`/`d_sup`) when there's no MATH table, so base-14
    /// output is untouched by this clamp.
    fn sup_shift_clamped(&self, s: Length, h_base: Length, d_sup: Length) -> Length {
        match self.c {
            None => self.sup_shift(s),
            Some(c) => {
                let shift_up = if self.cramped {
                    c.superscript_shift_up_cramped
                } else {
                    c.superscript_shift_up
                };
                let cand1 = s * shift_up;
                let cand2 = h_base - s * c.superscript_baseline_drop_max;
                let cand3 = s * c.superscript_bottom_min + d_sup;
                cand1.max(cand2).max(cand3)
            }
        }
    }

    /// `math.ml:545-553` `subscript_baseline_depth`, clamped: the MAGNITUDE
    /// of the downward shift, given the base's own ink depth (`d_base`) and
    /// the subscript's own ink height (`h_sub`). Mirrors
    /// `sup_shift_clamped`'s fallback behavior.
    fn sub_shift_clamped(&self, s: Length, d_base: Length, h_sub: Length) -> Length {
        match self.c {
            None => self.sub_shift(s),
            Some(c) => {
                let cand1 = s * c.subscript_shift_down;
                let cand2 = d_base + s * c.subscript_baseline_drop_min;
                let cand3 = h_sub - s * c.subscript_top_max;
                cand1.max(cand2).max(cand3)
            }
        }
    }

    /// `math.ml:562-573` `correct_script_baseline_heights`: when a base
    /// carries BOTH a subscript and a superscript, nudge the two
    /// already-clamped shift magnitudes apart so their ink keeps at least
    /// `sub_superscript_gap_min` clearance. `d_sup`/`h_sub` are the same ink
    /// extents `sup_shift_clamped`/`sub_shift_clamped` took; `sup`/`sub` are
    /// their (already clamped) outputs. A no-op when there's no MATH table
    /// — the flat fallback shifts are never additionally corrected, so
    /// base-14 output stays exactly `(sup, sub)`.
    fn correct_script_gap(
        &self,
        s: Length,
        d_sup: Length,
        h_sub: Length,
        sup: Length,
        sub: Length,
    ) -> (Length, Length) {
        let Some(c) = self.c else {
            return (sup, sub);
        };
        let gap_min = s * c.sub_superscript_gap_min;
        let gap = (sup - d_sup) - (h_sub - sub);
        if gap < gap_min {
            let corr = (gap_min - gap) * 0.5;
            (sup + corr, sub + corr)
        } else {
            (sup, sub)
        }
    }

    /// `math.ml:596-602` `upper_limit_baseline_height`, clamped: the
    /// MAGNITUDE of the upward shift for an `\overset`-like upper limit,
    /// given the base's own ink height (`h_base`) and the limit content's
    /// own ink depth (`d_up`). Falls back to the flat `sup_shift` (same
    /// shape upstream's superscript raise uses) with no MATH table.
    fn upper_limit_shift(&self, s: Length, h_base: Length, d_up: Length) -> Length {
        match self.c {
            None => self.sup_shift(s),
            Some(c) => {
                let cand1 = h_base + s * c.upper_limit_baseline_rise_min;
                let cand2 = h_base + s * c.upper_limit_gap_min + d_up;
                cand1.max(cand2)
            }
        }
    }

    /// `math.ml:605-611` `lower_limit_baseline_depth`, clamped: mirrors
    /// `upper_limit_shift` for a lower limit, given the base's own ink
    /// depth (`d_base`) and the limit content's own ink height (`h_low`).
    fn lower_limit_shift(&self, s: Length, d_base: Length, h_low: Length) -> Length {
        match self.c {
            None => self.sub_shift(s),
            Some(c) => {
                let cand1 = d_base + s * c.lower_limit_baseline_drop_min;
                let cand2 = d_base + s * c.lower_limit_gap_min + h_low;
                cand1.max(cand2)
            }
        }
    }

    /// `math.ml:982-991` `horz_fraction_bar`'s rule thickness (also
    /// `radical_bar_metrics`'s `t_bar` — both are "the same generic rule
    /// ratio" in the pre-MATH-table fixed-constant world):
    /// `fraction_rule_thickness`, or the fixed `0.04` fallback. Multiplied
    /// by the ambient LOCAL nesting `size` (not `ctx.font_size` — a
    /// fraction/radical's own metrics DO shrink with nesting, matching
    /// upstream's `FontInfo.actual_math_font_size`, unlike the sup/sub shift
    /// constants' documented `ctx.font_size` simplification above).
    fn frac_rule(&self, s: Length) -> Length {
        self.c
            .map(|c| s * c.fraction_rule_thickness)
            .unwrap_or(s * 0.04)
    }

    /// `math.ml:574-583` `numerator_baseline_height`, clamped: the
    /// MAGNITUDE of the upward shift a numerator needs given its own ink
    /// depth (`d_numer`, a positive extent below ITS baseline — this port's
    /// convention, see `sup_shift_clamped`'s doc comment; upstream's
    /// `Length.negate d_numer` becomes a plain ADD of `d_numer` here, not a
    /// subtract — getting this sign wrong would shrink the raise for a
    /// deeper numerator instead of growing it, overlapping the bar). Falls
    /// back to a flat, content-independent ratio with no MATH table
    /// (mirrors `sup_shift_clamped`'s None-branch style).
    fn frac_numer_shift(&self, s: Length, d_numer: Length) -> Length {
        match self.c {
            None => s * FRAC_NUMER_SHIFT_FALLBACK,
            Some(c) => {
                let std = s * c.fraction_numer_shift_up;
                let gap =
                    self.axis(s) + self.frac_rule(s) * 0.5 + s * c.fraction_numer_gap_min + d_numer;
                std.max(gap)
            }
        }
    }

    /// `math.ml:585-594` `denominator_baseline_depth`, clamped: mirrors
    /// `frac_numer_shift`. Returns the SIGNED (already-negative) drop the
    /// caller applies straight to `dy` — unlike the sup/sub methods'
    /// positive-magnitude-then-caller-negates convention — because
    /// upstream's own `d_denombl` is signed too, so there's no sign flip to
    /// make here (and `h_denom`, a HEIGHT not a depth, is subtracted
    /// directly, matching upstream's un-negated use of it).
    fn frac_denom_shift(&self, s: Length, h_denom: Length) -> Length {
        match self.c {
            None => -(s * FRAC_DENOM_SHIFT_FALLBACK),
            Some(c) => {
                let std = -(s * c.fraction_denom_shift_down);
                let gap =
                    self.axis(s) - self.frac_rule(s) * 0.5 - s * c.fraction_denom_gap_min - h_denom;
                std.min(gap)
            }
        }
    }

    /// `math.ml:620-626` `radical_bar_metrics`: `(h_bar, t_bar, l_extra)` —
    /// the bar's height above baseline (radicand height + gap, so the bar
    /// always clears the radicand with no separate raise needed), its rule
    /// thickness, and the extra ascender the WHOLE radical run reports
    /// above the bar. Fallback ratios (no MATH table):
    /// vertical_gap=0.06, rule=0.04 (same fixed ratio `frac_rule` falls back
    /// to), extra_ascender=0.06.
    fn radical_bar_metrics(&self, s: Length, h_cont: Length) -> (Length, Length, Length) {
        match self.c {
            Some(c) => (
                h_cont + s * c.radical_vertical_gap,
                s * c.radical_rule_thickness,
                s * c.radical_extra_ascender,
            ),
            None => (h_cont + s * 0.06, s * 0.04, s * 0.06),
        }
    }
}

/// The ink height/depth of an already-laid-out run, as positive magnitudes
/// (`MathGlyph.dy` is signed, up-positive; `.height`/`.depth` are always
/// non-negative extents from EACH glyph's own local baseline) — the same
/// aggregate `read_math`/`layout_math_value` compute for a whole
/// `PureHorzBox::Math`, reused here per sub-run so `MathC`'s clamp formulas
/// have an `h_base`/`d_sup`/etc to clamp against. Empty input -> `(ZERO,
/// ZERO)` (an empty base/script contributes no clamp pressure).
fn glyphs_extent(glyphs: &[MathGlyph]) -> (Length, Length) {
    let mut height = Length::ZERO;
    let mut depth = Length::ZERO;
    for g in glyphs {
        height = height.max(g.dy + g.height);
        depth = depth.max(g.depth - g.dy);
    }
    (height, depth)
}

/// `glyphs_extent` plus `rules`' own bounding boxes folded in — exactly the
/// aggregate `layout_math_value` computes for a whole `PureHorzBox::Math`
/// (see that function's doc comment on why a bare `Fill`, e.g. a fraction
/// bar/radical sign, needs its own bbox folded in rather than being silently
/// undercounted). Also reused to size a stretchy delimiter to its
/// enclosed run's REAL ink (glyphs + any drawn rules), not just its glyphs.
///
/// This — NOT bare `glyphs_extent` — is what every `layout_math_value` arm
/// must use for a sub-run's `h_base`/`d_base`/`d_sup`/`h_sub`/`d_numer`/…,
/// because it is upstream's `convert_to_low` return value: each arm's
/// `(_, h, d, _, _)` is the whole sub-run's `h_whole`/`d_whole`, and a
/// `MathParen`'s is `max(hC, hL, hR)` / `min(dC, dL, dR)` over the
/// DELIMITER boxes too (`math.ml:908-909`). A `math.satyh` delimiter is
/// `inline-graphics` ink, so it lands in `rules` and in nothing else: with
/// `glyphs_extent` a `\paren{…}` base reported only its CONTENT's height,
/// which is smaller than the delimiter it just sized, and
/// `sup_shift_clamped`'s `h_base - SuperscriptBaselineDropMax` candidate
/// therefore lost when upstream's wins. `${\paren{\frac{1}{1-v}}^{2}}` at
/// 12pt: `h_base` 16.116pt (content) vs upstream's 17.316pt (`hgtaxis +
/// halflen`, the paren's own declared box), i.e. a 1.2pt-too-low superscript
/// — `layout-tests/probes/math_box_extent.saty` row 4. The bbox of
/// `math.satyh`'s `paren-left`/`angle-left`/… path is exactly that declared
/// box (its extreme points ARE `ycenter ± halflen`), so folding the rule in
/// reproduces upstream's number rather than approximating it.
fn inner_ink_extent(glyphs: &[MathGlyph], rules: &[GraphicsElem]) -> (Length, Length) {
    let (mut height, mut depth) = glyphs_extent(glyphs);
    for r in rules {
        // `graphics_bbox` is now `Option` (`None` for an empty `Group`
        // — unreachable here under 0.0.6 math rules, but the fold is
        // version-blind and correct either way: a `None` rule contributes
        // nothing to the ink extent).
        if let Some(((_, min_y), (_, max_y))) = graphics_bbox(r) {
            height = height.max(max_y);
            depth = depth.max(-min_y);
        }
    }
    (height, depth)
}

/// `math.ml:1040-1075`'s superscript kern tuck: the italic correction of
/// the base's TRAILING glyph plus the two corner kerns — the base's
/// top-right sampled at the height the raised superscript's ink starts
/// (`l_base = sup_shift - d_sup`, `superscript_correction_heights`'s first
/// component), and the superscript's own bottom-left sampled (at the
/// superscript's OWN size) at the height the base's ink ends (`l_sup =
/// h_base - sup_shift`, that function's second component) — the extra
/// horizontal gap upstream inserts between a base and a raised superscript
/// so slanted glyphs (an italic integral, say) don't collide with what's
/// stacked above them. `size`/`script_size` are the local sizes the base/
/// script glyphs were actually measured at (NOT `ctx.font_size`, unlike the
/// shift magnitude — these feed a design-units conversion that must match
/// each glyph's own em square). Every lookup misses to `Length::ZERO` (no
/// MATH table, no glyph, no kern data, ...), so base-14 output is
/// untouched: this returns exactly `Length::ZERO` whenever `ctx.math_font`
/// has no MATH table.
#[allow(clippy::too_many_arguments)]
fn superscript_kern(
    interp: &Interp,
    ctx: &Context,
    size: Length,
    script_size: Length,
    base_glyphs: &[MathGlyph],
    script_glyphs: &[MathGlyph],
    sup_shift: Length,
    h_base: Length,
    d_sup: Length,
) -> Length {
    let font = ctx.math_font;
    let last_base = base_glyphs.last().and_then(|g| g.text.chars().last());
    let first_script = script_glyphs.first().and_then(|g| g.text.chars().next());
    let l_italic = last_base
        .and_then(|c| interp.metrics.italic_correction(font, c, size))
        .unwrap_or(Length::ZERO);
    let l_base = sup_shift - d_sup;
    let l_sup = h_base - sup_shift;
    let l_kernbase = last_base
        .and_then(|c| {
            interp
                .metrics
                .math_kern(font, c, size, MathCorner::TopRight, l_base)
        })
        .unwrap_or(Length::ZERO);
    let l_kernsup = first_script
        .and_then(|c| {
            interp
                .metrics
                .math_kern(font, c, script_size, MathCorner::BottomLeft, l_sup)
        })
        .unwrap_or(Length::ZERO);
    l_italic + l_kernbase + l_kernsup
}

/// A minimal stand-in for v0.0.6's per-codepoint math-class table
/// (`primitives.cppo.ml`) + `normalize_math_kind` (`math.ml:240`) — just
/// enough for `${a+b}` to get binary-operator spacing. Letters/digits/
/// everything else default to `Ord`.
fn ascii_math_kind(c: char) -> MathKind {
    match c {
        '+' | '-' | '*' | '/' => MathKind::Bin,
        '=' | '<' | '>' => MathKind::Rel,
        ',' | ';' | ':' | '.' => MathKind::Punct,
        _ => MathKind::Ord,
    }
}

/// `normalize_math_kind` (`math.ml:238-277`): a BINARY atom whose neighbours
/// make it unary is really an ORDINARY one, and gets none of `Bin`'s spacing.
/// Upstream demotes on `mkprev in {Op, Bin, Rel, Open, Punct}` or `mknext in
/// {Rel, Close, Punct}`; `MathEnd` — the sentinel `math.ml:1270` passes for
/// both ends of a formula — is included here on the LEFT, which is what makes
/// `${-------}` set seven tight glyphs rather than a leading binary minus
/// followed by six ordinaries, and what keeps `${-N, -N + 1}`'s minus signs
/// tight against their operands the way the reference sets them. Every other
/// class passes through unchanged.
///
/// Reachable at all only since the math lexer stopped gluing a run of symbols
/// into one token: before that a `--` was a single `Ord` atom and there was no
/// adjacent pair to normalize.
fn normalize_math_kind(prev: MathKind, next: MathKind, raw: MathKind) -> MathKind {
    if raw != MathKind::Bin {
        return raw;
    }
    let unary_left = matches!(
        prev,
        MathKind::Op
            | MathKind::Bin
            | MathKind::Rel
            | MathKind::Open
            | MathKind::Punct
            | MathKind::End
    );
    let unary_right = matches!(next, MathKind::Rel | MathKind::Close | MathKind::Punct);
    if unary_left || unary_right {
        MathKind::Ord
    } else {
        MathKind::Bin
    }
}

/// The six inter-atom space ratios `space_between_math_kinds` multiplies the
/// math font size by — `primitives.cppo.ml:528-533`'s `space_math_bin`, `_rel`,
/// `_op`, `_punct`, `_inner`, `_prefix`. Upstream keeps them as a
/// natural/shrink/stretch triple on `HorzBox.context_main` that no v0.0.6
/// primitive writes, and this port's math spacer emits a fixed kern rather than
/// glue, so only the natural component is needed.
const SPACE_MATH_BIN: f64 = 0.25;
const SPACE_MATH_REL: f64 = 0.375;
const SPACE_MATH_OP: f64 = 0.125;
const SPACE_MATH_PUNCT: f64 = 0.125;
const SPACE_MATH_INNER: f64 = 0.125;
const SPACE_MATH_PREFIX: f64 = 0.125;

/// `space_between_math_kinds` (`math.ml:319-410`), arm for arm and in the same
/// ORDER: OCaml's `match` is first-match, so `(Punct, Close)` must reach the
/// `(Punct, _)` arm and not `(_, Close)`. Every ratio is
/// `primitives.cppo.ml:528-533`'s.
///
/// `in_script` is `not (MathContext.is_in_base_level mathctx)` — inside a
/// sub/superscript upstream suppresses the whole table except the five operator
/// pairs. `font_size` is `FontInfo.actual_math_font_size mathctx`, the size of
/// the LEVEL being laid out and not the ambient base size, which is why callers
/// pass their local `size`.
///
/// Upstream's `space_correction` channel is pinned at `NoSpace` here, so the
/// three arms that read it — `(_, Close)`, `(Ord|Prefix, Open)` and the
/// fallthrough — all yield nothing: exact for `NoSpace`, and the conservative
/// reading of a trailing italics correction and the MATH table's
/// `space_after_script`.
fn space_before(prev: MathKind, cur: MathKind, in_script: bool, font_size: Length) -> Length {
    use MathKind::*;
    let ratio = if in_script {
        match (prev, cur) {
            (Op, Ord) | (Ord, Op) | (Op, Op) | (Close, Op) | (Inner, Op) => SPACE_MATH_OP,
            _ => return Length::ZERO,
        }
    } else {
        match (prev, cur) {
            (Punct, _) => SPACE_MATH_PUNCT,

            (Inner, Ord) | (Inner, Open) | (Inner, Punct) | (Inner, Inner) | (Ord, Inner)
            | (Prefix, Inner) | (Close, Inner) => SPACE_MATH_INNER,

            // `corr = NoSpace`: no italics correction to append.
            (_, Close) => return Length::ZERO,

            // `corr = NoSpace`: no `space_after_script` either.
            (Ord, Open) | (Prefix, Open) => return Length::ZERO,

            (Bin, Ord) | (Bin, Prefix) | (Bin, Op) | (Bin, Open) | (Bin, Inner) | (Ord, Bin)
            | (Close, Bin) | (Inner, Bin) => SPACE_MATH_BIN,

            (Rel, Ord) | (Rel, Op) | (Rel, Inner) | (Rel, Open) | (Rel, Prefix) | (Ord, Rel)
            | (Op, Rel) | (Inner, Rel) | (Close, Rel) => SPACE_MATH_REL,

            (Op, Ord) | (Op, Op) | (Op, Inner) | (Op, Prefix) | (Ord, Op) | (Close, Op)
            | (Inner, Op) => SPACE_MATH_OP,

            (Ord, Prefix) | (Inner, Prefix) => SPACE_MATH_PREFIX,

            (_, End) | (End, _) => return Length::ZERO,

            _ => return Length::ZERO,
        }
    };
    font_size * ratio
}

/// `not (MathContext.is_in_base_level mathctx)` for the `(ctx, size)` pair this
/// port threads instead of upstream's `math_context`. BOTH witnesses are
/// needed: `layout_math_atom`'s script arms shrink only the local `size` and
/// pass the ambient `ctx` down, while `enter_script` (`attach_scripts`,
/// `read-math`'s `Math::WithContext`) advances `Context::math_script_level` and
/// scales `font_size` together — so a `WithContext` captured under a script
/// arrives with `size == ctx.font_size` and is recognisable only by its level.
fn math_in_script(ctx: &Context, size: Length) -> bool {
    size != ctx.font_size || ctx.math_script_level != MathScriptLevel::Base
}

/// FontKey a math glyph c@size should measure/emit in: dedicated ctx.math_font
/// when it can render c, else text ctx.font. The one place math diverges from
/// text font; the MATH-table slice keys lookups on the same returned FontKey.
fn math_glyph_font(interp: &Interp, ctx: &Context, c: char, size: Length) -> FontKey {
    if interp.metrics.advance(ctx.math_font, c, size).is_some() {
        ctx.math_font
    } else {
        ctx.font
    }
}

/// gap-5 metrics-probe predicate, now math-font-aware.
fn math_char_available(interp: &Interp, ctx: &Context, c: char, size: Length) -> bool {
    interp.metrics.advance(ctx.math_font, c, size).is_some()
        || interp.metrics.advance(ctx.font, c, size).is_some()
}

/// Measure one math character at `size` under `math_glyph_font(ctx, c)` and
/// push it as a `MathGlyph` at the running `*x` (`dy = 0`; callers shift
/// scripts afterward), advancing `*x` past it.
fn push_char_glyph(
    interp: &mut Interp,
    ctx: &Context,
    c: char,
    size: Length,
    out: &mut Vec<MathGlyph>,
    x: &mut Length,
) -> Result<(), EvalError> {
    let font = math_glyph_font(interp, ctx, c, size);
    // `fontInfo.ml:379-383`: a math glyph below base level is set in the font's
    // `ssty` variant — a purpose-drawn form with its own advance, not the base
    // glyph shrunk (see `FontMetrics::math_script_variant`). Any miss falls
    // through to the base glyph unchanged.
    if math_in_script(ctx, size) {
        if let Some(v) = interp.metrics.math_script_variant(font, c, size) {
            out.push(MathGlyph {
                info: HorzStringInfo {
                    font,
                    size,
                    rising: Length::ZERO,
                    color: ctx.text_color,
                },
                text: c.to_string(),
                gid: Some(v.gid),
                dx: *x,
                dy: Length::ZERO,
                width: v.advance,
                height: v.height,
                depth: v.depth,
            });
            *x += v.advance;
            return Ok(());
        }
    }
    // Graceful degradation for a math character neither the math font nor the
    // text font can render (e.g. `⋯` U+22EF under the bundled faces): fall back
    // to a half-em advance and let the glyph degrade to `.notdef` at render
    // time (`gid: None`, resolved by `cid::encode_glyph_run`), exactly as the
    // text path does in `measure_run` — a missing glyph must not abort the whole
    // document. This only ever changes behavior for a glyph that would otherwise
    // be a hard error, so covered-glyph documents stay byte-identical.
    let advance = interp.metrics.advance(font, c, size).unwrap_or(size * 0.5);
    let (height, depth) = math_glyph_vextent(interp, font, c, size);
    out.push(MathGlyph {
        info: HorzStringInfo {
            font,
            size,
            rising: Length::ZERO,
            color: ctx.text_color,
        },
        text: c.to_string(),
        gid: None,
        dx: *x,
        dy: Length::ZERO,
        width: advance,
        height,
        depth,
    });
    *x += advance;
    Ok(())
}

/// One math glyph's vertical ink extent, the way upstream measures it:
/// `FontFormat.get_math_glyph_metrics` (`fontFormat.ml:2257-2264`) takes the
/// glyph's OWN bounding box and truncates each side towards the baseline —
/// `hgt = truncate_negative ymax` (so a wholly-subscripted glyph reports
/// height 0, never a negative height) and `dpt = truncate_positive ymin` (so a
/// glyph entirely above the baseline, `*` at ymin=+320, reports depth 0).
///
/// This is NOT the font-level ascender/descender:
/// `MathC::sub_shift_clamped`/`sup_shift_clamped` clamp against these extents
/// (`math.ml:527-552`), so feeding them latinmodern-math's hhea ascender
/// (806/1000 em) and descender (194/1000 em) instead of `m`'s real ink box
/// (ymax 442, ymin 0) made the `superscript_baseline_drop_max` /
/// `subscript_baseline_drop_min` candidate win every time. At 12pt that is
/// `9.672 - 3.0 = 6.672pt` of superscript rise where upstream's own clamp
/// picks `SuperscriptShiftUp = 4.356pt` (plus a gap correction, 4.525pt), and
/// `2.328 + 2.4 = 4.728pt` of subscript drop where upstream picks
/// `SubscriptShiftDown = 2.964pt` — measured by `layout-tests/probes/
/// math_script_drop.saty`.
///
/// Falls back to `ascender`/`descender` when the provider exposes no per-glyph
/// bbox (base-14 metrics, test stubs).
fn math_glyph_vextent(interp: &Interp, font: FontKey, c: char, size: Length) -> (Length, Length) {
    match interp.metrics.glyph_vextent(font, c, size) {
        Some((h, d)) => (h.max(Length::ZERO), d.max(Length::ZERO)),
        None => (
            interp.metrics.ascender(font, size),
            interp.metrics.descender(font, size),
        ),
    }
}

/// `push_char_glyph`'s big-operator sibling: try the v0.0.6 `BigOp`
/// vertical variant (`fontInfo.ml:386-401` — the 2nd `MathVariants` record if
/// present, else the 1st) unconditionally. Upstream's own guard is
/// `is_in_display && is_big`, but `math.ml`'s `convert_math_char` hardcodes
/// `is_in_display = true`, so it reduces to just `is_big` — a big operator
/// grows even inline, even at script size, exactly like upstream; the port
/// tracks no display/inline distinction and needs none here. On any miss (no
/// MATH table, no vertical construction for `c`, or a variant/hmtx/bbox
/// lookup failure — every base-14 call, always) falls back to
/// `push_char_glyph`, byte-identical to the base output.
fn push_big_char_glyph(
    interp: &mut Interp,
    ctx: &Context,
    c: char,
    size: Length,
    out: &mut Vec<MathGlyph>,
    x: &mut Length,
) -> Result<(), EvalError> {
    let font = math_glyph_font(interp, ctx, c, size);
    match interp
        .metrics
        .math_vertical_variant(font, c, size, VertVariantPolicy::BigOp)
    {
        Some(v) => {
            out.push(MathGlyph {
                info: HorzStringInfo {
                    font,
                    size,
                    rising: Length::ZERO,
                    color: ctx.text_color,
                },
                text: c.to_string(),
                gid: Some(v.gid),
                dx: *x,
                dy: Length::ZERO,
                width: v.advance,
                height: v.height,
                depth: v.depth,
            });
            *x += v.advance;
            Ok(())
        }
        None => push_char_glyph(interp, ctx, c, size, out, x),
    }
}

/// One stretchy-delimiter glyph: the smallest `MathVariants`
/// record whose `advance_measurement` covers `target` (else the largest
/// record — `VertVariantPolicy::AtLeast`), centered on the math axis
/// (`dy = axis - (h - d) / 2`; y-**up**, same sign convention as
/// `shift_and_append`'s `dy_shift` — see that function's doc comment on the
/// mirroring trap a flipped sign causes). Falls back to the baseline
/// base glyph (`push_char_glyph`) when there's no vertical construction.
fn push_delimiter_glyph(
    interp: &mut Interp,
    ctx: &Context,
    c: char,
    size: Length,
    target: Length,
    axis: Length,
    out: &mut Vec<MathGlyph>,
    x: &mut Length,
) -> Result<(), EvalError> {
    let font = math_glyph_font(interp, ctx, c, size);
    let variant =
        interp
            .metrics
            .math_vertical_variant(font, c, size, VertVariantPolicy::AtLeast(target));
    // `GlyphAssembly`: if even the largest discrete variant's own ink
    // extent (`height + depth`) still doesn't span `target` — a delimiter
    // taller than anything the font enumerates as a prepared variant — grow
    // it from the assembly parts instead (stack top + repeated extenders +
    // bottom). `None` (no MATH table / no assembly / base-14) leaves the
    // discrete/base path below byte-identical.
    let discrete_covers = variant
        .map(|v| (v.height + v.depth).0 >= target.0)
        .unwrap_or(false);
    if !discrete_covers {
        if let Some(parts) = interp.metrics.math_vertical_assembly(font, c, size, target) {
            if !parts.is_empty() {
                // Horizontal advance of the delimiter column: the largest
                // discrete variant's own hmtx advance when we have one (the
                // parts share the same nominal delimiter width), else the base
                // glyph's advance.
                let hadv = match variant {
                    Some(v) => v.advance,
                    None => interp
                        .metrics
                        .advance(font, c, size)
                        .unwrap_or(Length::ZERO),
                };
                // Total vertical extent of the stacked assembly (local, from
                // the bottom part's baseline at 0), then center it on the math
                // axis exactly like the discrete path centers a variant's ink.
                let total = parts
                    .last()
                    .map(|(_, dy, adv)| *dy + *adv)
                    .unwrap_or(Length::ZERO);
                let base_off = axis - total * 0.5;
                for (i, (gid, dy_local, adv)) in parts.iter().enumerate() {
                    out.push(MathGlyph {
                        info: HorzStringInfo {
                            font,
                            size,
                            rising: Length::ZERO,
                            color: ctx.text_color,
                        },
                        text: c.to_string(),
                        gid: Some(*gid),
                        dx: *x,
                        dy: base_off + *dy_local,
                        // Only the first part carries the column's horizontal
                        // width (all parts are stacked in the SAME x column);
                        // its baseline-relative extent is the part's vertical
                        // advance (up), so `glyphs_extent` folds the whole
                        // stacked column into the box's height/depth.
                        width: if i == 0 { hadv } else { Length::ZERO },
                        height: *adv,
                        depth: Length::ZERO,
                    });
                }
                *x += hadv;
                return Ok(());
            }
        }
    }
    match variant {
        Some(v) => {
            let dy = axis - (v.height - v.depth) * 0.5;
            out.push(MathGlyph {
                info: HorzStringInfo {
                    font,
                    size,
                    rising: Length::ZERO,
                    color: ctx.text_color,
                },
                text: c.to_string(),
                gid: Some(v.gid),
                dx: *x,
                dy,
                width: v.advance,
                height: v.height,
                depth: v.depth,
            });
            *x += v.advance;
            Ok(())
        }
        None => push_char_glyph(interp, ctx, c, size, out, x),
    }
}

/// Lay out `elems` in isolation (its own local `x` starting at 0, its own
/// spacing state) at `size` — the shape a `Sup`/`Sub`/`Primes` script needs
/// before its glyphs get re-anchored onto the base's running `x` and
/// shifted by the caller. `size` is the caller's `MathC::script_scale`-
/// derived script size (real MATH-table ratio when available, `SCRIPT_SCALE`
/// otherwise). Returns the glyphs (still at local coordinates) and
/// the script's total width.
fn layout_script(
    interp: &mut Interp,
    ctx: &Context,
    elems: &[MathElem],
    size: Length,
) -> Result<(Vec<MathGlyph>, Length), EvalError> {
    let mut glyphs = Vec::new();
    let mut x = Length::ZERO;
    let mut last_kind: Option<MathKind> = None;
    for e in elems {
        layout_math_elem(interp, ctx, e, size, &mut glyphs, &mut x, &mut last_kind)?;
    }
    Ok((glyphs, x))
}

/// Re-anchor an isolated script's glyphs (`layout_script`'s output) onto the
/// base's running `*x`, adding `dy_shift` to every glyph's vertical offset —
/// `dy_shift > 0` raises (superscript), `< 0` lowers (subscript). Advances
/// `*x` past the whole script.
fn place_script(
    out: &mut Vec<MathGlyph>,
    x: &mut Length,
    script_glyphs: Vec<MathGlyph>,
    script_width: Length,
    dy_shift: Length,
) {
    let base_x = *x;
    for mut g in script_glyphs {
        g.dx = base_x + g.dx;
        g.dy = g.dy + dy_shift;
        out.push(g);
    }
    *x = base_x + script_width;
}

/// The recursive core of `read_math`: lays out one `MathElem` into `out`,
/// advancing `*x` and threading `*last_kind` (the trailing `MathKind` of
/// whatever was laid out immediately before, for `space_before`) through
/// siblings — the analog of `convert_to_low` + `horz_of_low_math`
/// (`math.ml:753`/`:1016`), fused and with fixed constants.
fn layout_math_elem(
    interp: &mut Interp,
    ctx: &Context,
    elem: &MathElem,
    size: Length,
    out: &mut Vec<MathGlyph>,
    x: &mut Length,
    last_kind: &mut Option<MathKind>,
) -> Result<(), EvalError> {
    match elem {
        MathElem::Chars(s) => {
            for c in s.chars() {
                let kind = ascii_math_kind(c);
                if let Some(prev) = *last_kind {
                    *x += space_before(prev, kind, math_in_script(ctx, size), size);
                }
                push_char_glyph(interp, ctx, c, size, out, x)?;
                *last_kind = Some(kind);
            }
            Ok(())
        }
        MathElem::Group(elems) => {
            for e in elems {
                layout_math_elem(interp, ctx, e, size, out, x, last_kind)?;
            }
            Ok(())
        }
        MathElem::Sup(base, script) => {
            let base_start = out.len();
            layout_math_elem(interp, ctx, base, size, out, x, last_kind)?;
            let mc = MathC::of(interp, ctx);
            let script_size = ctx.font_size * mc.script_scale();
            let (h_base, _) = glyphs_extent(&out[base_start..]);
            let (script_glyphs, script_width) = layout_script(interp, ctx, script, script_size)?;
            let (_, d_sup) = glyphs_extent(&script_glyphs);
            let sup_shift = mc.sup_shift_clamped(ctx.font_size, h_base, d_sup);
            let kern = superscript_kern(
                interp,
                ctx,
                size,
                script_size,
                &out[base_start..],
                &script_glyphs,
                sup_shift,
                h_base,
                d_sup,
            );
            *x += kern;
            place_script(out, x, script_glyphs, script_width, sup_shift);
            Ok(())
        }
        MathElem::Sub(base, script) => {
            let base_start = out.len();
            layout_math_elem(interp, ctx, base, size, out, x, last_kind)?;
            let mc = MathC::of(interp, ctx);
            let script_size = ctx.font_size * mc.script_scale();
            let (_, d_base) = glyphs_extent(&out[base_start..]);
            let (script_glyphs, script_width) = layout_script(interp, ctx, script, script_size)?;
            let (h_sub, _) = glyphs_extent(&script_glyphs);
            let sub_shift = mc.sub_shift_clamped(ctx.font_size, d_base, h_sub);
            place_script(out, x, script_glyphs, script_width, -sub_shift);
            Ok(())
        }
        MathElem::Primes(base, n) => {
            let base_start = out.len();
            layout_math_elem(interp, ctx, base, size, out, x, last_kind)?;
            let mc = MathC::of(interp, ctx);
            let script_size = ctx.font_size * mc.script_scale();
            let (h_base, _) = glyphs_extent(&out[base_start..]);
            // Upstream desugars primes to exactly this: a superscript of `n`
            // U+2032 `′` chars (`parser.mly:1082`).
            let primes = vec![MathElem::Chars("\u{2032}".repeat(*n))];
            let (script_glyphs, script_width) = layout_script(interp, ctx, &primes, script_size)?;
            let (_, d_sup) = glyphs_extent(&script_glyphs);
            let sup_shift = mc.sup_shift_clamped(ctx.font_size, h_base, d_sup);
            let kern = superscript_kern(
                interp,
                ctx,
                size,
                script_size,
                &out[base_start..],
                &script_glyphs,
                sup_shift,
                h_base,
                d_sup,
            );
            *x += kern;
            place_script(out, x, script_glyphs, script_width, sup_shift);
            Ok(())
        }
        MathElem::Cmd { name, span, .. } => Err(EvalError {
            span: Some(*span),
            msg: format!("math command `{name}` needs the math package (phase 7 roadmap A)"),
        }),
        MathElem::Embed { span, .. } => Err(EvalError {
            span: Some(*span),
            msg: "embedding a program value in math needs the math package \
                  (phase 7 roadmap A)"
                .into(),
        }),
    }
}

/// Walk an elaborated `${…}` tree (`read_inline`'s `EmbedMath` arm) into one
/// `PureHorzBox::Math`, measuring every glyph through `interp.metrics` at
/// `ctx.font`/`ctx.font_size` — the same `FontMetrics` seam `text_to_boxes`
/// uses. Box-model rationale: a math run carries its own pre-shifted
/// sub-glyphs, since the line model has no per-box vertical slot.
pub fn read_math(
    interp: &mut Interp,
    ctx: &Context,
    elems: &[MathElem],
) -> Result<PureHorzBox, EvalError> {
    let mut glyphs: Vec<MathGlyph> = Vec::new();
    let mut x = Length::ZERO;
    let mut last_kind: Option<MathKind> = None;
    for e in elems {
        layout_math_elem(
            interp,
            ctx,
            e,
            ctx.font_size,
            &mut glyphs,
            &mut x,
            &mut last_kind,
        )?;
    }
    let width = x;
    let mut height = Length::ZERO;
    let mut depth = Length::ZERO;
    for g in &glyphs {
        height = height.max(g.dy + g.height);
        depth = depth.max(g.depth - g.dy);
    }
    Ok(PureHorzBox::Math {
        width,
        height,
        depth,
        glyphs,
        rules: Vec::new(),
    })
}

// ---- primitive bodies ----------------------------------------------------------

fn prim_read_inline(interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
    let it = args.pop().unwrap();
    let ctx = as_context(args.pop().unwrap())?;
    let (elems, env) = as_inline_text(it)?;
    Ok(Value::InlineBoxes(read_inline(interp, &ctx, &elems, &env)?))
}

fn prim_read_block(interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
    let bt = args.pop().unwrap();
    let ctx = as_context(args.pop().unwrap())?;
    let (elems, env) = as_block_text(bt)?;
    Ok(Value::BlockBoxes(read_block(interp, &ctx, &elems, &env)?))
}

/// `line-break : bool -> bool -> context -> inline-boxes -> block-boxes`
/// (vminst.ml `BackendLineBreaking`). The two leading bools tell the real
/// line breaker whether the paragraph's top/bottom edge may break across a
/// page; this port's `break_into_lines` does not yet model breakability
/// at all, so both are accepted (to keep the arity/signature faithful to
/// v0.0.6) and ignored for now.
///
/// This is upstream's `form_paragraph` seam — every stdlib caller
/// (`form-paragraph = line-break true true`, and every direct `line-break _
/// _ (ctx |> set-paragraph-margin …)` call for headings/itemize/footnotes)
/// relies on `line-break` itself to apply
/// `ctx.paragraph_top`/`paragraph_bottom` around the formed lines,
/// unconditionally of the two breakability bools (those only ever gate
/// page-break eligibility upstream, never whether the margin applies).
/// Prepending/appending `VertBox::Skip` here is a no-op in extent for a
/// caller that already zeroed the margin (e.g. `footnote-scheme.satyh`'s
/// `set-paragraph-margin 0pt 0pt`), and the leading skip specifically is
/// further discarded by `chop_page` when it lands at the very top of a
/// page/column (see that function's `pending_skip` handling) — mirroring
/// upstream's page-top glue suppression so a page's first paragraph does not
/// get a spurious gap above it.
fn prim_line_break(interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
    let ib = as_inline_boxes(args.pop().unwrap())?;
    let ctx = as_context(args.pop().unwrap())?;
    let _is_breakable_bottom = as_bool(args.pop().unwrap())?;
    let _is_breakable_top = as_bool(args.pop().unwrap())?;
    let lines = break_into_lines(&ctx, ib);
    // No lines were actually formed (empty inline content, `break_into_lines`'s
    // own `n == 0` early return) — don't manufacture a margin around nothing.
    let mut out = Vec::with_capacity(lines.len() + 2);
    if !lines.is_empty() {
        // `min_first_line_ascender` (9pt, `primitives.cppo.ml:516`) is folded
        // into the paragraph's OWN top margin, exactly as `lineBreak.ml:855-857`
        // does — `margin_top = paragraph_margin_top + max(0, 9pt - hgt)` over
        // the FIRST formed line's height. That padded value is what
        // `pageBreak.ml`'s `squash_margins` (`:596-601`) then max-collapses
        // against the previous block's bottom margin, so a larger predecessor
        // ABSORBS the pad instead of stacking it on top. Applying the floor
        // downstream to the line HEIGHT, after the collapse, is a different
        // function: it over-spaced every block whose predecessor had the larger
        // bottom margin — 5pt at every stdjabook section heading, whose 4pt
        // rule lines are shorter than the floor.
        //
        // The BOTTOM margin takes no pad: `min_last_descender` is assigned at
        // `lineBreak.ml:1144` and never read.
        let first_height = lines
            .iter()
            .find_map(|vb| match vb {
                VertBox::Line { height, .. } => Some(*height),
                _ => None,
            })
            .unwrap_or(Length::ZERO);
        let pad = (MIN_FIRST_ASCENDER - first_height).max(Length::ZERO);
        out.push(VertBox::ParagTop(ctx.paragraph_top + pad));
        out.extend(lines);
        out.push(VertBox::Skip(ctx.paragraph_bottom));
    }
    for vb in &mut out {
        if let VertBox::Line { contents, .. } = vb {
            resolve_outer_graphics_in_contents(interp, contents)?;
        }
    }
    Ok(Value::BlockBoxes(out))
}

/// Look up `field` in a scheme record's fields, erroring with the
/// available-fields hint (mirrors `evalUtil.ml`'s `report_bug_value` arms
/// for a missing/mistyped scheme field) if it's absent.
fn record_field(
    fields: &BTreeMap<String, Value>,
    record_name: &str,
    field: &str,
) -> Result<Value, EvalError> {
    match fields.get(field) {
        Some(v) => Ok(v.clone()),
        None => eval_error(format!(
            "{record_name} record is missing field '{field}' (available fields: {})",
            available_fields(fields)
        )),
    }
}

/// Extract `(text-origin, text-height)` from a `page-content-scheme`
/// record (`{| text-origin : point; text-height : length |}`) — the direct
/// port of `make_page_content_scheme_func`'s field pull (`evalUtil.ml:558-
/// 565`).
fn read_content_scheme(v: Value) -> Result<(Point, Length), EvalError> {
    let fields = match v {
        Value::Record(m) => m,
        other => {
            return eval_error(format!(
                "a page-content-scheme closure must return a record, got {}",
                other.type_name()
            ))
        }
    };
    let origin = as_point(record_field(&fields, "page-content-scheme", "text-origin")?)?;
    let height = as_length(record_field(&fields, "page-content-scheme", "text-height")?)?;
    Ok((origin, height))
}

/// Extract `(header-origin, header-content, footer-origin, footer-content)`
/// from a `page-parts` record — the direct port of
/// `make_page_parts_scheme_func`'s field pull (`evalUtil.ml:576-595`).
fn read_parts_scheme(v: Value) -> Result<(Point, Vec<VertBox>, Point, Vec<VertBox>), EvalError> {
    let fields = match v {
        Value::Record(m) => m,
        other => {
            return eval_error(format!(
                "a page-parts closure must return a record, got {}",
                other.type_name()
            ))
        }
    };
    let header_origin = as_point(record_field(&fields, "page-parts", "header-origin")?)?;
    let header_content = as_block_boxes(record_field(&fields, "page-parts", "header-content")?)?;
    let footer_origin = as_point(record_field(&fields, "page-parts", "footer-origin")?)?;
    let footer_content = as_block_boxes(record_field(&fields, "page-parts", "footer-content")?)?;
    Ok((header_origin, header_content, footer_origin, footer_content))
}

/// Upstream's `--page-number-limit` default (main.ml:1029). v0.0.6 guards
/// only the multicolumn loop (pageBreak.ml:765, `PageNumberLimitExceeded`);
/// the port guards the shared loop unconditionally — a hook-less run is
/// already bounded by the vbox count (`chop_page`'s progress guarantee), so
/// the guard can only fire when column hooks inject content, exactly the
/// case upstream added it for.
const PAGE_NUMBER_LIMIT: i64 = 10_000;

/// The real 4-arg `page-break`, v0.0.6 arm — upstream `BCDocument(pagesize,
/// SingleColumn, (fun () -> []), (fun () -> []), …)` (vminst.ml:1039): one
/// zero-shift column, no hooks. Forked from the v0.1 arm below ONLY in its
/// first-argument extraction (`as_page` vs `as_page_v01`) — deliberately two
/// separate functions per tag rather than one branching on a `version`
/// parameter, so that a "shared" function is genuinely shared code.
/// `page_break_core` below IS that shared code.
fn prim_page_break_v006(interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
    let bb = as_block_boxes(args.pop().unwrap())?;
    let pagepartsf = args.pop().unwrap();
    let pagecontf = args.pop().unwrap();
    let paper = as_page(args.pop().unwrap())?;
    page_break_core(
        interp,
        paper,
        vec![Length::ZERO],
        None,
        None,
        pagecontf,
        pagepartsf,
        bb,
    )
}

/// v0.1 arm of `page-break`. Identical to `prim_page_break_v006` above
/// except `as_page_v01` in place of `as_page`; everything downstream
/// (`page_break_core`, `chop_page`, `place_block_at`, `DocumentValue`
/// assembly) is the SAME shared code both arms call, unedited by this fork.
fn prim_page_break_v01(interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
    let bb = as_block_boxes(args.pop().unwrap())?;
    let pagepartsf = args.pop().unwrap();
    let pagecontf = args.pop().unwrap();
    let paper = as_page_v01(args.pop().unwrap())?;
    page_break_core(
        interp,
        paper,
        vec![Length::ZERO],
        None,
        None,
        pagecontf,
        pagepartsf,
        bb,
    )
}

/// `page-break-two-column : page -> length -> (unit -> block-boxes) ->
/// (pbinfo -> page-content-scheme) -> (pbinfo -> page-parts) ->
/// block-boxes -> document` (vminst.ml:1041 `BackendPageBreakingTwoColumn`),
/// v0.0.6 arm — upstream builds `MultiColumn([origin_shift])` with the
/// user's column hook and a trivial column-end hook (vminst.ml:1062); the
/// `length` is the x-shift of the SECOND column's origin. See
/// `prim_page_break_v006`'s doc comment for the fork rationale.
fn prim_page_break_two_column_v006(
    interp: &mut Interp,
    mut args: Vec<Value>,
) -> Result<Value, EvalError> {
    let bb = as_block_boxes(args.pop().unwrap())?;
    let pagepartsf = args.pop().unwrap();
    let pagecontf = args.pop().unwrap();
    let columnhookf = args.pop().unwrap();
    let origin_shift = as_length(args.pop().unwrap())?;
    let paper = as_page(args.pop().unwrap())?;
    page_break_core(
        interp,
        paper,
        vec![Length::ZERO, origin_shift],
        Some(columnhookf),
        None,
        pagecontf,
        pagepartsf,
        bb,
    )
}

/// v0.1 arm of `page-break-two-column`, using `as_page_v01` in place of
/// `as_page`.
fn prim_page_break_two_column_v01(
    interp: &mut Interp,
    mut args: Vec<Value>,
) -> Result<Value, EvalError> {
    let bb = as_block_boxes(args.pop().unwrap())?;
    let pagepartsf = args.pop().unwrap();
    let pagecontf = args.pop().unwrap();
    let columnhookf = args.pop().unwrap();
    let origin_shift = as_length(args.pop().unwrap())?;
    let paper = as_page_v01(args.pop().unwrap())?;
    page_break_core(
        interp,
        paper,
        vec![Length::ZERO, origin_shift],
        Some(columnhookf),
        None,
        pagecontf,
        pagepartsf,
        bb,
    )
}

/// `page-break-multicolumn : page -> length list -> (unit -> block-boxes)
/// -> (unit -> block-boxes) -> (pbinfo -> page-content-scheme) -> (pbinfo
/// -> page-parts) -> block-boxes -> document` (vminst.ml:1065
/// `BackendPageBreakingMultiColumn`), v0.0.6 arm — FAITHFUL: the shift list
/// gives columns 2..N's x-origin shifts; upstream prepends `Length.zero` for
/// column 1 (pageBreak.ml:762), so `stdjareport.satyh:403`'s `[]` is a
/// one-column layout whose hooks still fire per column/page.
fn prim_page_break_multicolumn_v006(
    interp: &mut Interp,
    mut args: Vec<Value>,
) -> Result<Value, EvalError> {
    let bb = as_block_boxes(args.pop().unwrap())?;
    let pagepartsf = args.pop().unwrap();
    let pagecontf = args.pop().unwrap();
    let columnendhookf = args.pop().unwrap();
    let columnhookf = args.pop().unwrap();
    let mut origin_shifts = vec![Length::ZERO];
    for v in as_list(args.pop().unwrap())? {
        origin_shifts.push(as_length(v)?);
    }
    let paper = as_page(args.pop().unwrap())?;
    page_break_core(
        interp,
        paper,
        origin_shifts,
        Some(columnhookf),
        Some(columnendhookf),
        pagecontf,
        pagepartsf,
        bb,
    )
}

/// v0.1 arm of `page-break-multicolumn`, using `as_page_v01` in place of
/// `as_page`.
fn prim_page_break_multicolumn_v01(
    interp: &mut Interp,
    mut args: Vec<Value>,
) -> Result<Value, EvalError> {
    let bb = as_block_boxes(args.pop().unwrap())?;
    let pagepartsf = args.pop().unwrap();
    let pagecontf = args.pop().unwrap();
    let columnendhookf = args.pop().unwrap();
    let columnhookf = args.pop().unwrap();
    let mut origin_shifts = vec![Length::ZERO];
    for v in as_list(args.pop().unwrap())? {
        origin_shifts.push(as_length(v)?);
    }
    let paper = as_page_v01(args.pop().unwrap())?;
    page_break_core(
        interp,
        paper,
        origin_shifts,
        Some(columnhookf),
        Some(columnendhookf),
        pagecontf,
        pagepartsf,
        bb,
    )
}

/// Apply a `unit -> block-boxes` column hook and PREPEND its result to the
/// remaining content — the port of `chop_single_column_with_insertion`
/// (pageBreak.ml:699-702; the upstream `normalize` is a no-op here because
/// block-boxes are already solid `Vec<VertBox>`).
fn apply_column_hook(
    interp: &mut Interp,
    hook: &Value,
    remaining: &mut Vec<VertBox>,
) -> Result<(), EvalError> {
    let inserted = as_block_boxes(interp.apply(hook.clone(), Value::Unit)?)?;
    remaining.splice(0..0, inserted);
    Ok(())
}

/// The shared per-page loop backing `page-break`, `page-break-two-column`,
/// and `page-break-multicolumn` — the port of `PageBreak.main` /
/// `main_multicolumn` (pageBreak.ml:705-781). Lang-side because it is the
/// one place that legally holds `&mut Interp` to apply the scheme/hook
/// closures (the `fire_hooks` seam). `origin_shifts` is the FULL column
/// list (leading zero included by the callers); `None` hooks are upstream's
/// `(fun () -> [])`.
///
/// Per page: apply `pagecontf` once; per column: fire `columnhookf`
/// (start of EVERY column, pageBreak.ml:700), chop one column at
/// `(x0 + shift, y0)` (footnotes bottom-place per column inside
/// `chop_page`), stop early when content runs out; then fire
/// `columnendhookf` exactly once (both upstream arms — exhausted
/// mid-columns `:751` and shifts-exhausted `:736` — reduce to "prepend its
/// output to the remainder"); then apply `pagepartsf` and place the parts.
#[allow(clippy::too_many_arguments)]
fn page_break_core(
    interp: &mut Interp,
    paper: PaperSize,
    origin_shifts: Vec<Length>,
    columnhookf: Option<Value>,
    columnendhookf: Option<Value>,
    pagecontf: Value,
    pagepartsf: Value,
    bb: Vec<VertBox>,
) -> Result<Value, EvalError> {
    let (paper_w, paper_h) = paper.dims();

    // Capture the flat pre-page-break `Vec<VertBox>` BEFORE
    // `chop_page`/`apply_column_hook` below start draining/mutating
    // `remaining` — this clone is the document's natural linear flow exactly
    // as `bb` arrived here (no pages, no injected headers/footers, no
    // column-hook-inserted content). Unconditional (not gated on which
    // output format was requested — see `DocumentValue::reflow_source`'s doc
    // comment): PDF and the faithful HTML backend never read the field, so
    // this costs them only the clone itself, never a byte of their rendered
    // output.
    let reflow_source = bb.clone();

    let mut remaining = bb;
    let mut pages: Vec<Page> = Vec::new();
    let mut pageno: i64 = 1;
    loop {
        if pageno > PAGE_NUMBER_LIMIT {
            return eval_error(format!(
                "page number limit exceeded ({PAGE_NUMBER_LIMIT}); a column hook keeps injecting content"
            ));
        }
        let mut pb_fields = BTreeMap::new();
        pb_fields.insert("page-number".to_string(), Value::Int(pageno));
        let pbinfo = Value::Record(pb_fields);

        // ---- content scheme: this page's text area (applied ONCE per page, shared by all its columns — pageBreak.ml:769) ----
        let sch = interp.apply(pagecontf.clone(), pbinfo.clone())?;
        let (origin, height) = read_content_scheme(sch)?;
        let (x0, y0) = origin;

        // ---- columns ----
        let mut lines = Vec::new();
        for shift in &origin_shifts {
            if let Some(hook) = &columnhookf {
                apply_column_hook(interp, hook, &mut remaining)?;
            }
            lines.extend(chop_page((x0 + *shift, y0), height, &mut remaining));
            if remaining.is_empty() {
                break; // content exhausted: remaining columns are skipped
            }
        }
        if let Some(hook) = &columnendhookf {
            apply_column_hook(interp, hook, &mut remaining)?;
        }

        // A trailing pure-skip/glue (e.g. the last block's `paragraph_bottom`)
        // can roll past the previous page's bottom into a final `chop_page`
        // that places NO real line — `chop_page` discards it as a page-top
        // skip, leaving an empty body. SATySFi never emits such a trailing
        // blank page (glue at the end of the vertical list is dropped), so when
        // the body is empty AND content is now exhausted, stop before turning
        // that leftover into a spurious blank page (header/footer included).
        if remaining.is_empty() && !lines.iter().any(|l| placed_line_extent(l).is_some()) {
            break;
        }

        // ---- parts scheme: this page's header + footer ----
        // Everything placed so far is body/column content; the header and
        // footer append AFTER it (see `Page::body_lines`).
        let body_lines = lines.len();
        let parts = interp.apply(pagepartsf.clone(), pbinfo)?;
        let (header_origin, header_content, footer_origin, footer_content) =
            read_parts_scheme(parts)?;
        lines.extend(place_block_at(header_origin, header_content));
        lines.extend(place_block_at(footer_origin, footer_content));

        pages.push(Page { lines, body_lines });
        if remaining.is_empty() {
            break;
        }
        pageno += 1;
    }

    // Every image `load-image` decoded while evaluating this document (see
    // `Interp::images`'s doc comment) rides along in the packaged
    // `DocumentValue` so the PDF writer can emit XObjects for the ones
    // actually placed on a page.
    let images = interp.images.clone();
    Ok(Value::Document(Rc::new(DocumentValue {
        geometry: PageGeometry::for_paper(paper_w, paper_h),
        pages,
        images,
        // Filled in by `compile_document_cst_with_trials` once `fire_hooks`
        // has walked the final trial's placed geometry (see
        // `DocumentValue::extras`'s doc comment) — hooks/decos haven't fired
        // yet at this point in `page-break`'s own evaluation.
        extras: DocExtras::default(),
        reflow_source: Some(reflow_source),
        // Filled in alongside `extras` once `fire_hooks` has run — see
        // `DocumentValue::reflow_links`'s doc comment.
        reflow_links: Vec::new(),
        reflow_dests: Vec::new(),
    })))
}

// ---- int arithmetic -------------------------------------------------------

// Wrapping arithmetic to match OCaml's native `int` (SATySFi's `int` is an
// OCaml int, which wraps on overflow) — and, decisively, so a debug build does
// not panic on the large intermediate products base's float bit-twiddling
// (`exp2i`, `ldexp`, `frexp`) computes.
binop_prim!(prim_int_add, as_int, Int, |a, b| a.wrapping_add(b));
binop_prim!(prim_int_sub, as_int, Int, |a, b| a.wrapping_sub(b));
binop_prim!(prim_int_mul, as_int, Int, |a, b| a.wrapping_mul(b));

// OCaml catches `Division_by_zero` and reports `"division by zero"`; `mod`
// (see `Mod` in vminst.ml) shares that behavior.
binop_prim_try!(prim_int_div, as_int, |a, b| if b == 0 {
    eval_error("division by zero")
} else {
    Ok(Value::Int(a / b))
});
binop_prim_try!(prim_int_mod, as_int, |a, b| if b == 0 {
    eval_error("division by zero")
} else {
    Ok(Value::Int(a % b))
});

// ---- int comparisons -------------------------------------------------------

cmp_prim!(prim_int_eq, as_int, |a, b| a == b);
cmp_prim!(prim_int_ne, as_int, |a, b| a != b);
cmp_prim!(prim_int_lt, as_int, |a, b| a < b);
cmp_prim!(prim_int_gt, as_int, |a, b| a > b);
cmp_prim!(prim_int_le, as_int, |a, b| a <= b);
cmp_prim!(prim_int_ge, as_int, |a, b| a >= b);

// ---- 0.1 bitwise ops -------------------------------------------------------
//
// `band`/`bor`/`bxor` mirror OCaml's `land`/`lor`/`lxor`; `bnot` mirrors
// `lnot` (bitwise complement). DOCUMENTED DEVIATION: this port's `int` is a
// 64-bit two's-complement `i64`, vs upstream's 63-bit boxed OCaml `int` — a
// value that actually uses bit 62 (the port's sign-adjacent bit upstream
// doesn't have) will complement/shift differently than upstream on that
// platform; upstream's own results are themselves platform-width-dependent
// there, and no bundled package relies on it.
binop_prim!(prim_band, as_int, Int, |a, b| a & b);
binop_prim!(prim_bor, as_int, Int, |a, b| a | b);
binop_prim!(prim_bxor, as_int, Int, |a, b| a ^ b);
unop_prim!(prim_bnot, as_int, Int, |a| !a);

// `<<`/`>>` (dev-0-1-0 vminst.ml :2495/:2477): logical shifts (OCaml's
// `lsl`/`lsr`, NOT arithmetic — `>>` on a negative int does NOT sign-extend,
// see the `-16 >> 2` witness in the test suite), with upstream's exact
// dynamic-error message when the shift amount is out of `0..=63`.
binop_prim_try!(
    prim_bit_shift_left,
    as_int,
    |a, b| if !(0..=63).contains(&b) {
        eval_error("Bit offset out of bounds for '<<'")
    } else {
        Ok(Value::Int(((a as u64) << b) as i64))
    }
);
binop_prim_try!(
    prim_bit_shift_right,
    as_int,
    |a, b| if !(0..=63).contains(&b) {
        eval_error("Bit offset out of bounds for '>>'")
    } else {
        Ok(Value::Int(((a as u64) >> b) as i64))
    }
);

// ---- bool -------------------------------------------------------------------

// Strict (both arguments already evaluated by the caller before these natives
// run): real SATySFi source-level `&&`/`||` short-circuit via elaboration into
// `if`, which is out of scope here.
binop_prim!(prim_bool_and, as_bool, Bool, |a, b| a && b);
binop_prim!(prim_bool_or, as_bool, Bool, |a, b| a || b);
unop_prim!(prim_bool_not, as_bool, Bool, |a| !a);

// ---- float --------------------------------------------------------------------

binop_prim!(prim_float_add, as_float, Float, |a, b| a + b);
binop_prim!(prim_float_sub, as_float, Float, |a, b| a - b);
binop_prim!(prim_float_mul, as_float, Float, |a, b| a * b);
binop_prim!(prim_float_div, as_float, Float, |a, b| a / b);
unop_prim!(prim_float_of_int, as_int, Float, |n| n as f64);

// `PrimitiveRound` in vminst.ml is, despite the name, `int_of_float`
// (truncation toward zero), not rounding to nearest.
unop_prim!(prim_round, as_float, Int, |x| x as i64);

// ---- 0.1 float comparisons (saphe-split vminst.ml:2679-2740) ----
cmp_prim!(prim_float_gt, as_float, |a, b| a > b);
cmp_prim!(prim_float_lt, as_float, |a, b| a < b);
cmp_prim!(prim_float_ge, as_float, |a, b| a >= b);
cmp_prim!(prim_float_le, as_float, |a, b| a <= b);

// ---- length ---------------------------------------------------------------------

binop_prim!(prim_length_add, as_length, Length, |a, b| a + b);
binop_prim!(prim_length_sub, as_length, Length, |a, b| a - b);
binop_prim!(prim_length_scale, (as_length, as_float), Length, |a, b| a
    * b);
binop_prim!(prim_length_div, as_length, Float, |a, b| a / b);
cmp_prim!(prim_length_lt, as_length, |a, b| a < b);

// `LengthGreaterThan` in vminst.ml is implemented as `len2 <% len1`, i.e.
// `a >' b` iff `b <' a` — the same ordering, just flipped operands.
cmp_prim!(prim_length_gt, as_length, |a, b| b < a);

// ---- string -----------------------------------------------------------------------

binop_prim!(prim_string_concat, as_str, Str, |a, b| a + &b);
unop_prim!(prim_arabic, as_int, Str, |n| n.to_string());
cmp_prim!(prim_string_same, as_str, |a, b| a == b);

// ---- list -----------------------------------------------------------------

/// `x :: xs` — prepend `x` onto the list `xs`.
fn prim_list_cons(_interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
    let tail = args.pop().unwrap();
    let head = args.pop().unwrap();
    let mut list = match tail {
        Value::List(v) => v,
        other => return eval_error(format!("expected list, got {}", other.type_name())),
    };
    list.insert(0, head);
    Ok(Value::List(list))
}

// ---- mutable-cell dereference ----------------------------------------------

/// `!` — read the current contents of a mutable cell (see the `prims!`
/// registration above for how this differs structurally, not semantically,
/// from v0.0.6's `Dereference`/`Location` handling).
fn prim_deref(_interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
    let v = args.pop().unwrap();
    match v {
        Value::Ref(cell) => Ok(cell.borrow().clone()),
        other => eval_error(format!(
            "expected a mutable cell for '!', got {}",
            other.type_name()
        )),
    }
}

// ---- string, continued -----------------------------------------------------

// `string-length : string -> int` (vminst.ml `PrimitiveStringLength`) —
// counts Unicode scalar values (`BatUTF8.length`), not UTF-8 bytes.
unop_prim!(prim_string_length, as_str, Int, |s| s.chars().count()
    as i64);

/// `string-sub : string -> int -> int -> string` (vminst.ml
/// `PrimitiveStringSub`) — a substring addressed by Unicode-scalar-value
/// offset/width (`BatUTF8.sub`), not byte offset. Upstream raises a dynamic
/// error ("illegal index for string-sub") on an out-of-range index; we do
/// the same.
fn prim_string_sub(_interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
    let wid = as_int(args.pop().unwrap())?;
    let pos = as_int(args.pop().unwrap())?;
    let s = as_str(args.pop().unwrap())?;
    if wid < 0 || pos < 0 {
        return eval_error("illegal index for string-sub");
    }
    let chars: Vec<char> = s.chars().collect();
    let pos = pos as usize;
    let wid = wid as usize;
    match pos.checked_add(wid) {
        Some(end) if end <= chars.len() => Ok(Value::Str(chars[pos..end].iter().collect())),
        _ => eval_error("illegal index for string-sub"),
    }
}

// `string-explode : string -> int list` (vminst.ml `PrimitiveStringExplode`)
// — the string's Unicode scalar values (code points) in order, not its bytes.
unop_prim!(prim_string_explode, as_str, List, |s| s
    .chars()
    .map(|c| Value::Int(c as i64))
    .collect());

fn prim_embed_string(_interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
    let s = as_str(args.pop().unwrap())?;
    Ok(Value::InlineText {
        elems: Rc::new(vec![IText::Text(s)]),
        env: Env::root(),
    })
}

// ---- context ops ------------------------------------------------------------

/// `set-font-size : length -> context -> context` (vminst.ml
/// `PrimitiveSetFontSize`).
fn prim_set_font_size(_interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
    let ctx = as_context(args.pop().unwrap())?;
    let size = as_length(args.pop().unwrap())?;
    Ok(Value::Context(Box::new(Context {
        font_size: size,
        ..ctx
    })))
}

/// `get-font-size : context -> length` (vminst.ml `PrimitiveGetFontSize`).
fn prim_get_font_size(_interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
    let ctx = as_context(args.pop().unwrap())?;
    Ok(Value::Length(ctx.font_size))
}

/// `set-leading : length -> context -> context` (vminst.ml
/// `PrimitiveSetLeading`; see the `prims!` table comment for why this is
/// the baseline-distance setter and not `set-min-gap-of-lines`).
fn prim_set_leading(_interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
    let ctx = as_context(args.pop().unwrap())?;
    let leading = as_length(args.pop().unwrap())?;
    Ok(Value::Context(Box::new(Context { leading, ..ctx })))
}

/// `set-paragraph-margin : length -> length -> context -> context`
/// (vminst.ml `PrimitiveSetParagraphMargin`).
fn prim_set_paragraph_margin(
    _interp: &mut Interp,
    mut args: Vec<Value>,
) -> Result<Value, EvalError> {
    let ctx = as_context(args.pop().unwrap())?;
    let bottom = as_length(args.pop().unwrap())?;
    let top = as_length(args.pop().unwrap())?;
    Ok(Value::Context(Box::new(Context {
        paragraph_top: top,
        paragraph_bottom: bottom,
        ..ctx
    })))
}

/// `get-text-width : context -> length` (vminst.ml `PrimitiveGetTextWidth`).
fn prim_get_text_width(_interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
    let ctx = as_context(args.pop().unwrap())?;
    Ok(Value::Length(ctx.paragraph_width))
}

/// `get-initial-context : length -> [math] inline-cmd -> context`
/// (vminst.ml `PrimitiveGetInitialContext`) — the second argument is the
/// default math command a bare `${…}` in inline text dispatches to (v0.0.6
/// `context_main.math_command`); interned via
/// `Interp::register_math_command`, carried as `Context::math_command`.
fn prim_get_initial_context(interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
    let cmd = args.pop().unwrap();
    let width = as_length(args.pop().unwrap())?;
    let mut ctx = Context::initial(width);
    ctx.math_command = Some(interp.register_math_command(cmd));
    // Overlay the configured `default-font.satysfi-hash` `scripts`
    // block, if any, so a bare document with a configured font root renders
    // CJK/etc. with zero `set-font` calls (`interp.metrics.
    // default_script_font` is `None` for every script on a provider with no
    // such config — `Base14Metrics` and a bare `TtfFontStore::load` both —
    // so this loop is a no-op there).
    for (idx, script) in [
        Script::HanIdeographic,
        Script::Kana,
        Script::Latin,
        Script::OtherScript,
    ]
    .into_iter()
    .enumerate()
    {
        if let Some((font, ratio, rising)) = interp.metrics.default_script_font(script) {
            ctx.font_scheme[idx] = ScriptFont {
                font,
                ratio,
                rising,
            };
            if script == Script::Latin {
                ctx.font = font;
            }
        }
    }
    // Overlay the configured `default-font.satysfi-hash` `"math"`
    // abbrev, if any, so a document with a bundled MATH-table font renders
    // real cramped/uncramped math metrics with zero `set-math-font` calls.
    // `interp.metrics.default_math_font` is `None` on a provider with no such
    // config, the same no-op-by-default shape as the `scripts` overlay above.
    if let Some(font) = interp.metrics.default_math_font() {
        ctx.math_font = font;
    }
    Ok(Value::Context(Box::new(ctx)))
}

/// `set-font-key : int -> context -> context` — LOCAL, non-upstream
/// primitive; see the `prims!` table comment on `"set-font-key"` for why it
/// exists. Sets `Context::font` directly to `FontKey(n)`.
fn prim_set_font_key(_interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
    let ctx = as_context(args.pop().unwrap())?;
    let key = as_int(args.pop().unwrap())?;
    if key < 0 || key > i64::from(u16::MAX) {
        return eval_error(format!("set-font-key: font key {key} is out of range"));
    }
    Ok(Value::Context(Box::new(Context {
        font: FontKey(key as u16),
        ..ctx
    })))
}

// ---- box combinators ---------------------------------------------------------

/// `++ : inline-boxes -> inline-boxes -> inline-boxes` (vminst.ml
/// `HorzConcat`).
fn prim_inline_concat(_interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
    let mut b = as_inline_boxes(args.pop().unwrap())?;
    let mut a = as_inline_boxes(args.pop().unwrap())?;
    a.append(&mut b);
    Ok(Value::InlineBoxes(a))
}

/// `+++ : block-boxes -> block-boxes -> block-boxes` (vminst.ml
/// `VertConcat`).
fn prim_block_concat(_interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
    let mut b = as_block_boxes(args.pop().unwrap())?;
    let mut a = as_block_boxes(args.pop().unwrap())?;
    a.append(&mut b);
    Ok(Value::BlockBoxes(a))
}

/// `inline-skip : length -> inline-boxes` (vminst.ml `BackendFixedEmpty`).
fn prim_inline_skip(_interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
    let width = as_length(args.pop().unwrap())?;
    Ok(Value::InlineBoxes(vec![HorzBox::Pure(
        PureHorzBox::FixedEmpty { width },
    )]))
}

/// `inline-glue : length -> length -> length -> inline-boxes` (vminst.ml
/// `BackendOuterEmpty`; params `(widnat, widshrink, widstretch)`, i.e.
/// natural, then shrink, then stretch — the same order `OuterEmpty`'s
/// fields are already declared in).
fn prim_inline_glue(_interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
    let stretchable = as_length(args.pop().unwrap())?;
    let shrinkable = as_length(args.pop().unwrap())?;
    let natural = as_length(args.pop().unwrap())?;
    Ok(Value::InlineBoxes(vec![HorzBox::Pure(
        PureHorzBox::OuterEmpty {
            natural,
            shrinkable,
            stretchable,
        },
    )]))
}

/// `block-skip : length -> block-boxes` (vminst.ml `BackendVertSkip`).
fn prim_block_skip(_interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
    let len = as_length(args.pop().unwrap())?;
    Ok(Value::BlockBoxes(vec![VertBox::Skip(len)]))
}

/// `list-mark : int -> block-boxes` — the block-level reflow marker
/// constructor `itemize.satyh`'s `listing`/`listing-item`/`listing-item-
/// breakable`/`enumerate`/`enumerate-item` call to fence list/item
/// boundaries. Returns a single-element `block-boxes` carrying an INERT
/// `VertBox::ListMark` — zero height/depth, stripped with zero contribution
/// by `chop_page`/`place_block_at`/`measure_block` before it can ever reach a
/// `PlacedLine`, so PDF and faithful HTML render identically whether or not
/// a document's stdlib calls this. Only `page_break_core`'s `reflow_source`
/// clone (taken BEFORE `chop_page` drains its input) retains it, for the
/// `html-support` branch's reflow HTML walker to read back.
///
/// `tag` encoding (the only "int tag" scheme any caller needs to know,
/// since this primitive is never reflected through the type system beyond
/// `int -> block-boxes`):
/// - `0` = `ListStart { ordered: false }` (opens a `<ul>`)
/// - `1` = `ListStart { ordered: true }` (opens an `<ol>`)
/// - `2` = `ListEnd`
/// - `3` = `ItemStart`
/// - `4` = `ItemEnd`
fn prim_list_mark(_interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
    let tag = as_int(args.pop().unwrap())?;
    let kind = match tag {
        0 => ListMarkKind::ListStart { ordered: false },
        1 => ListMarkKind::ListStart { ordered: true },
        2 => ListMarkKind::ListEnd,
        3 => ListMarkKind::ItemStart,
        4 => ListMarkKind::ItemEnd,
        other => return eval_error(format!("list-mark: unknown tag {other}")),
    };
    Ok(Value::BlockBoxes(vec![VertBox::ListMark(kind)]))
}

/// `inline-mark : int -> inline-boxes` — the inline-level reflow marker
/// constructor: `itemize.satyh`'s `make-bullet`/`enumerate-item` fence the
/// drawn bullet/number glyph run with `BulletStart`/`BulletEnd`, and the
/// repo-controlled `\emph`/`\bold` definitions (an opt-in, per-command wrap)
/// fence their body with `EmphStart`/`EmphEnd`. Same INERT-marker contract as
/// `list-mark` above — a zero-size `PureHorzBox::InlineMark`, ignored by
/// `measure`/`natural_metrics`/`justify_line`
/// (rustyfi-backend's `linebreak.rs`),
/// `math_glyphs_of_inline_boxes`/`math_boxes_of_inline_boxes` below, and both
/// the PDF and faithful HTML writers; read only by the `html-support`
/// branch's reflow HTML walker.
///
/// `tag` encoding:
/// - `0` = `EmphStart { strong: false }` (opens `<em>`)
/// - `1` = `EmphStart { strong: true }` (opens `<strong>`)
/// - `2` = `EmphEnd`
/// - `3` = `BulletStart`
/// - `4` = `BulletEnd`
fn prim_inline_mark(_interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
    let tag = as_int(args.pop().unwrap())?;
    let kind = match tag {
        0 => InlineMarkKind::EmphStart { strong: false },
        1 => InlineMarkKind::EmphStart { strong: true },
        2 => InlineMarkKind::EmphEnd,
        3 => InlineMarkKind::BulletStart,
        4 => InlineMarkKind::BulletEnd,
        other => return eval_error(format!("inline-mark: unknown tag {other}")),
    };
    Ok(Value::InlineBoxes(vec![HorzBox::Pure(
        PureHorzBox::InlineMark(kind),
    )]))
}

// ---- pure float primitives --------------------------------------------------
//
// All bodies below are `float -> float` (or `float -> float -> float`)
// straight wraps of the matching `f64` method — vminst.ml's OCaml bodies
// (`make_float (sin flt1)`, etc.) are themselves direct wraps of the same
// IEEE-754 libm functions, so there is no behavioral daylight here.

binop_prim!(prim_atan2, as_float, Float, |a, b| a.atan2(b));
unop_prim!(prim_sin, as_float, Float, |x| x.sin());
unop_prim!(prim_asin, as_float, Float, |x| x.asin());
unop_prim!(prim_cos, as_float, Float, |x| x.cos());
unop_prim!(prim_acos, as_float, Float, |x| x.acos());
unop_prim!(prim_tan, as_float, Float, |x| x.tan());
unop_prim!(prim_atan, as_float, Float, |x| x.atan());
// vminst.ml:2834 `FloatLogarithm`: OCaml's `log` is the NATURAL logarithm
// (`ln`), not `log10`.
unop_prim!(prim_log, as_float, Float, |x| x.ln());
unop_prim!(prim_exp, as_float, Float, |x| x.exp());
// `ceil`/`floor` return `float`, unlike `round` (above), which returns
// `int` — see this file's `prims!` table comment on `"ceil"`/`"floor"`.
unop_prim!(prim_ceil, as_float, Float, |x| x.ceil());
unop_prim!(prim_floor, as_float, Float, |x| x.floor());

// `show-float : float -> string` (vminst.ml:2319 `PrimitiveShowFloat`) —
// OCaml's `string_of_float`. See `ocaml_show_float`'s doc comment (below)
// for the emulation and its known fidelity limits.
unop_prim!(prim_show_float, as_float, Str, |x| ocaml_show_float(x));

/// A from-scratch emulation of OCaml's `Stdlib.string_of_float`: format via
/// a C `%.12g` equivalent (12 significant digits; fixed-point when the
/// decimal exponent falls in `-4..12`, scientific otherwise; trailing
/// fractional zeros trimmed), then apply `valid_float_lexem`'s post-pass —
/// append a trailing `.` when the result would otherwise print as a bare
/// integer (`"1."`, never `"1"`, so a `float`'s printed form always reads
/// as a float, not an `int`). Known limitation: this is a Rust
/// reimplementation of the same specification (OCaml itself defers to the
/// platform C library's `%.12g`), so it may disagree with OCaml in obscure
/// corner cases, though it agrees on ordinary values (verified by hand
/// against real OCaml output for `0.`, `-0.`, `1.`, `100.`, `0.0025`,
/// `1e+20`, `1e-05`).
fn ocaml_show_float(x: f64) -> String {
    if x.is_nan() {
        return "nan".to_string();
    }
    if x.is_infinite() {
        return if x < 0.0 { "-infinity" } else { "infinity" }.to_string();
    }
    const PREC: i32 = 12;
    // Style-E rendering at precision PREC-1 recovers the correctly-rounded
    // decimal exponent (a naive `log10().floor()` can be off by one right
    // at a power of ten, because of binary/decimal rounding).
    let sci = format!("{:.*e}", (PREC - 1) as usize, x);
    let epos = sci
        .find('e')
        .expect("scientific formatting always emits 'e'");
    let exp: i32 = sci[epos + 1..].parse().expect("well-formed exponent");
    let body = if exp < -4 || exp >= PREC {
        let mantissa = trim_trailing_fractional_zeros(&sci[..epos]);
        format!(
            "{mantissa}e{}{:02}",
            if exp < 0 { "-" } else { "+" },
            exp.abs()
        )
    } else {
        let decimals = (PREC - 1 - exp).max(0) as usize;
        trim_trailing_fractional_zeros(&format!("{:.*}", decimals, x)).to_string()
    };
    if body.bytes().all(|b| b.is_ascii_digit() || b == b'-') {
        format!("{body}.")
    } else {
        body
    }
}

/// Strip trailing zeros after a decimal point, then the point itself if
/// nothing remains after it (`"3.140" -> "3.14"`, `"5.000" -> "5"`);
/// already-integer-shaped strings (no `.`) pass through unchanged.
fn trim_trailing_fractional_zeros(s: &str) -> &str {
    if !s.contains('.') {
        return s;
    }
    s.trim_end_matches('0').trim_end_matches('.')
}

// `string-byte-length : string -> int` (vminst.ml:2159
// `PrimitiveStringByteLength`) — UTF-8 BYTE count (`String.length` in
// OCaml, whose native strings are raw byte sequences), unlike
// `string-length`'s Unicode-scalar-value count.
unop_prim!(prim_string_byte_length, as_str, Int, |s| s.len() as i64);

/// `string-sub-bytes : string -> int -> int -> string` (vminst.ml:2123
/// `PrimitiveStringSubBytes`) — byte-indexed substring (OCaml's
/// `String.sub`), unlike `string-sub`'s Unicode-scalar-value indexing.
/// Guards an out-of-range span exactly like `prim_string_sub`'s "illegal
/// index" dynamic error, AND a split landing inside a multi-byte UTF-8
/// sequence — impossible for OCaml's byte-oriented strings, but a
/// `Value::Str` here is a Rust `String`, which must stay valid UTF-8.
fn prim_string_sub_bytes(_interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
    let wid = as_int(args.pop().unwrap())?;
    let pos = as_int(args.pop().unwrap())?;
    let s = as_str(args.pop().unwrap())?;
    if wid < 0 || pos < 0 {
        return eval_error("illegal index for string-sub-bytes");
    }
    let (pos, wid) = (pos as usize, wid as usize);
    match pos.checked_add(wid) {
        Some(end) if end <= s.len() && s.is_char_boundary(pos) && s.is_char_boundary(end) => {
            Ok(Value::Str(s[pos..end].to_string()))
        }
        _ => eval_error("illegal index for string-sub-bytes"),
    }
}

/// `string-unexplode : int list -> string` (vminst.ml:2196
/// `PrimitiveStringUnexplode`) — the inverse of `string-explode` (above):
/// each int is a Unicode scalar value (code point), concatenated into one
/// UTF-8 string. Upstream's `Uchar.of_int` raises on an int that isn't a
/// valid Unicode scalar value (a surrogate, or out of range); reported here
/// as the same kind of dynamic error rather than panicking.
fn prim_string_unexplode(_interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
    let items = as_list(args.pop().unwrap())?;
    let mut s = String::new();
    for v in items {
        let n = as_int(v)?;
        match u32::try_from(n).ok().and_then(char::from_u32) {
            Some(c) => s.push(c),
            None => {
                return eval_error(format!(
                    "string-unexplode: {n} is not a valid Unicode scalar value"
                ))
            }
        }
    }
    Ok(Value::Str(s))
}

/// `normalize-string-to-nfc : string -> string` (dev-0-1-0 vminst.ml:2050
/// `NormalizeStringToNFC`) — REAL: UAX #15 Normalization Form C, via the
/// `unicode-normalization` crate (`UnicodeNormalization::nfc`), a pure-Rust
/// stand-in for upstream's uunf-backed `NormalizeString.of_utf8_nfc`.
/// DOCUMENTED NON-RISK: this crate's embedded Unicode table version may lag
/// or lead upstream's uunf pin — both track recent Unicode, and no bundled
/// package/test relies on a normalization pair that changed between
/// versions.
fn prim_normalize_string_to_nfc(
    _interp: &mut Interp,
    mut args: Vec<Value>,
) -> Result<Value, EvalError> {
    let s = as_str(args.pop().unwrap())?;
    Ok(Value::Str(s.nfc().collect()))
}

/// `normalize-string-to-nfd : string -> string` (dev-0-1-0 vminst.ml:2066
/// `NormalizeStringToNFD`) — REAL: UAX #15 Normalization Form D, same
/// crate/caveats as [`prim_normalize_string_to_nfc`] above.
fn prim_normalize_string_to_nfd(
    _interp: &mut Interp,
    mut args: Vec<Value>,
) -> Result<Value, EvalError> {
    let s = as_str(args.pop().unwrap())?;
    Ok(Value::Str(s.nfd().collect()))
}

/// `split-grapheme-cluster : string -> list string` (dev-0-1-0 vminst.ml:
/// 2082 `SplitOnGraphemeCluster` / `GraphemeCluster.split_utf8`) — REAL: UAX
/// #29 EXTENDED grapheme clusters, via the `unicode-segmentation` crate's
/// `graphemes(s, true)` (`true` selects the extended, not legacy, cluster
/// rules — what upstream's uuseg default segmenter produces).
fn prim_split_grapheme_cluster(
    _interp: &mut Interp,
    mut args: Vec<Value>,
) -> Result<Value, EvalError> {
    let s = as_str(args.pop().unwrap())?;
    let clusters: Vec<Value> = s
        .graphemes(true)
        .map(|g| Value::Str(g.to_string()))
        .collect();
    Ok(Value::List(clusters))
}

/// `display-message : string -> unit` (vminst.ml:2056
/// `PrimitiveDisplayMessage`) — upstream prints via `print_endline`
/// (STDOUT); this port deliberately prints to STDERR instead (`eprintln!`),
/// keeping stdout reserved for actual document output. This matches the
/// existing house convention: the CLI's own "output written" status line
/// (`rustyfi`'s `main.rs`) is likewise stderr-only, never stdout — a
/// documented deviation, not an oversight.
fn prim_display_message(_interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
    let msg = as_str(args.pop().unwrap())?;
    eprintln!("{msg}");
    Ok(Value::Unit)
}

/// `abort-with-message : string -> 'a` (vminst.ml:3133 `AbortWithMessage`)
/// — raises a dynamic error carrying `msg` verbatim. The polymorphic result
/// type (`prim_types.rs`'s `poly1`) is vacuously satisfiable: this always
/// evaluates to `Err`, never actually producing a value of whatever type
/// the call site expected.
fn prim_abort_with_message(_interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
    let msg = as_str(args.pop().unwrap())?;
    eval_error(msg)
}

// ---- images (raster images) -----------

/// `load-image : string -> image` (v0.0.6 vminstdef.yaml:540). Resolves
/// `path` against the process's current working directory — this port
/// has no "job directory" threaded through `Interp` yet, so this is a
/// deliberately simple stand-in for v0.0.6's real job-directory-relative
/// resolution, good enough for a CLI invoked from the document's own
/// directory and for this crate's fixture-driven tests (which pass an
/// absolute path).
///
/// Decoding is eager (via the `image` crate, to 8-bit `DeviceRGB` — see
/// `ImageResource`'s doc comment for the alpha-dropping/format caveats),
/// matching v0.0.6's `ImageInfo.add_image` (imageInfo.ml): a missing or
/// undecodable file is a clean `EvalError` here, not deferred to the PDF
/// writer.
///
/// JPEG DCTDecode passthrough: in addition to the eager RGB8 decode above
/// (still needed for `use-image-by-width`'s aspect ratio and the HTML
/// backend's `<img>` data URI), this re-reads the same path's raw bytes and
/// sniffs them for a baseline JPEG (`ImageResource::sniff_baseline_jpeg_dct`)
/// so the PDF writer can embed the ORIGINAL DCT-encoded bytes instead of
/// re-encoding the flattened samples. The second read is best-effort: a
/// failure just leaves `jpeg_dct` as `None` and falls back to flat-RGB8
/// embedding, since the file already decoded fine above.
fn prim_load_image(interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
    let path = as_str(args.pop().unwrap())?;
    let decoded = image::open(&path).map_err(|e| EvalError {
        span: None,
        msg: format!("load-image: cannot decode '{path}': {e}"),
    })?;
    let rgb = decoded.to_rgb8();
    let (px_w, px_h) = rgb.dimensions();
    let jpeg_dct = std::fs::read(&path)
        .ok()
        .and_then(ImageResource::sniff_baseline_jpeg_dct);
    let id = ImageId(interp.images.len());
    interp.images.push(ImageResource {
        samples: rgb.into_raw(),
        px_w,
        px_h,
        jpeg_dct,
        pdf: None,
    });
    Ok(Value::Image(id))
}

/// `use-image-by-width : image -> length -> inline-boxes` (v0.0.6
/// vminstdef.yaml:554). Computes the on-page height from the source
/// image's own pixel aspect ratio (v0.0.6
/// `ImageInfo.get_height_from_width`, imageInfo.ml:44): `height = width *
/// px_h / px_w`.
fn prim_use_image_by_width(interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
    let width = as_length(args.pop().unwrap())?;
    let image = as_image(args.pop().unwrap())?;
    let resource = interp.images.get(image.0).ok_or_else(|| EvalError {
        span: None,
        msg: format!("internal error: image id {} out of range", image.0),
    })?;
    let (iw, ih) = resource.intrinsic_dims_pt();
    if iw == 0.0 {
        return eval_error("use-image-by-width: image has zero width, cannot scale");
    }
    let height = width * (ih / iw);
    Ok(Value::InlineBoxes(vec![HorzBox::Pure(
        PureHorzBox::Image {
            width,
            height,
            image,
        },
    )]))
}

/// `load-pdf-image : string -> int -> image` (v0.0.6 vminstdef.yaml:525-538
/// `BackendRegisterPdfImage`; dev-0-1-0 renames it `PrimitiveLoadPdfImage`
/// with the identical type/body). Loads page `pageno` (1-based) of the PDF
/// at `path`, parsed eagerly with `lopdf`, and stores a `PdfPageResource` —
/// the page's `/MediaBox` (for `use-image-by-width`'s aspect ratio), its
/// content stream(s) (already inflated/concatenated by
/// `lopdf::Document::get_page_content`), and its imported `/Resources`
/// object subtree (for the PDF writer's Form XObject).
///
/// Path resolution is cwd-relative, the same documented deviation as
/// `prim_load_image`/`prim_read_file` (no job-directory threaded through
/// `Interp` yet).
///
/// Errors (all clean `EvalError`, no panics):
/// - file missing/unreadable → "cannot open '<path>': <e>";
/// - malformed/unparseable PDF → "cannot parse PDF '<path>': <e>";
/// - `pageno < 1` → "page number must be >= 1 (got <n>)";
/// - `pageno` beyond the page count → "'<path>' has no page <n>";
/// - `/Encrypt` present in the trailer → "'<path>' is encrypted; not
///   supported" (decryption is never attempted);
/// - no usable `/MediaBox` (missing at every level of the inherited page
///   tree, wrong array length, or non-numeric entries) → "page <n> of
///   '<path>' has no usable MediaBox".
#[cfg(feature = "pdf-image")]
fn prim_load_pdf_image(interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
    let pageno = as_int(args.pop().unwrap())?;
    let path = as_str(args.pop().unwrap())?;
    if pageno < 1 {
        return eval_error(format!(
            "load-pdf-image: page number must be >= 1 (got {pageno})"
        ));
    }
    let doc = lopdf::Document::load(&path).map_err(|e| {
        let msg = match &e {
            lopdf::Error::IO(io_e) => format!("load-pdf-image: cannot open '{path}': {io_e}"),
            other => format!("load-pdf-image: cannot parse PDF '{path}': {other}"),
        };
        EvalError { span: None, msg }
    })?;
    if doc.is_encrypted() {
        return eval_error(format!(
            "load-pdf-image: '{path}' is encrypted; not supported"
        ));
    }
    let pages = doc.get_pages();
    let page_id = *pages.get(&(pageno as u32)).ok_or_else(|| EvalError {
        span: None,
        msg: format!("load-pdf-image: '{path}' has no page {pageno}"),
    })?;
    let page_dict = doc.get_dictionary(page_id).map_err(|e| EvalError {
        span: None,
        msg: format!("load-pdf-image: cannot parse PDF '{path}': {e}"),
    })?;
    let media_box = resolve_pdf_media_box(&doc, page_dict).ok_or_else(|| EvalError {
        span: None,
        msg: format!("load-pdf-image: page {pageno} of '{path}' has no usable MediaBox"),
    })?;
    let content = doc.get_page_content(page_id).map_err(|e| EvalError {
        span: None,
        msg: format!("load-pdf-image: cannot parse PDF '{path}': {e}"),
    })?;
    let resources = import_pdf_resources(&doc, page_dict);
    let id = ImageId(interp.images.len());
    interp.images.push(ImageResource {
        samples: Vec::new(),
        px_w: 0,
        px_h: 0,
        jpeg_dct: None,
        pdf: Some(PdfPageResource {
            media_box,
            content,
            resources,
        }),
    });
    Ok(Value::Image(id))
}

/// Without the `pdf-image` feature no PDF reader is linked in, so the
/// primitive can only fail — which it does at the call site, naming why.
///
/// The name stays REGISTERED rather than being gated out of the primitive
/// tables: `typecheck::PRIMITIVE_NAMES`, `prim_types::primitive_type` and this
/// table are cross-checked against each other (`tests/typecheck.rs`), and a
/// document that reaches for `load-pdf-image` is better told that this build
/// cannot read PDFs than that the name does not exist.
#[cfg(not(feature = "pdf-image"))]
fn prim_load_pdf_image(_interp: &mut Interp, _args: Vec<Value>) -> Result<Value, EvalError> {
    eval_error(
        "load-pdf-image: this build has no PDF reader (the `pdf-image` feature \
         is off). It is off for WebAssembly, where the primitive could not work \
         regardless: it takes a filesystem path."
            .to_string(),
    )
}

/// `/MediaBox` lookup with page-tree inheritance (`lopdf` does not resolve
/// this automatically, unlike upstream camlpdf's `Pdfpage` helpers): walk
/// `page_dict`, then its `/Parent` chain, returning the first `/MediaBox`
/// found as `(x0, y0, x1, y1)` in raw PDF points. `None`
/// if no ancestor carries a well-formed 4-element numeric array, or if a
/// `/Parent` cycle is detected.
#[cfg(feature = "pdf-image")]
fn resolve_pdf_media_box(
    doc: &lopdf::Document,
    page_dict: &lopdf::Dictionary,
) -> Option<(f64, f64, f64, f64)> {
    let mut cur = page_dict;
    let mut seen: BTreeSet<(u32, u16)> = BTreeSet::new();
    loop {
        if let Ok(obj) = cur.get(b"MediaBox") {
            if let Ok(arr) = obj.as_array() {
                if arr.len() == 4 {
                    let mut v = [0f64; 4];
                    let mut ok = true;
                    for (slot, item) in v.iter_mut().zip(arr.iter()) {
                        match item.as_float() {
                            Ok(f) => *slot = f as f64,
                            Err(_) => {
                                ok = false;
                                break;
                            }
                        }
                    }
                    if ok {
                        return Some((v[0], v[1], v[2], v[3]));
                    }
                }
            }
        }
        match cur.get(b"Parent").and_then(|o| o.as_reference()) {
            Ok(parent_id) => {
                if !seen.insert(parent_id) {
                    return None; // cycle
                }
                cur = doc.get_dictionary(parent_id).ok()?;
            }
            Err(_) => return None,
        }
    }
}

/// Import the page's `/Resources` subtree (walking page-tree inheritance
/// like `resolve_pdf_media_box`) into a neutral `ImportedObjects` table for
/// the PDF writer. Local id `0` always holds the
/// (possibly inline) `/Resources` dictionary itself; every other entry is a
/// real source PDF object number, keyed by `convert_pdf_object`'s
/// transitive walk of every `Reference` reachable from it.
#[cfg(feature = "pdf-image")]
fn import_pdf_resources(doc: &lopdf::Document, page_dict: &lopdf::Dictionary) -> ImportedObjects {
    let mut out: Vec<(u32, ObjRepr)> = Vec::new();
    let mut seen: BTreeSet<u32> = BTreeSet::new();
    let root_repr = match resolve_pdf_resources_object(doc, page_dict) {
        Some(obj) => convert_pdf_object(doc, obj, &mut out, &mut seen),
        None => ObjRepr::Dict(Vec::new()),
    };
    out.insert(0, (0, root_repr));
    ImportedObjects(out)
}

/// `/Resources` lookup with page-tree inheritance, mirroring
/// `resolve_pdf_media_box` but returning the raw (possibly-inline)
/// `&lopdf::Object` rather than a decoded value, since `/Resources` may
/// legally be either a direct dictionary or an indirect reference.
#[cfg(feature = "pdf-image")]
fn resolve_pdf_resources_object<'a>(
    doc: &'a lopdf::Document,
    page_dict: &'a lopdf::Dictionary,
) -> Option<&'a lopdf::Object> {
    let mut cur = page_dict;
    let mut seen: BTreeSet<(u32, u16)> = BTreeSet::new();
    loop {
        if let Ok(obj) = cur.get(b"Resources") {
            return Some(obj);
        }
        match cur.get(b"Parent").and_then(|o| o.as_reference()) {
            Ok(parent_id) => {
                if !seen.insert(parent_id) {
                    return None;
                }
                cur = doc.get_dictionary(parent_id).ok()?;
            }
            Err(_) => return None,
        }
    }
}

/// Recursively convert one `lopdf::Object` into the neutral `ObjRepr`
/// grammar, following every `Reference` transitively and
/// appending newly-visited indirect objects to `out` keyed by their source
/// object number (`seen` guards against re-visiting/cycles — a shared
/// object referenced from multiple places is emitted once and pointed at by
/// `ObjRepr::Ref` from every occurrence). Stream objects are copied
/// **verbatim** (still-filtered bytes, `/Filter`/`/DecodeParms` kept as-is;
/// only `/Length` is dropped since the writer derives it) — unlike the
/// page's own content stream (`Document::get_page_content`, inflated
/// separately in `prim_load_pdf_image`), a resource stream (font program,
/// embedded image XObject, ICC profile, ...) is re-emitted byte-for-byte,
/// so no decode/re-encode risk is taken on data this importer doesn't need
/// to understand.
#[cfg(feature = "pdf-image")]
fn convert_pdf_object(
    doc: &lopdf::Document,
    obj: &lopdf::Object,
    out: &mut Vec<(u32, ObjRepr)>,
    seen: &mut BTreeSet<u32>,
) -> ObjRepr {
    use lopdf::Object as LObj;
    match obj {
        LObj::Null => ObjRepr::Null,
        LObj::Boolean(b) => ObjRepr::Bool(*b),
        LObj::Integer(n) => ObjRepr::Int(*n),
        LObj::Real(r) => ObjRepr::Real(*r as f64),
        LObj::Name(n) => ObjRepr::Name(n.clone()),
        LObj::String(s, _) => ObjRepr::String(s.clone()),
        LObj::Array(items) => ObjRepr::Array(
            items
                .iter()
                .map(|it| convert_pdf_object(doc, it, out, seen))
                .collect(),
        ),
        LObj::Dictionary(d) => ObjRepr::Dict(convert_pdf_dict(doc, d, out, seen)),
        LObj::Stream(s) => {
            let dict_entries = convert_pdf_dict(doc, &s.dict, out, seen)
                .into_iter()
                .filter(|(k, _)| k.as_slice() != b"Length")
                .collect();
            ObjRepr::Stream(dict_entries, s.content.clone())
        }
        LObj::Reference((obj_num, gen)) => {
            let (obj_num, gen) = (*obj_num, *gen);
            if obj_num != 0 && seen.insert(obj_num) {
                if let Ok(target) = doc.get_object((obj_num, gen)) {
                    let repr = convert_pdf_object(doc, target, out, seen);
                    out.push((obj_num, repr));
                }
            }
            ObjRepr::Ref(obj_num)
        }
    }
}

#[cfg(feature = "pdf-image")]
fn convert_pdf_dict(
    doc: &lopdf::Document,
    dict: &lopdf::Dictionary,
    out: &mut Vec<(u32, ObjRepr)>,
    seen: &mut BTreeSet<u32>,
) -> Vec<(Vec<u8>, ObjRepr)> {
    dict.iter()
        .map(|(k, v)| (k.clone(), convert_pdf_object(doc, v, out, seen)))
        .collect()
}

/// `read-file : string -> list string` (dev-0-1-0 vminst.ml:3073
/// `PrimitiveReadFile`) — REAL, with two documented
/// deviations:
///
/// 1. **Path resolution**: resolves `path` against the process's current
///    working directory, the same `load-image` precedent
///    (`prim_load_image`'s doc comment) — this port has no job-directory
///    notion threaded through `Interp` yet. Upstream resolves against
///    `OptionState.job_directory ()` (the input document's own directory).
/// 2. **Containment tightening**: upstream rejects any `..` path component
///    (`"cannot access files by using '..'"`, vminst.ml:3084-3090) but
///    otherwise resolves `Filename.concat jobdir path` literally — an
///    absolute `path` silently escapes the job directory upstream. This
///    port ALSO rejects absolute paths (same error class), making the
///    containment upstream's own message implies actually real.
///
/// Line splitting is faithful to OCaml's `input_line` loop: split on `'\n'`,
/// drop a trailing empty piece (file ends with `\n`), keep `'\r'` (do NOT
/// use `BufRead::lines`, which strips `\r\n`) — an empty file yields `[]`.
/// Non-UTF-8 content is a clean `EvalError` (upstream's OCaml strings are
/// byte-transparent; this port's `Value::Str` must stay valid UTF-8 —
/// documented deviation).
fn prim_read_file(_interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
    let path_str = as_str(args.pop().unwrap())?;
    let path = std::path::Path::new(&path_str);
    if path.is_absolute() {
        return eval_error(
            "read-file: cannot access files by using an absolute path (job-directory containment)",
        );
    }
    if path
        .components()
        .any(|c| matches!(c, std::path::Component::ParentDir))
    {
        return eval_error("cannot access files by using '..'");
    }
    let bytes = std::fs::read(path).map_err(|e| EvalError {
        span: None,
        msg: format!("read-file: cannot open '{path_str}': {e}"),
    })?;
    let text = String::from_utf8(bytes).map_err(|_| EvalError {
        span: None,
        msg: format!("read-file '{path_str}': not valid UTF-8"),
    })?;
    let mut lines: Vec<Value> = text
        .split('\n')
        .map(|s| Value::Str(s.to_string()))
        .collect();
    if matches!(lines.last(), Some(Value::Str(s)) if s.is_empty()) {
        lines.pop();
    }
    Ok(Value::List(lines))
}

/// `(string) option` — `register-document-information`'s `title`/`subject`/
/// `author` fields, parsed the same way [`as_border_option`] reads a
/// `Value::Ctor`.
fn as_option_string(v: Value) -> Result<Option<String>, EvalError> {
    match v {
        Value::Ctor(name, payload) => match (name.as_str(), payload.map(|b| *b)) {
            ("None", None) => Ok(None),
            ("Some", Some(Value::Str(s))) => Ok(Some(s)),
            (other, _) => eval_error(format!(
                "expected a string option (None / Some(string)), got variant '{other}'"
            )),
        },
        other => eval_error(format!("expected an option, got {}", other.type_name())),
    }
}

/// `register-document-information : document-information-dictionary ->
/// unit` (dev-0-1-0 vminst.ml:2978 `PrimitiveRegisterDocumentInformation`)
/// — REAL: extracts `title`/`subject`/`author`
/// (`option string`) and `keywords` (`list string`) from the record
/// argument (`t_doc_info_dictionary()`'s shape, `prim_types.rs`) and stores
/// them onto `Interp::doc_info` — LAST WRITE WINS (upstream's `register`,
/// `documentInformationDictionary.ml`), matching the `outline`/
/// `annotations`/`destinations` accumulator policy (`eval.rs`): reset per
/// trial (fresh `Interp`), the final trial's value drained into
/// `DocExtras::doc_info` (`lib.rs`) and emitted as the PDF `/Info`
/// dictionary by both writers (`rustyfi-pdf`'s `lib.rs`/`cid.rs`).
fn prim_register_document_information(
    interp: &mut Interp,
    mut args: Vec<Value>,
) -> Result<Value, EvalError> {
    let fields = match args.pop().unwrap() {
        Value::Record(m) => m,
        other => {
            return eval_error(format!(
                "register-document-information: expected a document-information-dictionary \
                 record, got {}",
                other.type_name()
            ))
        }
    };
    let record_name = "document-information-dictionary";
    let title = as_option_string(record_field(&fields, record_name, "title")?)?;
    let subject = as_option_string(record_field(&fields, record_name, "subject")?)?;
    let author = as_option_string(record_field(&fields, record_name, "author")?)?;
    let keywords = as_list(record_field(&fields, record_name, "keywords")?)?
        .into_iter()
        .map(as_str)
        .collect::<Result<Vec<_>, _>>()?;
    interp.doc_info = Some(DocInfo {
        title,
        subject,
        author,
        keywords,
    });
    Ok(Value::Unit)
}

// ============================================================================
// ---- graphics primitives ------
// `start-path`/`line-to`/`terminate-path`/`close-with-line`/`fill`/`stroke`/
// `inline-graphics`. Argument order matches `tools/gencode/vminst.ml`
// (point-first for `line-to`, width-first for `stroke`).
// ============================================================================

/// `start-path : point -> pre-path` (vminst.ml:713).
fn prim_start_path(_interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
    let start = as_point(args.pop().unwrap())?;
    Ok(Value::PrePath(PrePath {
        start,
        segs: Vec::new(),
    }))
}

/// `line-to : point -> pre-path -> pre-path` (vminst.ml:727) — appends a
/// straight segment to the pre-path's forward-accumulated `segs`.
fn prim_line_to(_interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
    let mut pp = as_prepath(args.pop().unwrap())?;
    let pt = as_point(args.pop().unwrap())?;
    pp.segs.push(PathSeg::Line(pt));
    Ok(Value::PrePath(pp))
}

/// `terminate-path : pre-path -> path` (vminst.ml:759) — finishes an OPEN
/// subpath (no closing segment).
fn prim_terminate_path(_interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
    let pp = as_prepath(args.pop().unwrap())?;
    Ok(Value::Path(Path {
        subpaths: vec![Subpath {
            start: pp.start,
            segs: pp.segs,
            closing: Closing::Open,
        }],
    }))
}

/// `close-with-line : pre-path -> path` (vminst.ml:773) — closes the subpath
/// with a straight segment back to its start (PDF `h`).
fn prim_close_with_line(_interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
    let pp = as_prepath(args.pop().unwrap())?;
    Ok(Value::Path(Path {
        subpaths: vec![Subpath {
            start: pp.start,
            segs: pp.segs,
            closing: Closing::Line,
        }],
    }))
}

/// `fill : color -> path -> graphics` (vminst.ml:2398) — a filled region;
/// the PDF writer (`place_graphics`, rustyfi-pdf) paints it with the
/// even-odd rule, matching upstream's `op_f'`.
fn prim_fill(_interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
    let path = as_path(args.pop().unwrap())?;
    let color = as_color(args.pop().unwrap())?;
    Ok(Value::Graphics(GraphicsElem::Fill(color, path)))
}

/// `stroke : length -> color -> path -> graphics` (vminst.ml:2381) — width
/// first, then color, then path.
fn prim_stroke(_interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
    let path = as_path(args.pop().unwrap())?;
    let color = as_color(args.pop().unwrap())?;
    let wid = as_length(args.pop().unwrap())?;
    Ok(Value::Graphics(GraphicsElem::Stroke(wid, color, path)))
}

/// Apply a graphics callback under the eager-call window, returning its
/// resolved elements with every `register-destination` it made appended as a
/// [`GraphicsElem::Destination`] marker. Markers go AFTER the real elements, so
/// ink z-order is untouched and a callback that registers nothing yields the
/// same `elems` as before.
///
/// The window is deliberately NOT opened inside a page-break walk
/// (`current_page` is `Some` — a deco can build an `inline-graphics` of its
/// own): a box built there is drawn straight into `page_graphics`, which
/// `fire_hooks` never re-walks, so a marker minted for it would be silently
/// dropped. There the direct registration is available and correct.
fn apply_graphics_callback(
    interp: &mut Interp,
    version: RustyfiVersion,
    apply: impl FnOnce(&mut Interp) -> Result<Value, EvalError>,
) -> Result<Vec<GraphicsElem>, EvalError> {
    let defer = interp.current_page.is_none();
    let saved = if defer {
        interp.pending_dests.replace(Vec::new())
    } else {
        None
    };
    let result = apply(interp).and_then(|v| coerce_graphics_result_for(version, v));
    let pending = if defer {
        interp.pending_dests.take().unwrap_or_default()
    } else {
        Vec::new()
    };
    if defer {
        interp.pending_dests = saved;
    }
    let mut elems = result?;
    elems.extend(
        pending
            .into_iter()
            .map(|(key, pt)| GraphicsElem::Destination { key, pt }),
    );
    Ok(elems)
}

/// `inline-graphics : length -> length -> length -> (point -> graphics
/// list) -> inline-boxes` (vminst.ml:1872 `BackendInlineGraphics`) — a box
/// of size `(w, h, d)` carrying the callback's resolved graphics elements,
/// the minimal on-page sink for a `graphics` value.
///
/// **Eager-callback shortcut.** Upstream defers the callback until
/// the box's *placed* point is known on the page, then calls
/// `gfun(placed_point)`. A lang closure cannot live inside a backend box
/// (`PureHorzBox::Graphics` only holds resolved `GraphicsElem`s), and the
/// placed point isn't known until page-break/render time — so instead this
/// calls `gfun` immediately at `(0pt, 0pt)`, and the PDF writer
/// (`place_graphics`, rustyfi-pdf) translates the *whole* box to its placed
/// position via a single `cm` at render time. This equals upstream's
/// behavior if and only if `gfun` uses its point argument purely additively
/// (shift-covariant) — true of every real `Gr`/`deco` generator, but not
/// enforced by this signature.
///
/// **The one SIDE EFFECT that survives the shortcut** is
/// `register-destination`: at construction time there is no page, so
/// `annotation.ml:15`'s gate would refuse it and fail the document (azmath's
/// `equation.satyh` anchors every `\label`ed equation this way).
/// [`apply_graphics_callback`] turns each call into a
/// `GraphicsElem::Destination` marker riding in `elems` — rather than a field
/// of its own, so it inherits the `origin_independent` probe below and the
/// existing `fire_hooks`/`shift_graphics` pipeline.
fn prim_inline_graphics(
    interp: &mut Interp,
    version: RustyfiVersion,
    mut args: Vec<Value>,
) -> Result<Value, EvalError> {
    let gfun = args.pop().unwrap();
    let d = as_length(args.pop().unwrap())?;
    let h = as_length(args.pop().unwrap())?;
    let w = as_length(args.pop().unwrap())?;
    // The callback's result type is `list graphics` under v0.0.6, one
    // `graphics` collection under v0.1 — see `coerce_graphics_result`'s doc
    // comment.
    let gf = gfun.clone();
    let elems = apply_graphics_callback(interp, version, move |it| {
        let origin = make_point_value((Length::ZERO, Length::ZERO));
        it.apply(gf, origin)
    })?;
    // Detect a PAGE-ABSOLUTE callback: run it again at a far-off probe point
    // and compare. If the output is byte-identical the callback ignored its
    // placed-point argument (`fun _ -> …`, e.g. slydifi's frame background /
    // figbox's `draw-text pt`), so its coordinates are already page-absolute
    // and the PDF writer must NOT translate them by the box's placed position
    // (which is often a negative text-origin, shifting the decoration off the
    // page). A position-relative callback yields different output here, so
    // `origin_independent` stays false and the per-box `cm` applies as before.
    // Upstream (`handlePdf.ml`) always calls the callback with the true placed
    // point and never post-translates; this recovers that for the constant
    // case without a post-layout deferral. (The extra evaluation must be free
    // of observable side effects — true of every `Gr`/`draw-text` generator;
    // `register-destination` is captured per call rather than committed, so
    // the probe's copy is dropped.)
    //
    // The comparison includes the markers on purpose: an ANCHOR-ONLY callback
    // draws no ink at either point, so comparing ink alone would classify it
    // page-absolute and pin every anchor at the raw callback argument.
    let origin_independent = {
        let probe = make_point_value((Length::pt(4096.0), Length::pt(2731.0)));
        match apply_graphics_callback(interp, version, move |it| it.apply(gfun, probe)) {
            Ok(e2) => e2 == elems,
            Err(_) => false,
        }
    };
    Ok(Value::InlineBoxes(vec![HorzBox::Pure(
        PureHorzBox::Graphics {
            width: w,
            height: h,
            depth: d,
            elems,
            origin_independent,
        },
    )]))
}

/// `inline-graphics-outer : length -> length -> (length -> point -> graphics
/// list) -> inline-boxes` (vminst.ml:1891 `BackendInlineGraphicsOuter`) — a
/// graphics box whose width stretches like `inline-fil` (upstream widinfo
/// `Fils(1)`). The callback needs the RESOLVED width, unknown until line
/// layout, so it is deferred through `Interp::outer_graphics` (the `HookId`
/// pattern) and fired by `resolve_outer_graphics_in_contents` (called from
/// `line-break`/`tabular`/`draw-text`) with the width `justify_line` wrote
/// into the box and the point `(0pt, 0pt)` — the same shift-covariance
/// shortcut as `inline-graphics` above (the writer's `cm` supplies the
/// placed point); the width argument is faithful.
fn prim_inline_graphics_outer(
    interp: &mut Interp,
    version: RustyfiVersion,
    mut args: Vec<Value>,
) -> Result<Value, EvalError> {
    let gfun = args.pop().unwrap();
    let d = as_length(args.pop().unwrap())?;
    let h = as_length(args.pop().unwrap())?;
    interp.outer_graphics.push((gfun, version));
    let fn_id = GraphicsFnId(interp.outer_graphics.len() - 1);
    Ok(Value::InlineBoxes(vec![HorzBox::Pure(
        PureHorzBox::GraphicsOuter {
            height: h,
            depth: d,
            width: Length::ZERO,
            fn_id,
        },
    )]))
}

/// Fire every deferred `inline-graphics-outer` callback in an already-
/// justified run, replacing its `GraphicsOuter` marker with a resolved
/// `Graphics` box (see `prim_inline_graphics_outer`). Idempotent (a resolved
/// box no longer matches) and cheap when nothing matches (one pass, no
/// allocation).
fn resolve_outer_graphics_in_contents(
    interp: &mut Interp,
    contents: &mut [(Length, PureHorzBox)],
) -> Result<(), EvalError> {
    for (_, bx) in contents.iter_mut() {
        if let PureHorzBox::GraphicsOuter {
            height,
            depth,
            width,
            fn_id,
        } = bx
        {
            let (w, h, d) = (*width, *height, *depth);
            let (gfun, gver) = match interp.outer_graphics.get(fn_id.0) {
                Some((f, v)) => (f.clone(), *v),
                None => {
                    return eval_error(format!(
                        "inline-graphics-outer: dangling callback index {}",
                        fn_id.0
                    ))
                }
            };
            // Same per-version coercion as `prim_inline_graphics`
            // above, shared with `tabular`'s per-cell use. The generation is
            // the one the callback was REGISTERED under, carried alongside it in
            // `Interp::outer_graphics`: this pass is a DEFERRED one
            // (`line-break`/`tabular`/`draw-text`), so `interp.version` here
            // is the entry document's, not the callback author's.
            //
            // Deferred to LINE-BREAK time, not page break, so a
            // `register-destination` here still has no page: same capture as
            // `prim_inline_graphics`.
            let elems = apply_graphics_callback(interp, gver, move |it| {
                let partial = it.apply(gfun, Value::Length(w))?;
                it.apply(partial, make_point_value((Length::ZERO, Length::ZERO)))
            })?;
            *bx = PureHorzBox::Graphics {
                width: w,
                height: h,
                depth: d,
                elems,
                origin_independent: false,
            };
        }
    }
    Ok(())
}

/// `tabular : (cell list) list -> (length list -> length list -> graphics
/// list) -> inline-boxes` (vminst.ml:539) — solve the grid (backend
/// `rustyfi_backend::tabular::main`) and eagerly drive the rule callback
/// with the solved box-local grid-line coordinates.
///
/// **Why eager is faithful here, unlike `inline-graphics`.** The callback's
/// arguments are the grid-line coordinates, fully determined by cell
/// content alone (`main` computes them before any placement) — so calling
/// it once at construction time with the true box-local `xs`/`ys` is exactly
/// what upstream's later, placement-time call produces once the PDF
/// writer's per-box `cm` translate (shared with `place_graphics`, see
/// `rustyfi-pdf`) shifts the resulting rule paths into position. No
/// shift-covariance caveat (contrast `prim_inline_graphics` above).
fn prim_tabular(
    interp: &mut Interp,
    version: RustyfiVersion,
    mut args: Vec<Value>,
) -> Result<Value, EvalError> {
    let rulesf = args.pop().unwrap();
    let rows = as_cell_grid(args.pop().unwrap())?;
    let mut solved = rustyfi_backend::tabular::main(rows);
    for cell in &mut solved.cells {
        resolve_outer_graphics_in_contents(interp, &mut cell.contents)?;
    }

    let xs = make_length_list(&solved.xs);
    let ys = make_length_list(&solved.ys);
    let partial = interp.apply(rulesf, xs)?;
    let gval = interp.apply(partial, ys)?;
    // The rules callback returns `list graphics` under v0.0.6, one
    // `graphics` collection under v0.1 — per the CALLER's generation
    // (`version`), which is the one whose `tabular` type this call was
    // checked against.
    let rules = coerce_graphics_result_for(version, gval)?;

    Ok(Value::InlineBoxes(vec![HorzBox::Pure(
        PureHorzBox::Tabular(TabularBox {
            width: solved.width,
            height: solved.height,
            depth: Length::ZERO,
            cells: solved.cells,
            rules,
        }),
    )]))
}

// ============================================================================
// ---- gr.satyh graphics primitives -------------------------------------------
// ============================================================================

/// `bezier-to : point -> point -> point -> pre-path -> pre-path`
/// (vminst.ml:742) — appends a cubic Bézier segment (`ptS`/`ptT` control
/// points, `pt1` destination) to the pre-path's forward-accumulated `segs`.
fn prim_bezier_to(_interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
    let mut pp = as_prepath(args.pop().unwrap())?;
    let pt1 = as_point(args.pop().unwrap())?;
    let pt_t = as_point(args.pop().unwrap())?;
    let pt_s = as_point(args.pop().unwrap())?;
    pp.segs.push(PathSeg::Bezier(pt_s, pt_t, pt1));
    Ok(Value::PrePath(pp))
}

/// `close-with-bezier : point -> point -> pre-path -> path` (vminst.ml:787)
/// — closes the subpath with a cubic Bézier back to its start (`ptS`/`ptT`
/// control points; the destination is always the subpath's own `start`, per
/// `Closing::Bezier`'s doc comment).
fn prim_close_with_bezier(_interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
    let pp = as_prepath(args.pop().unwrap())?;
    let pt_t = as_point(args.pop().unwrap())?;
    let pt_s = as_point(args.pop().unwrap())?;
    Ok(Value::Path(Path {
        subpaths: vec![Subpath {
            start: pp.start,
            segs: pp.segs,
            closing: Closing::Bezier(pt_s, pt_t),
        }],
    }))
}

/// `shift-path : point -> path -> path` (vminst.ml:663) — translate every
/// point of the path by the given vector (`rustyfi_backend::shift_path`).
fn prim_shift_path(_interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
    let path = as_path(args.pop().unwrap())?;
    let v = as_point(args.pop().unwrap())?;
    Ok(Value::Path(shift_path(v, &path)))
}

/// `linear-transform-path : float -> float -> float -> float -> path ->
/// path` (vminst.ml:678) — apply the 2x2 matrix `(a, b, c, d)` to every
/// point of the path (`rustyfi_backend::linear_transform_path`).
fn prim_linear_transform_path(
    _interp: &mut Interp,
    mut args: Vec<Value>,
) -> Result<Value, EvalError> {
    let path = as_path(args.pop().unwrap())?;
    let d = as_float(args.pop().unwrap())?;
    let c = as_float(args.pop().unwrap())?;
    let b = as_float(args.pop().unwrap())?;
    let a = as_float(args.pop().unwrap())?;
    Ok(Value::Path(linear_transform_path((a, b, c, d), &path)))
}

/// `shift-graphics : point -> graphics -> graphics` (vminst.ml:2451) —
/// translate every point of the graphics element by the given vector.
fn prim_shift_graphics(_interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
    let g = as_graphics(args.pop().unwrap())?;
    let v = as_point(args.pop().unwrap())?;
    Ok(Value::Graphics(shift_graphics(v, &g)))
}

/// `linear-transform-graphics : float -> float -> float -> float -> graphics
/// -> graphics` (vminst.ml:2432). **Eager, unlike upstream**:
/// `graphicD.ml`'s `make_linear_trans` lazily wraps the element in a
/// `LinearTrans` node, deferring the matrix to a PDF `cm` operator at render
/// time — which also scales any wrapped `Stroke`/`DashedStroke`'s effective
/// line width (width is specified in the pre-transform coordinate space).
/// This port instead rewrites every point up front (a pure coordinate map,
/// no PDF change needed) and leaves `width` untouched, so
/// a non-uniform `scale-graphics` (`gr.satyh`) will NOT scale a stroke's
/// line width the way upstream does — invisible for pure rotation
/// (`rotate-graphics`, orthonormal, preserves lengths) and for `Fill`, which
/// is the only `GraphicsElem` shape any bundled package actually
/// strokes-then-scales.
fn prim_linear_transform_graphics(
    _interp: &mut Interp,
    mut args: Vec<Value>,
) -> Result<Value, EvalError> {
    let g = as_graphics(args.pop().unwrap())?;
    let d = as_float(args.pop().unwrap())?;
    let c = as_float(args.pop().unwrap())?;
    let b = as_float(args.pop().unwrap())?;
    let a = as_float(args.pop().unwrap())?;
    Ok(Value::Graphics(linear_transform_graphics((a, b, c, d), &g)))
}

/// `get-graphics-bbox : graphics -> point * point` (v0.0.6 vminst.ml:2466)
/// — the v006 fork side. `.unwrap_or(…)` is UNREACHABLE under 0.0.6 (no
/// 0.0.6-visible constructor produces `Group`/`Clip`, so `graphics_bbox`
/// never returns `None` here); documented rather than `.expect`ed so a
/// future faithful `Group`/`Clip` leak (a bug) fails soft instead of
/// panicking.
fn prim_get_graphics_bbox_v006(
    _interp: &mut Interp,
    mut args: Vec<Value>,
) -> Result<Value, EvalError> {
    let g = as_graphics(args.pop().unwrap())?;
    let (pmin, pmax) =
        graphics_bbox(&g).unwrap_or(((Length::ZERO, Length::ZERO), (Length::ZERO, Length::ZERO)));
    Ok(Value::Tuple(vec![
        make_point_value(pmin),
        make_point_value(pmax),
    ]))
}

/// `get-graphics-bbox : graphics -> option (point * point)` (dev-0-1-0
/// vminst.ml:2301) — the v01 fork side: `graphics` is a collection,
/// so an empty `unite-graphics []` (or an empty `Clip`'s contents-blind
/// bbox is still `Some`, but an empty `Group` folds to nothing)
/// legitimately has no bbox — surfaced as the SATySFi `option` variant,
/// the `probe-cross-reference` building pattern.
fn prim_get_graphics_bbox_v01(
    _interp: &mut Interp,
    mut args: Vec<Value>,
) -> Result<Value, EvalError> {
    let g = as_graphics(args.pop().unwrap())?;
    Ok(match graphics_bbox(&g) {
        Some((pmin, pmax)) => Value::Ctor(
            "Some".to_string(),
            Some(Box::new(Value::Tuple(vec![
                make_point_value(pmin),
                make_point_value(pmax),
            ]))),
        ),
        None => Value::Ctor("None".to_string(), None),
    })
}

/// `unite-graphics : list graphics -> graphics` (dev-0-1-0 vminst.ml:3119)
/// — `GraphicD.concat` = `List.concat`, ported as the `Group` container.
/// `unite-graphics []` is legal and yields the
/// empty collection (the `None`-bbox witness `get-graphics-bbox` exercises
/// above).
fn prim_unite_graphics(_interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
    let items = as_list(args.pop().unwrap())?;
    let mut elems = Vec::with_capacity(items.len());
    for it in items {
        elems.push(as_graphics(it)?);
    }
    Ok(Value::Graphics(GraphicsElem::Group(elems)))
}

/// `clip-graphics-by-path : path -> graphics -> graphics` (dev-0-1-0
/// vminst.ml:3105) — `GraphicD.make_clip gr pathlst` = `Clip(paths, gr)`;
/// the port's single-element `g` (possibly itself a `Group`) IS the
/// collection upstream's `gr` argument names.
fn prim_clip_graphics_by_path(
    _interp: &mut Interp,
    mut args: Vec<Value>,
) -> Result<Value, EvalError> {
    let g = as_graphics(args.pop().unwrap())?;
    let path = as_path(args.pop().unwrap())?;
    Ok(Value::Graphics(GraphicsElem::Clip(path, vec![g])))
}

/// `get-path-bbox : path -> point * point` (vminst.ml:696
/// `PathGetBoundingBox`) — `rustyfi_backend::path_bbox` (see that function's
/// doc comment for the exact cubic-extrema policy shared with
/// `get-graphics-bbox`).
fn prim_get_path_bbox(_interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
    let path = as_path(args.pop().unwrap())?;
    let (pmin, pmax) = path_bbox(&path);
    Ok(Value::Tuple(vec![
        make_point_value(pmin),
        make_point_value(pmax),
    ]))
}

/// `dashed-stroke : length -> (length*length*length) -> color -> path ->
/// graphics` (vminst.ml:2414) — width first, then the dash pattern, then
/// color, then path (mirrors `stroke`'s argument order with one extra
/// dash-pattern argument inserted).
fn prim_dashed_stroke(_interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
    let path = as_path(args.pop().unwrap())?;
    let color = as_color(args.pop().unwrap())?;
    let dash = as_dash(args.pop().unwrap())?;
    let wid = as_length(args.pop().unwrap())?;
    Ok(Value::Graphics(GraphicsElem::DashedStroke(
        wid, dash, color, path,
    )))
}

/// `draw-text : point -> inline-boxes -> graphics` (vminst.ml:2363
/// `PrimitiveDrawText`) — FAITHFUL: lays the run out at natural width
/// (upstream `LineBreak.natural`; here `natural_metrics` + `fit_cell` at that
/// width, so slack is 0 and every box keeps its natural advance) and stores
/// the placed run in `GraphicsElem::Text`. Also resolves any
/// `inline-graphics-outer` marker the run carries (`resolve_outer_graphics_
/// in_contents` — width 0 there, since slack is 0 at natural width, upstream
/// identical: `widperfil = 0`).
fn prim_draw_text(interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
    let ib = as_inline_boxes(args.pop().unwrap())?;
    let pt = as_point(args.pop().unwrap())?;
    let (width, height, depth) = natural_metrics(&ib);
    let (mut contents, _, _) = fit_cell(ib, width);
    resolve_outer_graphics_in_contents(interp, &mut contents)?;
    Ok(Value::Graphics(GraphicsElem::Text {
        pt,
        contents,
        width,
        height,
        depth,
        transform: None,
    }))
}

// ============================================================================
// ---- pervasives.satyh prims -------------------
// ============================================================================

/// `get-natural-metrics : inline-boxes -> length * length * length`
/// (vminst.ml:2020 `PrimitiveGetNaturalMetrics`) — FAITHFUL: delegates to
/// `rustyfi_backend::natural_metrics` (see that function's doc comment for
/// why no depth sign-flip is needed here, unlike upstream).
fn prim_get_natural_metrics(
    _interp: &mut Interp,
    mut args: Vec<Value>,
) -> Result<Value, EvalError> {
    let ib = as_inline_boxes(args.pop().unwrap())?;
    let (width, height, depth) = natural_metrics(&ib);
    Ok(Value::Tuple(vec![
        Value::Length(width),
        Value::Length(height),
        Value::Length(depth),
    ]))
}

/// Build the atomic `PureHorzBox::Frame` for `inline-frame-outer`/`-inner`
/// (upstream keeps both atomic too; `-breakable` is transparent instead, see
/// [`prim_inline_frame_breakable`]): fit `inner` at its natural width
/// (`fit_cell` — the same
/// no-Context fit tabular cells use), pad the fitted run by `pads`, intern
/// `deco` into `interp.decos`. `deco` is fired lang-side, after
/// placement, by `fire_hooks`/`fire_inline_frame` — this constructor never
/// calls it.
fn make_inline_frame(
    interp: &mut Interp,
    version: RustyfiVersion,
    (pad_l, pad_r, pad_t, pad_b): (Length, Length, Length, Length),
    deco: Value,
    inner: Vec<HorzBox>,
) -> Value {
    let (w, _, _) = natural_metrics(&inner);
    let (contents, height, depth) = fit_cell(inner, w);
    let contents = contents.into_iter().map(|(x, b)| (x + pad_l, b)).collect();
    let id = DecoId(interp.decos.len());
    // `version` is the CALLING code's generation, threaded in by the
    // per-version prim rows below — fire time is a post-page-break pass with
    // no version context of its own, so this is the only moment the answer
    // is available. See `DecoEntry`'s doc comment.
    interp.decos.push(DecoEntry::Inline { deco, version });
    Value::InlineBoxes(vec![HorzBox::Pure(PureHorzBox::Frame {
        width: pad_l + w + pad_r,
        height: height + pad_t,
        depth: depth + pad_b,
        deco: id,
        contents,
    })])
}

/// `inline-frame-outer : paddings -> deco -> inline-boxes -> inline-boxes`
/// (vminst.ml:1787 `BackendOuterFrame`) — FAITHFUL: builds the atomic
/// `PureHorzBox::Frame`; see [`make_inline_frame`]. Upstream's
/// outer/inner distinction is glue participation in the enclosing line
/// (`PHGOuterFrame` vs `PHGInnerFrame`), which this atomic box model
/// collapses — both this and [`prim_inline_frame_inner`] build the exact
/// same box.
fn prim_inline_frame_outer(
    interp: &mut Interp,
    version: RustyfiVersion,
    mut args: Vec<Value>,
) -> Result<Value, EvalError> {
    let inner = as_inline_boxes(args.pop().unwrap())?;
    let deco = args.pop().unwrap();
    let pads = as_paddings(args.pop().unwrap())?;
    Ok(make_inline_frame(interp, version, pads, deco, inner))
}

/// `inline-frame-inner : paddings -> deco -> inline-boxes -> inline-boxes`
/// (vminst.ml:1807 `BackendInnerFrame`) — same construction as
/// [`prim_inline_frame_outer`]; see that function's doc comment for the
/// outer/inner distinction this atomic model collapses.
fn prim_inline_frame_inner(
    interp: &mut Interp,
    version: RustyfiVersion,
    mut args: Vec<Value>,
) -> Result<Value, EvalError> {
    let inner = as_inline_boxes(args.pop().unwrap())?;
    let deco = args.pop().unwrap();
    let pads = as_paddings(args.pop().unwrap())?;
    Ok(make_inline_frame(interp, version, pads, deco, inner))
}

/// `set-manual-rising : length -> context -> context` (vminst.ml:1661
/// `PrimitiveSetManualRising`) — FAITHFUL store into
/// `Context::manual_rising`, the same shape as `set-font-size`/
/// `set-leading` above. Read by `text_to_boxes`'s `flush_word`, which adds
/// it to the script font's own baseline raise; the default is
/// `Length::ZERO`, so a document that never calls this is unaffected.
fn prim_set_manual_rising(_interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
    let ctx = as_context(args.pop().unwrap())?;
    let rising = as_length(args.pop().unwrap())?;
    Ok(Value::Context(Box::new(Context {
        manual_rising: rising,
        ..ctx
    })))
}

/// `script-guard : script -> inline-boxes -> inline-boxes` (vminst.ml:1908
/// `BackendScriptGuard`).
///
/// STAND-IN: upstream wraps `hblst` in a `HorzScriptGuard` that tells the
/// line breaker which script to assume at each edge, for inter-script
/// spacing rules (`lineBreak.ml`'s script-boundary handling). This port's
/// line breaker has no script-aware spacing at all yet, so this is the
/// identity function: the `script` argument is accepted (so callers like
/// pervasives.satyh's `\SATySFi`/`\LaTeX`/`\TeX` type-check and run) and
/// discarded.
fn prim_script_guard(_interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
    let ib = as_inline_boxes(args.pop().unwrap())?;
    let _script = args.pop().unwrap();
    Ok(Value::InlineBoxes(ib))
}

/// Unwrap `inline-boxes`' `Vec<HorzBox>` down to the bare `Vec<PureHorzBox>`
/// a `PureHorzBox::Discretionary` slot stores (mirrors `prim_line_break`'s
/// identical unwrap, linebreak.rs's only other consumer of this shape).
fn into_pure(boxes: Vec<HorzBox>) -> Vec<PureHorzBox> {
    boxes.into_iter().map(|HorzBox::Pure(p)| p).collect()
}

/// `discretionary : int -> inline-boxes -> inline-boxes -> inline-boxes ->
/// inline-boxes` (vminst.ml:1969 `BackendDiscretionary`), params `(pb,
/// hblst0, hblst1, hblst2)` — FAITHFUL: builds the same
/// `PureHorzBox::Discretionary` the UAX#14 line breaker already produces
/// internally. `hblst0` (`no_break`) renders when this point is NOT chosen
/// as a line break; `hblst1`/`hblst2` (`pre_break`/`post_break`) render at
/// the end/start of the two lines a break here would produce.
fn prim_discretionary(_interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
    let post_break = as_inline_boxes(args.pop().unwrap())?;
    let pre_break = as_inline_boxes(args.pop().unwrap())?;
    let no_break = as_inline_boxes(args.pop().unwrap())?;
    let penalty = as_int(args.pop().unwrap())?;
    Ok(Value::InlineBoxes(vec![HorzBox::Pure(
        PureHorzBox::Discretionary {
            penalty: penalty.clamp(i32::MIN as i64, i32::MAX as i64) as i32,
            pre_break: into_pure(pre_break),
            post_break: into_pure(post_break),
            no_break: into_pure(no_break),
        },
    )]))
}

/// `get-axis-height : context -> length` (vminst.ml:1739
/// `PrimitiveGetAxisHeight`), needed by `picture.satyh`'s `Picture.node`
/// (Tier-2 decoration/graphics wave) — centers text vertically around the
/// math axis.
///
/// FAITHFUL: reads `axis_height` from `ctx.math_font`'s OpenType MATH
/// table via `MathC` (`FontInfo.get_axis_height mfabbrev fontsize`), falling
/// back to a fixed `0.25` ratio of `ctx.font_size` (`pervasives.satyh`'s
/// `\SATySFi`/`\LaTeX` manual-rising ratio) whenever the font has no MATH
/// table — so base-14/non-math output is unchanged.
fn prim_get_axis_height(interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
    let ctx = as_context(args.pop().unwrap())?;
    let mc = MathC::of(interp, &ctx);
    Ok(Value::Length(mc.axis(ctx.font_size)))
}

// ============================================================================
// ---- page-break hooks + cross-references -----------------------------------
// ============================================================================

/// `hook-page-break : (page-break-info -> point -> unit) -> inline-boxes`
/// (vminstdef.yaml:576). Pushes the closure argument onto `interp.hooks`
/// (the lang-side table `fire_hooks` reads back after placement) and
/// returns an inline box carrying only the opaque `HookId` — exactly
/// `prim_load_image`'s shape (`ImageId`/`interp.images`), applied to a
/// deferred *computation* instead of a resource. The backend places this
/// box like any other zero-width content and never sees the closure.
fn prim_hook_page_break(interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
    let closure = args.pop().unwrap();
    let id = HookId(interp.hooks.len());
    interp.hooks.push(closure);
    Ok(Value::InlineBoxes(vec![HorzBox::Pure(
        PureHorzBox::HookPageBreak { id },
    )]))
}

/// `hook-page-break-block : (page-break-info -> point -> unit) ->
/// block-boxes` (vminst.ml:632 `BackendHookPageBreakBlock`) — the
/// block-level analog of `prim_hook_page_break` above, FAITHFUL: same
/// `interp.hooks` push, same opaque `HookId`, but wrapped in a
/// `VertBox::HookPageBreak` marker instead of an inline box. `chop_page`/
/// `place_block_at` (rustyfi-backend) place it as a zero-height
/// `PlacedLine` carrying the SAME `PureHorzBox::HookPageBreak` wrapper the
/// inline primitive uses, so `fire_hooks` (lib.rs) fires it through the
/// exact same scan with no changes of its own.
fn prim_hook_page_break_block(
    interp: &mut Interp,
    mut args: Vec<Value>,
) -> Result<Value, EvalError> {
    let closure = args.pop().unwrap();
    let id = HookId(interp.hooks.len());
    interp.hooks.push(closure);
    Ok(Value::BlockBoxes(vec![VertBox::HookPageBreak(id)]))
}

/// `register-cross-reference : string -> string -> unit` (vminstdef.yaml:1793).
/// Callable anywhere (not just from a hook) — ordinary strict primitive
/// over the shared `crossrefs` table.
fn prim_register_cross_reference(
    interp: &mut Interp,
    mut args: Vec<Value>,
) -> Result<Value, EvalError> {
    let value = as_str(args.pop().unwrap())?;
    let key = as_str(args.pop().unwrap())?;
    interp.crossrefs.borrow_mut().register(key, value);
    Ok(Value::Unit)
}

/// `get-cross-reference : string -> string option` (vminstdef.yaml:1808).
/// A miss is recorded (`CrossRefs::get`) so an unresolved forward reference
/// forces another fixpoint trial; the result surfaces as the SATySFi
/// `option` variant (`None` / `Some(string)`).
fn prim_get_cross_reference(interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
    let key = as_str(args.pop().unwrap())?;
    Ok(match interp.crossrefs.borrow_mut().get(&key) {
        Some(v) => Value::Ctor("Some".to_string(), Some(Box::new(Value::Str(v)))),
        None => Value::Ctor("None".to_string(), None),
    })
}

/// `probe-cross-reference : string -> string option` (vminst.ml:3043
/// `BackendProbeCrossReference`) — FAITHFUL: `get-cross-reference` minus the
/// miss bookkeeping (`CrossRefs::probe`, crossRef.ml:112), so a `None` here
/// never forces another fixpoint trial.
fn prim_probe_cross_reference(
    interp: &mut Interp,
    mut args: Vec<Value>,
) -> Result<Value, EvalError> {
    let key = as_str(args.pop().unwrap())?;
    Ok(match interp.crossrefs.borrow().probe(&key) {
        Some(v) => Value::Ctor("Some".to_string(), Some(Box::new(Value::Str(v)))),
        None => Value::Ctor("None".to_string(), None),
    })
}

// ============================================================================
// ---- annot.satyh's prim surface (link annotations + the frame/script
// stand-ins it needs) --------------------------------------------------------
// ============================================================================

/// `get-leftmost-script`/`get-rightmost-script : inline-boxes -> script
/// option` (vminstdef.yaml:1754/1767 `BackendGetLeftmostScript`/
/// `BackendGetRightmostScript`) — STAND-IN: upstream inspects the actual
/// Unicode script of the first/last character in `hblst`
/// (`LineBreak.get_leftmost_script`/`get_rightmost_script`), which
/// `annot.satyh`'s `\href` uses to `script-guard` the link's edges so
/// inter-script spacing isn't inserted right at the boundary. This port's
/// `PureHorzBox::InnerString` carries no per-character script tag (no
/// script-aware line breaking at all yet — `script-guard` above is already
/// an identity stand-in for the same reason), so both primitives
/// unconditionally return `None`: `\href` then takes its `None` arm
/// (`inline-nil`, no guard inserted) — a safe, honest default rather than
/// fabricating a script this port cannot actually see.
fn prim_get_leftmost_script(
    _interp: &mut Interp,
    mut args: Vec<Value>,
) -> Result<Value, EvalError> {
    let _ib = as_inline_boxes(args.pop().unwrap())?;
    Ok(Value::Ctor("None".to_string(), None))
}

/// See [`prim_get_leftmost_script`] — the rightmost-edge twin, identical
/// stand-in reasoning.
fn prim_get_rightmost_script(
    _interp: &mut Interp,
    mut args: Vec<Value>,
) -> Result<Value, EvalError> {
    let _ib = as_inline_boxes(args.pop().unwrap())?;
    Ok(Value::Ctor("None".to_string(), None))
}

/// `inline-frame-breakable : paddings -> deco-set -> inline-boxes ->
/// inline-boxes` (vminstdef.yaml:1672 `BackendOuterFrameBreakable`) —
/// FAITHFUL: upstream's `HorzFrameBreakable` is *transparent* to the
/// paragraph breaker (`lineBreak.ml:1094` threads the enclosing width map
/// straight through the frame's contents), so the frame's own glue and
/// discretionaries are break candidates of the enclosing paragraph, and
/// `cut` (`:824`) re-frames the chosen fragments one line at a time —
/// `decoS` for a frame that came out unbroken, `decoH`/`decoM`/`decoT` per
/// fragment for one that split.
///
/// This port's breaker is a flat index DP rather than upstream's recursive
/// one, so transparency is spelled by SPLICING: the contents go straight into
/// the returned box list, bracketed by a zero-width
/// [`PureHorzBox::InlineFrameMarker`] pair that `fire_hooks` walks to
/// reassemble the fragments and fire the right closure for each. The
/// horizontal paddings become `FixedEmpty` boxes inside the bracket, exactly
/// upstream's `append_horz_padding` (`lineBreak.ml:79`); the vertical ones
/// ride on the markers (which is how they still reach the line's height and
/// depth) and are re-applied per fragment at fire time.
///
/// The atomic `PureHorzBox::Frame` is NOT usable here — it fires only
/// `decoS` and, being width-rigid, can neither break nor let an interior
/// `inline-fil` stretch. It is reserved for `inline-frame-outer`/`-inner`,
/// which upstream really does keep atomic.
fn prim_inline_frame_breakable(
    interp: &mut Interp,
    version: RustyfiVersion,
    mut args: Vec<Value>,
) -> Result<Value, EvalError> {
    let inner = as_inline_boxes(args.pop().unwrap())?;
    let decoset = as_decoset(args.pop().unwrap())?;
    let (pad_l, pad_r, pad_t, pad_b) = as_paddings(args.pop().unwrap())?;
    let (_, height, depth) = natural_metrics(&inner);
    let id = DecoId(interp.decos.len());
    // `version` is the CALLING code's generation — see `make_inline_frame`'s
    // identical comment and `DecoEntry`'s doc comment.
    interp.decos.push(DecoEntry::InlineBreakable {
        pads: Paddings {
            l: pad_l,
            r: pad_r,
            t: pad_t,
            b: pad_b,
        },
        decoset,
        version,
    });
    let marker = |end| {
        HorzBox::Pure(PureHorzBox::InlineFrameMarker {
            id,
            end,
            height: height + pad_t,
            depth: depth + pad_b,
        })
    };
    let mut out = Vec::with_capacity(inner.len() + 4);
    out.push(marker(false));
    // Upstream emits both padding boxes unconditionally; a zero-width
    // `FixedEmpty` is inert everywhere in this port too, but skipping it keeps
    // the box stream (and every placed-line snapshot) unchanged for the
    // zero-padding callers, which is every bundled one.
    if pad_l != Length::ZERO {
        out.push(HorzBox::Pure(PureHorzBox::FixedEmpty { width: pad_l }));
    }
    out.extend(inner);
    if pad_r != Length::ZERO {
        out.push(HorzBox::Pure(PureHorzBox::FixedEmpty { width: pad_r }));
    }
    out.push(marker(true));
    Ok(Value::InlineBoxes(out))
}

/// `deco-set` = `Value::Tuple` of 4 closures (`(decoS, decoH, decoM,
/// decoT)`, evalUtil.ml:169 `get_decoset`) — no type check on the elements
/// themselves (they're closures, applied later by `apply_deco`).
fn as_decoset(v: Value) -> Result<[Value; 4], EvalError> {
    match v {
        Value::Tuple(vs) if vs.len() == 4 => {
            let mut it = vs.into_iter();
            let a = it.next().unwrap();
            let b = it.next().unwrap();
            let c = it.next().unwrap();
            let d = it.next().unwrap();
            Ok([a, b, c, d])
        }
        other => eval_error(format!(
            "expected a deco-set (4-tuple of decorations), got {}",
            other.type_name()
        )),
    }
}

/// 0.0.6 graphics-producing callbacks return `list graphics` (`tL tGR`);
/// 0.1's return one `graphics` collection (`tGR` — dev-0-1-0
/// `primitives.cppo.ml:75-85`). STRICT per
/// version: a 0.1 program returning a list here is a bug the type checker
/// already rejected; don't mask it with tolerant decoding. Shared by every
/// coercion site (`prim_inline_graphics`, `inline-graphics-outer`/
/// `tabular`'s `resolve_outer_graphics_in_contents`, `tabular`'s own rules
/// callback, and `apply_deco` below).
///
/// `version` is EXPLICIT rather than read off `interp.version`, and that is
/// the whole point. `interp.version` is one whole-program field, set once by
/// `lib.rs`'s `eval_document_trials`; in a cross-version program it names
/// the ENTRY document's generation, while the callback being decoded here
/// may have been written by a spliced 0.0.6 dependency. Every caller gets
/// the right answer from a place that genuinely knows it: the six carrier
/// prim bodies are registered per version
/// (`version_forked_prims!`, folded at compile time by
/// `compile.rs`'s `Ast::VersionScope` arm), and the two DEFERRED consumers
/// read the generation captured when the closure was interned
/// (`DecoEntry::version`, `Interp::outer_graphics`'s second component).
fn coerce_graphics_result_for(
    version: RustyfiVersion,
    v: Value,
) -> Result<Vec<GraphicsElem>, EvalError> {
    if version.graphics_is_collection() {
        Ok(vec![as_graphics(v)?])
    } else {
        as_list(v)?.into_iter().map(as_graphics).collect()
    }
}

/// `make_frame_deco` (evalUtil.ml:604): apply a curried
/// `point -> length -> length -> length -> graphics list` deco and coerce
/// the result. Depths here are already user-sign (nonnegative), so no
/// negate (upstream negates because ITS internal depths are nonpositive).
/// The deco closure's result is `list graphics` under v0.0.6, one `graphics`
/// collection under v0.1 — see `coerce_graphics_result`'s doc comment.
///
/// `version` is the generation the closure was CAPTURED under
/// (`DecoEntry::version`), not `interp.version`: this runs from `lib.rs`'s
/// post-page-break firing pass, which is outside every `VersionScope`
/// window, so `interp.version` there is the entry document's generation. In
/// a single-version program the two are the same value.
pub(crate) fn apply_deco(
    interp: &mut Interp,
    version: RustyfiVersion,
    deco: Value,
    pt: Point,
    w: Length,
    h: Length,
    d: Length,
) -> Result<Vec<GraphicsElem>, EvalError> {
    let v = interp.apply(deco, make_point_value(pt))?;
    let v = interp.apply(v, Value::Length(w))?;
    let v = interp.apply(v, Value::Length(h))?;
    let v = interp.apply(v, Value::Length(d))?;
    coerce_graphics_result_for(version, v)
}

/// `(length * color) option` — `register-link-to-uri`/`-to-location`'s
/// trailing border argument (vminstdef.yaml:2755/2775's `vborderopt`),
/// parsed the same way [`as_color`]/[`as_page`] read a `Value::Ctor`.
fn as_border_option(v: Value) -> Result<Option<(Length, Color)>, EvalError> {
    match v {
        Value::Ctor(name, payload) => match (name.as_str(), payload.map(|b| *b)) {
            ("None", None) => Ok(None),
            ("Some", Some(Value::Tuple(vs))) if vs.len() == 2 => {
                let mut it = vs.into_iter();
                let w = as_length(it.next().unwrap())?;
                let c = as_color(it.next().unwrap())?;
                Ok(Some((w, c)))
            }
            (other, _) => eval_error(format!(
                "expected a border option (None / Some(length * color)), got variant '{other}'"
            )),
        },
        other => eval_error(format!("expected an option, got {}", other.type_name())),
    }
}

/// `register-destination : string -> point -> unit` (vminstdef.yaml:2738) —
/// FAITHFUL: upstream `NamedDest.register` + `notify_pagebreak` collapsed
/// into one step, since our firing window (`fire_hooks`) already knows the
/// page. Errors outside that window (`annotation.ml:15`'s
/// `State.during_page_break` gate).
///
/// **ONE exception, a re-timing rather than a relaxation of the gate.** Inside
/// an eagerly-applied `inline-graphics` callback this port is running code
/// upstream would only run DURING page breaking (see `prim_inline_graphics`),
/// so refusing here would refuse a call upstream accepts. Such a call is
/// recorded in `Interp::pending_dests` instead, and the caller mints a
/// `GraphicsElem::Destination` marker from it. Outside that one window the gate
/// is unchanged: no page, no destination.
fn prim_register_destination(
    interp: &mut Interp,
    mut args: Vec<Value>,
) -> Result<Value, EvalError> {
    let (x, y) = as_point(args.pop().unwrap())?;
    let key = as_str(args.pop().unwrap())?;
    if interp.current_page.is_none() {
        if let Some(pending) = interp.pending_dests.as_mut() {
            pending.push((key, (x, y)));
            return Ok(Value::Unit);
        }
    }
    let Some(page) = interp.current_page else {
        return eval_error(
            "register-destination can only be called during page breaking \
             (from a page-break hook or a decoration)",
        );
    };
    let name = interp.dest_name(&key);
    // See `prim_register_link_to_uri`'s identical comment —
    // `register-location-frame`'s `decoR` fires this from inside a firing
    // block-frame deco.
    if let Some(deco_id) = interp.current_deco_id {
        interp.dest_decos.push((deco_id, name.clone()));
    }
    interp.destinations.push(NamedDest { page, name, x, y });
    Ok(Value::Unit)
}

/// Shared body of `register-link-to-uri` / `register-link-to-location`
/// (vminstdef.yaml:2753/2773): pops the common `point/w/h/d/border` suffix,
/// builds `annotation.ml:22`'s rect `(x, y - d, x + w, y + h)` (PDF y-up
/// points; our depths are already nonnegative), and pushes the `Annot`.
fn register_link(
    interp: &mut Interp,
    mut args: Vec<Value>,
    prim_name: &str,
    make_action: impl FnOnce(&mut Interp, String) -> AnnotAction,
) -> Result<Value, EvalError> {
    let border = as_border_option(args.pop().unwrap())?;
    let dpt = as_length(args.pop().unwrap())?;
    let hgt = as_length(args.pop().unwrap())?;
    let wid = as_length(args.pop().unwrap())?;
    let (x, y) = as_point(args.pop().unwrap())?;
    let target = as_str(args.pop().unwrap())?;
    let Some(page) = interp.current_page else {
        return eval_error(format!(
            "{prim_name} can only be called during page breaking \
             (from a page-break hook or a decoration)"
        ));
    };
    let action = make_action(interp, target);
    // Tag this link with the DecoId of whatever deco closure is currently
    // firing (set by `fire_hooks`'s two `apply_deco` call sites, `lib.rs`) —
    // `annot.satyh`'s `\href` always calls this from inside one, so
    // `current_deco_id` is `Some` for every real `\href`; a hand-built test
    // calling this prim directly (not through a firing deco) legitimately
    // leaves it `None`, and the reflow backend just won't find a Frame to
    // wrap for that link.
    if let Some(deco_id) = interp.current_deco_id {
        interp.link_decos.push((deco_id, action.clone()));
    }
    interp.annotations.push(Annot {
        page,
        rect: (x, y - dpt, x + wid, y + hgt),
        action,
        border,
    });
    Ok(Value::Unit)
}

/// `register-link-to-uri : string -> point -> length -> length -> length ->
/// (length * color) option -> unit` (vminstdef.yaml:2753
/// `BackendRegisterLinkToUri`) — FAITHFUL: see [`register_link`].
fn prim_register_link_to_uri(interp: &mut Interp, args: Vec<Value>) -> Result<Value, EvalError> {
    register_link(interp, args, "register-link-to-uri", |_, uri| {
        AnnotAction::Uri(uri)
    })
}

/// `register-link-to-location : string -> point -> length -> length ->
/// length -> (length * color) option -> unit` (vminstdef.yaml:2773
/// `BackendRegisterLinkToLocation`) — FAITHFUL: same shape as
/// [`prim_register_link_to_uri`], but upstream's action is
/// `GotoName(NamedDest.get name)` — the key goes through the SAME name table
/// as [`prim_register_destination`], so a link to a not-(yet-)registered
/// destination still mints a stable name (a viewer no-ops on it), exactly
/// like upstream.
fn prim_register_link_to_location(
    interp: &mut Interp,
    args: Vec<Value>,
) -> Result<Value, EvalError> {
    register_link(interp, args, "register-link-to-location", |interp, key| {
        AnnotAction::GotoName(interp.dest_name(&key))
    })
}

// ============================================================================
// The faithful `Value::Math` primitive layer `math.satyh` is built
// out of. Every `math-*` primitive here builds or consumes a
// `Value::Math(Rc<Vec<Math>>)` (`value.rs`'s `Math`); a `math`-typed
// argument may equally arrive as a `Value::MathText` (a `${…}` literal —
// `as_math` accepts either, reflecting a `MathText`'s `MathElem` tree into
// `Math` nodes on the fly, see below).
// ============================================================================

use crate::value::{Math, MathElement, MathVariantStyle};

/// `math-class` = `Value::Ctor("MathOrd"|"MathBin"|…, None)` — mirrors
/// `as_color`/`as_page`'s shape exactly.
fn as_math_kind(v: Value) -> Result<MathKind, EvalError> {
    match v {
        Value::Ctor(name, None) => match name.as_str() {
            "MathOrd" => Ok(MathKind::Ord),
            "MathBin" => Ok(MathKind::Bin),
            "MathRel" => Ok(MathKind::Rel),
            "MathOp" => Ok(MathKind::Op),
            "MathPunct" => Ok(MathKind::Punct),
            "MathOpen" => Ok(MathKind::Open),
            "MathClose" => Ok(MathKind::Close),
            "MathPrefix" => Ok(MathKind::Prefix),
            "MathInner" => Ok(MathKind::Inner),
            other => eval_error(format!("expected a math-class constructor, got '{other}'")),
        },
        other => eval_error(format!("expected a math-class, got {}", other.type_name())),
    }
}

/// `math-char-class` = `Value::Ctor("MathItalic"|…, None)`, resolved to the
/// backend's [`MathCharClass`] (see `value.rs`'s
/// `Math::ChangeCharClass` doc comment).
fn as_math_char_class(v: Value) -> Result<MathCharClass, EvalError> {
    match v {
        Value::Ctor(name, None) => match name.as_str() {
            "MathItalic" => Ok(MathCharClass::Italic),
            "MathBoldItalic" => Ok(MathCharClass::BoldItalic),
            "MathRoman" => Ok(MathCharClass::Roman),
            "MathBoldRoman" => Ok(MathCharClass::BoldRoman),
            "MathScript" => Ok(MathCharClass::Script),
            "MathBoldScript" => Ok(MathCharClass::BoldScript),
            "MathFraktur" => Ok(MathCharClass::Fraktur),
            "MathBoldFraktur" => Ok(MathCharClass::BoldFraktur),
            "MathDoubleStruck" => Ok(MathCharClass::DoubleStruck),
            // V0_1-only registration — these 5
            // ctor names are only ever declared by `builtin_variants` under
            // V0_1, so under V0_0 this arm is simply never reached: the
            // ctor name itself is rejected earlier, at typecheck, as
            // unknown.
            "MathSansSerif" => Ok(MathCharClass::SansSerif),
            "MathBoldSansSerif" => Ok(MathCharClass::BoldSansSerif),
            "MathItalicSansSerif" => Ok(MathCharClass::ItalicSansSerif),
            "MathBoldItalicSansSerif" => Ok(MathCharClass::BoldItalicSansSerif),
            "MathTypewriter" => Ok(MathCharClass::Typewriter),
            other => eval_error(format!(
                "expected a math-char-class constructor, got '{other}'"
            )),
        },
        other => eval_error(format!(
            "expected a math-char-class, got {}",
            other.type_name()
        )),
    }
}

/// `math-variant-char`'s 9-field style record (`value.rs`'s
/// `MathVariantStyle`; `prim_types::t_math_variant_style`'s runtime
/// counterpart).
fn as_math_variant_style(v: Value) -> Result<MathVariantStyle, EvalError> {
    match v {
        Value::Record(mut fields) => {
            let mut take = |label: &str| -> Result<String, EvalError> {
                match fields.remove(label) {
                    Some(v) => as_str(v),
                    None => eval_error(format!(
                        "math-variant-char style record missing field '{label}'"
                    )),
                }
            };
            Ok(MathVariantStyle {
                italic: take("italic")?,
                bold_italic: take("bold-italic")?,
                roman: take("roman")?,
                bold_roman: take("bold-roman")?,
                script: take("script")?,
                bold_script: take("bold-script")?,
                fraktur: take("fraktur")?,
                bold_fraktur: take("bold-fraktur")?,
                double_struck: take("double-struck")?,
            })
        }
        other => eval_error(format!(
            "expected a math-variant-char style record, got {}",
            other.type_name()
        )),
    }
}

/// A `math` argument: either an already-faithful `Value::Math` (built by
/// another `math-*` primitive), or a `${…}` literal `Value::MathText`,
/// reflected into `Math` nodes on the fly via [`reflect_math_elem`] — see
/// `value.rs`'s `Value::Math` doc comment for why both are interchangeable.
fn as_math(interp: &mut Interp, v: Value) -> Result<Rc<Vec<Math>>, EvalError> {
    match v {
        Value::Math(m) => Ok(m),
        Value::MathText { elems, env } => {
            let mut out = Vec::new();
            for e in elems.iter() {
                reflect_math_elem(interp, e, &env, &mut out)?;
            }
            Ok(Rc::new(out))
        }
        other => eval_error(format!("expected math, got {}", other.type_name())),
    }
}

/// Reflect one elaborated `${…}` literal `MathElem` (a fused,
/// math-class-free form) into zero-or-more faithful `Math` atoms, pushed
/// onto `out` — the "less churn" resolution:
/// `MathElem` stays the fast path for a bare `${x^2}` in prose
/// (`read_inline`'s `EmbedMath` arm, untouched), and only gets reflected
/// into `Value::Math` at a command/primitive boundary (here — whenever a
/// `${…}` literal is passed where a faithful `math` value is expected).
/// `Cmd`/`Embed` are resolved by actually evaluating them against `env` (the
/// literal's own captured environment) and recursively reflecting/flattening
/// the result — the "Embed of a `#…` program value that itself
/// evaluates to math" case.
fn reflect_math_elem(
    interp: &mut Interp,
    elem: &MathElem,
    env: &Env,
    out: &mut Vec<Math>,
) -> Result<(), EvalError> {
    match elem {
        MathElem::Chars(s) => {
            // One atom per MATHCHAR token ("one atom per run" —
            // the lexer already grouped a symbol run or a single latin
            // digit/letter into `s`); class + codepoint remap are both
            // deferred to `layout_math_atom`'s `VariantCharPending` arm,
            // where `Context::math_class_map`/`math_variant_char_map` and
            // the current font are available.
            out.push(Math::Pure(MathElement::VariantCharPending(s.clone())));
            Ok(())
        }
        MathElem::Group(elems) => {
            for e in elems {
                reflect_math_elem(interp, e, env, out)?;
            }
            Ok(())
        }
        MathElem::Sub(base, script) => {
            let mut base_v = Vec::new();
            reflect_math_elem(interp, base, env, &mut base_v)?;
            let mut script_v = Vec::new();
            for e in script {
                reflect_math_elem(interp, e, env, &mut script_v)?;
            }
            out.push(Math::Sub(base_v, script_v));
            Ok(())
        }
        MathElem::Sup(base, script) => {
            let mut base_v = Vec::new();
            reflect_math_elem(interp, base, env, &mut base_v)?;
            let mut script_v = Vec::new();
            for e in script {
                reflect_math_elem(interp, e, env, &mut script_v)?;
            }
            out.push(Math::Sup(base_v, script_v));
            Ok(())
        }
        MathElem::Primes(base, n) => {
            let mut base_v = Vec::new();
            reflect_math_elem(interp, base, env, &mut base_v)?;
            let primes: String = std::iter::repeat('\u{2032}').take(*n).collect();
            out.push(Math::Sup(
                base_v,
                vec![Math::Pure(MathElement::Char {
                    class: MathKind::Ord,
                    big: false,
                    chars: primes,
                })],
            ));
            Ok(())
        }
        MathElem::Cmd { cmd, args, .. } => {
            let mut v = cmd.run(env, interp)?;
            for arg in args {
                // `arg.opts` is always empty here — the math-mode application
                // grammar has no `?(l=e)` bundle form (see `MathElem::Cmd`'s
                // doc comment, `ast.rs`) — but fold through `apply_with_opts`
                // uniformly with `read_inline`/`read_block` regardless.
                let mut opt_vals = Vec::with_capacity(arg.opts.len());
                for (label, e) in &arg.opts {
                    opt_vals.push((label.clone(), e.run(env, interp)?));
                }
                let arg_v = arg.arg.run(env, interp)?;
                v = interp.apply_with_opts(v, opt_vals, arg_v)?;
            }
            let m = as_math(interp, v)?;
            out.extend(m.iter().cloned());
            Ok(())
        }
        MathElem::Embed { expr, span: _ } => {
            let v = expr.run(env, interp)?;
            let m = as_math(interp, v)?;
            out.extend(m.iter().cloned());
            Ok(())
        }
    }
}

fn single_math(m: Math) -> Value {
    Value::Math(Rc::new(vec![m]))
}

// ============================================================================
// V0_1's `math-text`/`math-boxes` split + `read-math`.
// Everything below is additive and V0_1-only — no 0.0.6 path calls any of
// this (`as_math`/`reflect_math_elem`/`single_math` above stay byte-
// identical and untouched).
// ============================================================================

fn single_math_boxes(m: Math) -> Value {
    Value::MathBoxes(Rc::new(vec![m]))
}

/// V0_1 strict `math-boxes` extractor: accepts only `Value::MathBoxes` — a
/// `math-text` literal reaching a V0_1 `math-*` primitive is a genuine 0.1
/// type error (well-typed programs never hit this; it's the runtime
/// fallback for a call built by hand, e.g. from a unit test).
fn as_math_boxes(v: Value) -> Result<Rc<Vec<Math>>, EvalError> {
    match v {
        Value::MathBoxes(m) => Ok(m),
        other => eval_error(format!(
            "expected math-boxes, got {} (V0_1: math-text and math-boxes \
             are distinct types — bridge with `read-math`)",
            other.type_name()
        )),
    }
}

/// V0_1 strict `math-text` extractor: accepts only `Value::MathText`,
/// returning its elements together with the environment they were captured
/// under (needed to evaluate any `#x` embed / math-command lookup inside).
fn as_math_text(v: Value) -> Result<(Rc<Vec<MathElem>>, Env), EvalError> {
    match v {
        Value::MathText { elems, env } => Ok((elems, env)),
        other => eval_error(format!("expected math-text, got {}", other.type_name())),
    }
}

/// `option math-text` extractor (`None`/`Some math-text`) — `%math-attach-
/// scripts`' sub/sup arguments.
fn as_option_math_text(v: Value) -> Result<Option<(Rc<Vec<MathElem>>, Env)>, EvalError> {
    match v {
        Value::Ctor(name, None) if name == "None" => Ok(None),
        Value::Ctor(name, Some(payload)) if name == "Some" => {
            let (elems, env) = as_math_text(*payload)?;
            Ok(Some((elems, env)))
        }
        other => eval_error(format!(
            "expected an option (None/Some), got {}",
            other.type_name()
        )),
    }
}

/// Wrap a raw (ambient-`env`-sharing) script `MathElem` slice as an `option
/// math-text` VALUE — `Cmd`'s uniform V0_1 calling convention always
/// passes its command's sub/sup arguments this way, never pre-reflected.
fn option_math_text_value(opt: Option<&[MathElem]>, env: &Env) -> Value {
    match opt {
        None => Value::Ctor("None".to_string(), None),
        Some(elems) => Value::Ctor(
            "Some".to_string(),
            Some(Box::new(Value::MathText {
                elems: Rc::new(elems.to_vec()),
                env: env.clone(),
            })),
        ),
    }
}

/// `math-char-class` ctor-name mapper — the inverse of `as_math_char_class`
/// (above), used by `get-math-char-class` and by `set-math-variant-char`'s
/// V0_1 body (which must build a `math-char-class` VALUE to feed the
/// caller's selector closure).
fn math_char_class_ctor_name(c: MathCharClass) -> &'static str {
    match c {
        MathCharClass::Italic => "MathItalic",
        MathCharClass::BoldItalic => "MathBoldItalic",
        MathCharClass::Roman => "MathRoman",
        MathCharClass::BoldRoman => "MathBoldRoman",
        MathCharClass::Script => "MathScript",
        MathCharClass::BoldScript => "MathBoldScript",
        MathCharClass::Fraktur => "MathFraktur",
        MathCharClass::BoldFraktur => "MathBoldFraktur",
        MathCharClass::DoubleStruck => "MathDoubleStruck",
        MathCharClass::SansSerif => "MathSansSerif",
        MathCharClass::BoldSansSerif => "MathBoldSansSerif",
        MathCharClass::ItalicSansSerif => "MathItalicSansSerif",
        MathCharClass::BoldItalicSansSerif => "MathBoldItalicSansSerif",
        MathCharClass::Typewriter => "MathTypewriter",
    }
}

fn math_char_class_value(c: MathCharClass) -> Value {
    Value::Ctor(math_char_class_ctor_name(c).to_string(), None)
}

/// Port of `dev-0-1-0 src/frontend/context.ml:52-68`: bump `ctx`'s
/// `math_script_level` and scale `font_size`
/// accordingly. `Base -> Script`: scale by the font's MATH-table
/// `script_scale_down` (fallback `0.7`, consistent with the engine's other
/// fixed-fraction fallbacks). `Script -> ScriptScript`: scale by
/// `script_script_scale_down / script_scale_down` (fallback `5.0/7.0`).
/// `ScriptScript`: no-op — saturates at the deepest level, matching
/// upstream (no `ScriptScriptScript`).
fn enter_script(interp: &Interp, ctx: &Context) -> Context {
    let mc = MathC::of(interp, ctx);
    let (scale, next_level) = match ctx.math_script_level {
        MathScriptLevel::Base => (
            mc.c.map(|c| c.script_scale_down).unwrap_or(0.7),
            MathScriptLevel::Script,
        ),
        MathScriptLevel::Script => (
            mc.c.map(|c| c.script_script_scale_down / c.script_scale_down)
                .unwrap_or(5.0 / 7.0),
            MathScriptLevel::ScriptScript,
        ),
        MathScriptLevel::ScriptScript => return ctx.clone(),
    };
    Context {
        font_size: ctx.font_size * scale,
        math_script_level: next_level,
        ..ctx.clone()
    }
}

/// Flatten a `Sub`/`Sup` `MathElem`'s (at most two-deep) nesting into `(base,
/// sub_opt, sup_opt)` — `elaborate.rs::fold_math_scripts` always builds a
/// both-scripts element as `Sup(Box::new(Sub(base, sub)), sup)` regardless
/// of source order (`x_a^b` and `x^b_a` both fold this way), so a bare
/// `Sub`/`Sup` and the fused two-level shape are the only cases to handle.
/// `elem` MUST be `MathElem::Sub` or `MathElem::Sup` — every caller already
/// matched on that.
fn flatten_math_scripts(elem: &MathElem) -> (&MathElem, Option<&[MathElem]>, Option<&[MathElem]>) {
    match elem {
        MathElem::Sup(base, sup) => match base.as_ref() {
            MathElem::Sub(inner, sub) => {
                (inner.as_ref(), Some(sub.as_slice()), Some(sup.as_slice()))
            }
            _ => (base.as_ref(), None, Some(sup.as_slice())),
        },
        MathElem::Sub(base, sub) => (base.as_ref(), Some(sub.as_slice()), None),
        _ => unreachable!("flatten_math_scripts called on a non-Sub/Sup MathElem"),
    }
}

/// `attach_scripts` — mirrors upstream's
/// `append_sub_and_super_scripts` + its `enter_script` iteration
/// (`evaluator.cppo.ml:901-904`): reflects `sub_opt`/`sup_opt` (each an
/// already-extracted math-text payload — an ambient-env script slice for
/// the `reflect_scripted_v01` caller, or a genuine runtime `Value::MathText`
/// for the `%math-attach-scripts` primitive caller, both the SAME shape)
/// under `enter_script(interp, ctx)` — so commands *inside* a script observe
/// script-level context — then wraps `Math::Sub`/`Math::Sup` around `base`.
/// Both scripts present wraps as `Sup(Sub(base, sub), sup)`, matching the
/// shape `layout_math_atom`'s `check_subscript` already knows how to merge.
fn attach_scripts(
    interp: &mut Interp,
    ctx: &Context,
    base: Vec<Math>,
    sub_opt: Option<(Rc<Vec<MathElem>>, Env)>,
    sup_opt: Option<(Rc<Vec<MathElem>>, Env)>,
) -> Result<Vec<Math>, EvalError> {
    if sub_opt.is_none() && sup_opt.is_none() {
        return Ok(base);
    }
    let script_ctx = enter_script(interp, ctx);
    let mut cur = base;
    if let Some((elems, senv)) = sub_opt {
        let mut sub_v = Vec::new();
        for e in elems.iter() {
            reflect_math_elem_v01(interp, &script_ctx, e, &senv, &mut sub_v)?;
        }
        cur = vec![Math::Sub(cur, sub_v)];
    }
    if let Some((elems, senv)) = sup_opt {
        let mut sup_v = Vec::new();
        for e in elems.iter() {
            reflect_math_elem_v01(interp, &script_ctx, e, &senv, &mut sup_v)?;
        }
        cur = vec![Math::Sup(cur, sup_v)];
    }
    Ok(cur)
}

/// One base `MathElem` (already stripped of any wrapping `Sub`/`Sup`) plus
/// its (possibly absent) `sub`/`sup` script slices — the shared tail of
/// `reflect_math_elem_v01`'s `Sub`/`Sup` arm (after flattening) AND its bare
/// `Cmd` arm (`sub = sup = None`). `base` a `Cmd`: route ctx+sub+sup into
/// the application per the uniform V0_1 calling convention — a
/// SEPARATE math-command value shape does not exist in this port, so every
/// V0_1 math command, scripted or not, is applied exactly this way. `base`
/// anything else: reflect it plainly, then `attach_scripts`.
fn reflect_scripted_v01(
    interp: &mut Interp,
    ctx: &Context,
    base: &MathElem,
    sub: Option<&[MathElem]>,
    sup: Option<&[MathElem]>,
    env: &Env,
    out: &mut Vec<Math>,
) -> Result<(), EvalError> {
    if let MathElem::Cmd { cmd, args, .. } = base {
        let mut v = cmd.run(env, interp)?;
        for arg in args {
            // `arg.opts` is always empty here too (see the bare-`Cmd` arm
            // above, `reflect_math_elem`) — folded through `apply_with_opts`
            // uniformly regardless.
            let mut opt_vals = Vec::with_capacity(arg.opts.len());
            for (label, e) in &arg.opts {
                opt_vals.push((label.clone(), e.run(env, interp)?));
            }
            let arg_v = arg.arg.run(env, interp)?;
            v = interp.apply_with_opts(v, opt_vals, arg_v)?;
        }
        // A 0.0.6-authored math command reached from a 0.1 document: the two
        // generations invoke a command differently, though `math` relabels
        // to `math-text` and both type-check. 0.0.6 gets `\cmd a1..an ->
        // math` with scripts attached STRUCTURALLY afterward
        // (`reflect_math_elem`'s `Sub`/`Sup` arms); 0.1 applies three extra
        // arguments (`ctx sub sup -> math-boxes`, `sub`/`sup : math-text
        // option`) so a command can typeset its own scripts. Applying those
        // three to a 0.0.6 command used to die with `cannot apply a value of
        // type math as a function`.
        //
        // Discrimination here is DYNAMIC, and total: after its declared
        // arguments a 0.1 command is by construction still a function (ends
        // `.. -> context -> ..`), so a math VALUE at this point can only be
        // a 0.0.6 command's result — a static check can't recover the
        // authoring generation, since `Ast::VersionScope` governs which
        // `PrimDef` the body folds to and nothing on the resulting closure
        // records where it came from. `as_math` runs 0.0.6's own reflection
        // (so nested commands in a returned `${..}` literal stay 0.0.6
        // commands), and its `Rc<Vec<Math>>` payload is byte-for-byte what
        // `Value::MathBoxes` carries, so crossing needs no conversion;
        // untaken scripts then attach via `attach_scripts`, the same
        // structural `Math::Sub`/`Math::Sup` shape 0.0.6's own reflector
        // would have built. A 0.0.6 command still can't RESTYLE its own
        // scripts — it never could, in 0.0.6 either.
        if matches!(v, Value::Math(_) | Value::MathText { .. }) {
            let base_v = as_math(interp, v)?.as_ref().clone();
            let sub_opt = sub.map(|s| (Rc::new(s.to_vec()), env.clone()));
            let sup_opt = sup.map(|s| (Rc::new(s.to_vec()), env.clone()));
            let attached = attach_scripts(interp, ctx, base_v, sub_opt, sup_opt)?;
            out.extend(attached);
            return Ok(());
        }
        v = interp.apply(v, Value::Context(Box::new(ctx.clone())))?;
        v = interp.apply(v, option_math_text_value(sub, env))?;
        v = interp.apply(v, option_math_text_value(sup, env))?;
        let m = as_math_boxes(v)?;
        out.extend(m.iter().cloned());
        return Ok(());
    }
    let mut base_v = Vec::new();
    reflect_math_elem_v01(interp, ctx, base, env, &mut base_v)?;
    let sub_opt = sub.map(|s| (Rc::new(s.to_vec()), env.clone()));
    let sup_opt = sup.map(|s| (Rc::new(s.to_vec()), env.clone()));
    let attached = attach_scripts(interp, ctx, base_v, sub_opt, sup_opt)?;
    out.extend(attached);
    Ok(())
}

/// V0_1 twin of `reflect_math_elem` (differs only where upstream's
/// `read_pdf_mode_math_text` (`evaluator.cppo.ml:887-930`) differs from
/// 0.0.6 reflection): `Chars`/`Group`/`Primes` are
/// identical to the v006 arms (class/variant resolution stays deferred to
/// layout, where `ctx`'s maps live); `Sub`/`Sup` flatten and route through
/// [`reflect_scripted_v01`]; a bare `Cmd` also routes through it (with
/// `sub = sup = None`) so the uniform ctx+sub+sup calling convention
/// applies uniformly, scripted or not; `Embed` (`#x`) requires the embedded
/// value to be `math-text` (it typechecked as `math-text`) and
/// recurses — upstream `MathTextValueGroup` (`evaluator.cppo.ml:944-949`);
/// scripts on an embed attach via [`reflect_scripted_v01`]'s generic
/// (non-`Cmd`) path, same as any other non-command base.
fn reflect_math_elem_v01(
    interp: &mut Interp,
    ctx: &Context,
    elem: &MathElem,
    env: &Env,
    out: &mut Vec<Math>,
) -> Result<(), EvalError> {
    match elem {
        MathElem::Chars(s) => {
            out.push(Math::Pure(MathElement::VariantCharPending(s.clone())));
            Ok(())
        }
        MathElem::Group(elems) => {
            for e in elems {
                reflect_math_elem_v01(interp, ctx, e, env, out)?;
            }
            Ok(())
        }
        MathElem::Primes(base, n) => {
            let mut base_v = Vec::new();
            reflect_math_elem_v01(interp, ctx, base, env, &mut base_v)?;
            let primes: String = std::iter::repeat('\u{2032}').take(*n).collect();
            out.push(Math::Sup(
                base_v,
                vec![Math::Pure(MathElement::Char {
                    class: MathKind::Ord,
                    big: false,
                    chars: primes,
                })],
            ));
            Ok(())
        }
        MathElem::Sub(_, _) | MathElem::Sup(_, _) => {
            let (base, sub, sup) = flatten_math_scripts(elem);
            reflect_scripted_v01(interp, ctx, base, sub, sup, env, out)
        }
        MathElem::Cmd { .. } => reflect_scripted_v01(interp, ctx, elem, None, None, env, out),
        MathElem::Embed { expr, span: _ } => {
            let v = expr.run(env, interp)?;
            let (elems2, env2) = as_math_text(v)?;
            for e in elems2.iter() {
                reflect_math_elem_v01(interp, ctx, e, &env2, out)?;
            }
            Ok(())
        }
    }
}

/// `read-math : context -> math-text -> math-boxes` (dev-0-1-0
/// vminst.ml:790-793). Reflects every element of
/// `mt` under `ctx` via [`reflect_math_elem_v01`], then wraps the whole run
/// in a single `Math::WithContext` node so `ctx` (including any color/font/
/// size override the caller composed onto it) reaches the layout engine —
/// see [`layout_math_list`]'s `Math::WithContext` arm.
fn prim_read_math(interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
    let mt = args.pop().unwrap();
    let ctx = as_context(args.pop().unwrap())?;
    let (elems, env) = as_math_text(mt)?;
    let mut out = Vec::new();
    for e in elems.iter() {
        reflect_math_elem_v01(interp, &ctx, e, &env, &mut out)?;
    }
    Ok(Value::MathBoxes(Rc::new(vec![Math::WithContext(
        Box::new(ctx),
        out,
    )])))
}

/// `stringify-math : text-info -> math-text -> string` (vminst.ml:858) —
/// STAND-IN: the text-mode backend is out of scope for this PDF port (same
/// scoping note as `prim_convert_string_for_math`'s doc comment); registered
/// so 0.1 packages that reference it still typecheck.
fn prim_stringify_math(_interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
    let _mt = args.pop().unwrap();
    let _tctx = args.pop().unwrap();
    eval_error(
        "stringify-math: the text-mode backend is out of scope for this PDF port \
         (see primitives.rs's prim_convert_string_for_math doc comment)"
            .to_string(),
    )
}

/// `set-math-char : int -> int -> math-class -> context -> context`
/// (vminst.ml:59) — REAL: inserts `(char(cp_from)) -> (char(cp_to), kind)`
/// into `Context::math_class_map` (single-char string key, matching the
/// map's existing token-keying convention — see `prim_convert_string_for_
/// math`'s doc comment on how that map is consulted).
fn prim_set_math_char(_interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
    let mut ctx = as_context(args.pop().unwrap())?;
    let kind = as_math_kind(args.pop().unwrap())?;
    let cpto = as_int(args.pop().unwrap())?;
    let cpfrom = as_int(args.pop().unwrap())?;
    let from = u32::try_from(cpfrom)
        .ok()
        .and_then(char::from_u32)
        .ok_or_else(|| EvalError {
            span: None,
            msg: format!("set-math-char: {cpfrom} is not a valid Unicode codepoint"),
        })?;
    let to = u32::try_from(cpto)
        .ok()
        .and_then(char::from_u32)
        .ok_or_else(|| EvalError {
            span: None,
            msg: format!("set-math-char: {cpto} is not a valid Unicode codepoint"),
        })?;
    Arc::make_mut(&mut ctx.math_class_map).insert(from.to_string(), (to.to_string(), kind));
    Ok(Value::Context(Box::new(ctx)))
}

/// `set-math-char-class : math-char-class -> context -> context`
/// (vminst.ml:445) — REAL: sets `Context::math_char_class`.
fn prim_set_math_char_class(
    _interp: &mut Interp,
    mut args: Vec<Value>,
) -> Result<Value, EvalError> {
    let ctx = as_context(args.pop().unwrap())?;
    let cls = as_math_char_class(args.pop().unwrap())?;
    Ok(Value::Context(Box::new(Context {
        math_char_class: cls,
        ..ctx
    })))
}

/// `get-math-char-class : context -> math-char-class` (vminst.ml:459) —
/// REAL: inverse of `as_math_char_class`.
fn prim_get_math_char_class(
    _interp: &mut Interp,
    mut args: Vec<Value>,
) -> Result<Value, EvalError> {
    let ctx = as_context(args.pop().unwrap())?;
    Ok(math_char_class_value(ctx.math_char_class))
}

/// `embed-inline-to-math : math-class -> inline-boxes -> math-boxes`
/// (vminst.ml:432) — REAL data, stand-in render (`MathElement::
/// EmbeddedBoxes`'s doc comment).
fn prim_embed_inline_to_math(
    _interp: &mut Interp,
    mut args: Vec<Value>,
) -> Result<Value, EvalError> {
    let ib = as_inline_boxes(args.pop().unwrap())?;
    let class = as_math_kind(args.pop().unwrap())?;
    Ok(single_math_boxes(Math::Pure(MathElement::EmbeddedBoxes {
        class,
        boxes: ib,
    })))
}

/// `get-math-axis-height-ratio : context -> float` (vminst.ml:1305) — REAL:
/// the axis-height ratio `MathC` already scales font sizes by
/// (`MathC::axis`).
fn prim_get_math_axis_height_ratio(
    interp: &mut Interp,
    mut args: Vec<Value>,
) -> Result<Value, EvalError> {
    let ctx = as_context(args.pop().unwrap())?;
    let ratio = MathC::of(interp, &ctx)
        .c
        .map(|c| c.axis_height)
        .unwrap_or(0.25);
    Ok(Value::Float(ratio))
}

/// `%math-attach-scripts : context -> math-boxes -> option math-text ->
/// option math-text -> math-boxes` — hidden:
/// the synthesized script-attacher `val math` commands WITHOUT `with sub
/// sup` lower to. Body = [`attach_scripts`] directly — the same function
/// `reflect_scripted_v01`'s non-`Cmd` path calls.
fn prim_math_attach_scripts(interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
    let sup_v = args.pop().unwrap();
    let sub_v = args.pop().unwrap();
    let base_v = args.pop().unwrap();
    let ctx = as_context(args.pop().unwrap())?;
    let base = as_math_boxes(base_v)?;
    let sub_opt = as_option_math_text(sub_v)?;
    let sup_opt = as_option_math_text(sup_v)?;
    let out = attach_scripts(interp, &ctx, (*base).clone(), sub_opt, sup_opt)?;
    Ok(Value::MathBoxes(Rc::new(out)))
}

/// `load-hyphenation-dictionary : string -> hyphenation` (`vminst.ml`'s
/// `LoadHyphenationDictionary`: upstream calls `LoadHyph.main abspath` to
/// build a `BCHyphenation` constant). REAL: unlike upstream, which
/// loads a dictionary from an on-disk `.rustyfi-hyph` path, this port has no
/// filesystem-loaded pattern data — the argument is instead treated as a
/// dictionary NAME (`"english"`/`"en-US"`, matching the `hyph-english.satyh`
/// stdlib package's usage) and mapped to the compiled-in `HyphenLang` tag.
/// An unrecognized name is a hard error rather than a silent no-op, since a
/// document that asks for a dictionary and gets none would silently render
/// without hyphenation. The heavy `hyphenation::Standard` dictionary itself
/// is not loaded here — only the lightweight tag is; the actual load is
/// deferred (load-once, cached) to `crate::hyphenation::hyphenate_word`'s
/// first call for that tag.
fn prim_load_hyphenation_dictionary(
    _interp: &mut Interp,
    mut args: Vec<Value>,
) -> Result<Value, EvalError> {
    let arg = as_str(args.pop().unwrap())?;
    // Accept either a bare dictionary NAME ("english"/"en-US") or an
    // upstream-style PATH ending `.../<name>.rustyfi-hyph` — this is what
    // the real, vendored `hyph-english.satyh` stand-in package actually
    // passes (`here ^ "/../hyph/english.rustyfi-hyph"`, mirroring
    // upstream's `LoadHyph.main abspath` convention). This port has no
    // on-disk pattern-file loader (the dictionary is compiled in via
    // `embed_en-us`), so the path's file stem doubles as the dictionary
    // name.
    let stem = std::path::Path::new(&arg)
        .file_stem()
        .and_then(|s| s.to_str())
        .unwrap_or(arg.as_str())
        .to_ascii_lowercase();
    let tag = match stem.as_str() {
        "english" | "en-us" => HyphenLang::EnglishUS,
        // en-GB (en-GB option): "british"/"en-GB"/"british-english",
        // mirroring the "english"/ "en-US" naming pair above.
        "british" | "en-gb" | "british-english" => HyphenLang::EnglishGB,
        _ => {
            return eval_error(format!(
                "load-hyphenation-dictionary: unknown dictionary {arg:?} \
                 (supported: \"english\"/\"en-US\", \"british\"/\"en-GB\"/\"british-english\", \
                 bare or as a `.../<name>.rustyfi-hyph`-style path)"
            ))
        }
    };
    Ok(Value::Hyphenation(tag))
}

/// `load-unicode-char-database : string -> string -> string ->
/// unicode-char-database` (`vminst.ml`'s `LoadUnicodeCharDatabase`:
/// upstream builds `(ScriptDataMap, LineBreakDataMap)` from the three
/// Unicode data file paths into a `BCUnidata` constant). STAND-IN: no-op,
/// same rationale as `prim_load_hyphenation_dictionary` above — all three
/// paths are popped and dropped.
fn prim_load_unicode_char_database(
    _interp: &mut Interp,
    mut args: Vec<Value>,
) -> Result<Value, EvalError> {
    args.truncate(0);
    Ok(Value::Unit)
}

/// `set-hyphenation-dictionary : hyphenation -> context -> context`
/// (`vminst.ml`'s setter: upstream stores `{ ctx with hyphen_dictionary }`).
/// REAL: writes `Context::hyphen_dictionary = Some(tag)`. This is the
/// ONLY way a `Context` acquires a dictionary — `Context::initial` seeds
/// `None`, so a document that never calls this gets no hyphenation at all.
fn prim_set_hyphenation_dictionary(
    _interp: &mut Interp,
    mut args: Vec<Value>,
) -> Result<Value, EvalError> {
    let ctx = as_context(args.pop().unwrap())?;
    let tag = as_hyphenation(args.pop().unwrap())?;
    Ok(Value::Context(Box::new(Context {
        hyphen_dictionary: Some(tag),
        ..ctx
    })))
}

/// `set-unicode-char-database : unicode-char-database -> context ->
/// context` (`vminst.ml`'s setter: upstream stores `{ ctx with script_map;
/// line_break_map }`). STAND-IN no-op, same shape as
/// `prim_set_hyphenation_dictionary` above.
fn prim_set_unicode_char_database(
    _interp: &mut Interp,
    mut args: Vec<Value>,
) -> Result<Value, EvalError> {
    let ctx = args.pop().unwrap();
    let _db = args.pop().unwrap();
    Ok(ctx)
}

fn prim_math_char_v006(interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
    let s = as_str(args.pop().unwrap())?;
    let class = as_math_kind(args.pop().unwrap())?;
    let _ = interp;
    Ok(single_math(Math::Pure(MathElement::Char {
        class,
        big: false,
        chars: s,
    })))
}

/// `math-char : context -> math-class -> string -> math-boxes` (dev-0-1-0
/// vminst.ml:358) — ctx ACCEPTED, not stored on the atom (coarse,
/// `read-math`-granularity context capture only).
fn prim_math_char_v01(interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
    let s = as_str(args.pop().unwrap())?;
    let class = as_math_kind(args.pop().unwrap())?;
    let _ctx = as_context(args.pop().unwrap())?;
    let _ = interp;
    Ok(single_math_boxes(Math::Pure(MathElement::Char {
        class,
        big: false,
        chars: s,
    })))
}

fn prim_math_big_char_v006(interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
    let s = as_str(args.pop().unwrap())?;
    let class = as_math_kind(args.pop().unwrap())?;
    let _ = interp;
    Ok(single_math(Math::Pure(MathElement::Char {
        class,
        big: true,
        chars: s,
    })))
}

/// `math-big-char : context -> math-class -> string -> math-boxes`
/// (vminst.ml:374) — same fork as `math-char`.
fn prim_math_big_char_v01(interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
    let s = as_str(args.pop().unwrap())?;
    let class = as_math_kind(args.pop().unwrap())?;
    let _ctx = as_context(args.pop().unwrap())?;
    let _ = interp;
    Ok(single_math_boxes(Math::Pure(MathElement::Char {
        class,
        big: true,
        chars: s,
    })))
}

fn prim_math_char_with_kern_v006(
    interp: &mut Interp,
    mut args: Vec<Value>,
) -> Result<Value, EvalError> {
    let kern_r = args.pop().unwrap();
    let kern_l = args.pop().unwrap();
    let s = as_str(args.pop().unwrap())?;
    let class = as_math_kind(args.pop().unwrap())?;
    let _ = interp;
    Ok(single_math(Math::Pure(MathElement::CharWithKern {
        class,
        big: false,
        chars: s,
        kern_l: Box::new(kern_l),
        kern_r: Box::new(kern_r),
    })))
}

/// `math-char-with-kern : context -> math-class -> string -> kernf -> kernf
/// -> math-boxes` (vminst.ml:390).
fn prim_math_char_with_kern_v01(
    interp: &mut Interp,
    mut args: Vec<Value>,
) -> Result<Value, EvalError> {
    let kern_r = args.pop().unwrap();
    let kern_l = args.pop().unwrap();
    let s = as_str(args.pop().unwrap())?;
    let class = as_math_kind(args.pop().unwrap())?;
    let _ctx = as_context(args.pop().unwrap())?;
    let _ = interp;
    Ok(single_math_boxes(Math::Pure(MathElement::CharWithKern {
        class,
        big: false,
        chars: s,
        kern_l: Box::new(kern_l),
        kern_r: Box::new(kern_r),
    })))
}

fn prim_math_big_char_with_kern_v006(
    interp: &mut Interp,
    mut args: Vec<Value>,
) -> Result<Value, EvalError> {
    let kern_r = args.pop().unwrap();
    let kern_l = args.pop().unwrap();
    let s = as_str(args.pop().unwrap())?;
    let class = as_math_kind(args.pop().unwrap())?;
    let _ = interp;
    Ok(single_math(Math::Pure(MathElement::CharWithKern {
        class,
        big: true,
        chars: s,
        kern_l: Box::new(kern_l),
        kern_r: Box::new(kern_r),
    })))
}

/// `math-big-char-with-kern : context -> math-class -> string -> kernf ->
/// kernf -> math-boxes` (vminst.ml:411) — same fork as
/// `math-char-with-kern`.
fn prim_math_big_char_with_kern_v01(
    interp: &mut Interp,
    mut args: Vec<Value>,
) -> Result<Value, EvalError> {
    let kern_r = args.pop().unwrap();
    let kern_l = args.pop().unwrap();
    let s = as_str(args.pop().unwrap())?;
    let class = as_math_kind(args.pop().unwrap())?;
    let _ctx = as_context(args.pop().unwrap())?;
    let _ = interp;
    Ok(single_math_boxes(Math::Pure(MathElement::CharWithKern {
        class,
        big: true,
        chars: s,
        kern_l: Box::new(kern_l),
        kern_r: Box::new(kern_r),
    })))
}

/// `math-concat : math -> math -> math` (vminst.ml:193) — FAITHFUL: a plain
/// list append (`math` is always a flat sequence of atoms; see `value.rs`'s
/// `Value::Math` doc comment).
fn prim_math_concat_v006(interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
    let m2 = args.pop().unwrap();
    let m1 = args.pop().unwrap();
    let m1 = as_math(interp, m1)?;
    let m2 = as_math(interp, m2)?;
    let mut out = (*m1).clone();
    out.extend((*m2).iter().cloned());
    Ok(Value::Math(Rc::new(out)))
}

/// `math-concat : math-boxes -> math-boxes -> math-boxes` (vminst.ml:181).
fn prim_math_concat_v01(_interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
    let m2 = as_math_boxes(args.pop().unwrap())?;
    let m1 = as_math_boxes(args.pop().unwrap())?;
    let mut out = (*m1).clone();
    out.extend((*m2).iter().cloned());
    Ok(Value::MathBoxes(Rc::new(out)))
}

fn prim_math_group_v006(interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
    let m = args.pop().unwrap();
    let cls2 = as_math_kind(args.pop().unwrap())?;
    let cls1 = as_math_kind(args.pop().unwrap())?;
    let inner = as_math(interp, m)?;
    Ok(single_math(Math::Group(cls1, cls2, (*inner).clone())))
}

/// `math-group : math-class -> math-class -> math-boxes -> math-boxes`
/// (vminst.ml:194).
fn prim_math_group_v01(_interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
    let m = as_math_boxes(args.pop().unwrap())?;
    let cls2 = as_math_kind(args.pop().unwrap())?;
    let cls1 = as_math_kind(args.pop().unwrap())?;
    Ok(single_math_boxes(Math::Group(cls1, cls2, (*m).clone())))
}

fn prim_math_sup_v006(interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
    let m2 = args.pop().unwrap();
    let m1 = args.pop().unwrap();
    let base = as_math(interp, m1)?;
    let script = as_math(interp, m2)?;
    Ok(single_math(Math::Sup((*base).clone(), (*script).clone())))
}

/// `math-sup : context -> math-boxes -> (context -> math-boxes) ->
/// math-boxes` (vminst.ml:208) — the script argument is a context-taking
/// callback, run under `enter_script`.
fn prim_math_sup_v01(interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
    let f = args.pop().unwrap();
    let base_v = args.pop().unwrap();
    let ctx = as_context(args.pop().unwrap())?;
    let base = as_math_boxes(base_v)?;
    let script_ctx = enter_script(interp, &ctx);
    let script_v = interp.apply(f, Value::Context(Box::new(script_ctx)))?;
    let script = as_math_boxes(script_v)?;
    Ok(single_math_boxes(Math::Sup(
        (*base).clone(),
        (*script).clone(),
    )))
}

fn prim_math_sub_v006(interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
    let m2 = args.pop().unwrap();
    let m1 = args.pop().unwrap();
    let base = as_math(interp, m1)?;
    let script = as_math(interp, m2)?;
    Ok(single_math(Math::Sub((*base).clone(), (*script).clone())))
}

/// `math-sub : context -> math-boxes -> (context -> math-boxes) ->
/// math-boxes` (vminst.ml:228) — same shape as `math-sup`.
fn prim_math_sub_v01(interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
    let f = args.pop().unwrap();
    let base_v = args.pop().unwrap();
    let ctx = as_context(args.pop().unwrap())?;
    let base = as_math_boxes(base_v)?;
    let script_ctx = enter_script(interp, &ctx);
    let script_v = interp.apply(f, Value::Context(Box::new(script_ctx)))?;
    let script = as_math_boxes(script_v)?;
    Ok(single_math_boxes(Math::Sub(
        (*base).clone(),
        (*script).clone(),
    )))
}

fn prim_math_frac_v006(interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
    let m2 = args.pop().unwrap();
    let m1 = args.pop().unwrap();
    let num = as_math(interp, m1)?;
    let den = as_math(interp, m2)?;
    Ok(single_math(Math::Fraction((*num).clone(), (*den).clone())))
}

/// `math-frac : context -> math-boxes -> math-boxes -> math-boxes`
/// (vminst.ml:248).
fn prim_math_frac_v01(_interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
    let m2 = as_math_boxes(args.pop().unwrap())?;
    let m1 = as_math_boxes(args.pop().unwrap())?;
    let _ctx = as_context(args.pop().unwrap())?;
    Ok(single_math_boxes(Math::Fraction(
        (*m1).clone(),
        (*m2).clone(),
    )))
}

/// `math-radical : math option -> math -> math` (vminst.ml:274) — `None`
/// degree is `\sqrt`; upstream's `MathRadicalWithDegree` (`\sqrt[n]`) is
/// unimplemented too (`math.ml:886`), carried faithfully but not rendered
/// specially, matching upstream by parity (see `value.rs`'s `Math::Radical`).
fn prim_math_radical_v006(interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
    let m2 = args.pop().unwrap();
    let opt = args.pop().unwrap();
    let radicand = as_math(interp, m2)?;
    let degree = match opt {
        Value::Ctor(name, payload) if name == "None" && payload.is_none() => None,
        Value::Ctor(name, Some(payload)) if name == "Some" => {
            Some((*as_math(interp, *payload)?).clone())
        }
        other => {
            return eval_error(format!(
                "expected a math option (None/Some), got {}",
                other.type_name()
            ))
        }
    };
    Ok(single_math(Math::Radical(degree, (*radicand).clone())))
}

/// `math-radical : context -> option math-boxes -> math-boxes ->
/// math-boxes` (vminst.ml:262).
fn prim_math_radical_v01(_interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
    let m2 = args.pop().unwrap();
    let opt = args.pop().unwrap();
    let _ctx = as_context(args.pop().unwrap())?;
    let radicand = as_math_boxes(m2)?;
    let degree = match opt {
        Value::Ctor(name, payload) if name == "None" && payload.is_none() => None,
        Value::Ctor(name, Some(payload)) if name == "Some" => {
            Some((*as_math_boxes(*payload)?).clone())
        }
        other => {
            return eval_error(format!(
                "expected a math-boxes option (None/Some), got {}",
                other.type_name()
            ))
        }
    };
    Ok(single_math_boxes(Math::Radical(
        degree,
        (*radicand).clone(),
    )))
}

fn prim_math_lower_v006(interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
    let m2 = args.pop().unwrap();
    let m1 = args.pop().unwrap();
    let base = as_math(interp, m1)?;
    let lower = as_math(interp, m2)?;
    Ok(single_math(Math::LowerLimit(
        (*base).clone(),
        (*lower).clone(),
    )))
}

/// `math-lower : context -> math-boxes -> (context -> math-boxes) ->
/// math-boxes` (vminst.ml:338) — same script-callback shape as `math-sup`.
fn prim_math_lower_v01(interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
    let f = args.pop().unwrap();
    let base_v = args.pop().unwrap();
    let ctx = as_context(args.pop().unwrap())?;
    let base = as_math_boxes(base_v)?;
    let script_ctx = enter_script(interp, &ctx);
    let script_v = interp.apply(f, Value::Context(Box::new(script_ctx)))?;
    let lower = as_math_boxes(script_v)?;
    Ok(single_math_boxes(Math::LowerLimit(
        (*base).clone(),
        (*lower).clone(),
    )))
}

fn prim_math_upper_v006(interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
    let m2 = args.pop().unwrap();
    let m1 = args.pop().unwrap();
    let base = as_math(interp, m1)?;
    let upper = as_math(interp, m2)?;
    Ok(single_math(Math::UpperLimit(
        (*base).clone(),
        (*upper).clone(),
    )))
}

/// `math-upper : context -> math-boxes -> (context -> math-boxes) ->
/// math-boxes` (vminst.ml:318) — same script-callback shape as `math-sup`.
fn prim_math_upper_v01(interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
    let f = args.pop().unwrap();
    let base_v = args.pop().unwrap();
    let ctx = as_context(args.pop().unwrap())?;
    let base = as_math_boxes(base_v)?;
    let script_ctx = enter_script(interp, &ctx);
    let script_v = interp.apply(f, Value::Context(Box::new(script_ctx)))?;
    let upper = as_math_boxes(script_v)?;
    Ok(single_math_boxes(Math::UpperLimit(
        (*base).clone(),
        (*upper).clone(),
    )))
}

/// `math-pull-in-scripts : math-class -> math-class -> (math option -> math
/// option -> math) -> math` (vminst.ml:368) — FAITHFUL construction: the
/// resolver closure is stored opaquely here, only ever invoked by
/// `layout_pull_in_scripts` — with
/// the subscript/superscript actually pulled in off an enclosing `Sub`/`Sup`
/// (`{scripts} m^{sup}`-style), or with `(None, None)` for the common
/// unscripted case (a bare `\sum`/`\int` with nothing pulled in).
fn prim_math_pull_in_scripts(
    interp: &mut Interp,
    mut args: Vec<Value>,
) -> Result<Value, EvalError> {
    let resolver = args.pop().unwrap();
    let cls2 = as_math_kind(args.pop().unwrap())?;
    let cls1 = as_math_kind(args.pop().unwrap())?;
    let _ = interp;
    Ok(single_math(Math::PullInScripts(
        cls1,
        cls2,
        Box::new(resolver),
    )))
}

fn prim_math_color(interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
    let m = args.pop().unwrap();
    let color = as_color(args.pop().unwrap())?;
    let inner = as_math(interp, m)?;
    Ok(single_math(Math::ChangeColor(color, (*inner).clone())))
}

fn prim_math_char_class(interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
    let m = args.pop().unwrap();
    let cls = as_math_char_class(args.pop().unwrap())?;
    let inner = as_math(interp, m)?;
    Ok(single_math(Math::ChangeCharClass(cls, (*inner).clone())))
}

fn prim_math_variant_char(interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
    let style = as_math_variant_style(args.pop().unwrap())?;
    let class = as_math_kind(args.pop().unwrap())?;
    let _ = interp;
    Ok(single_math(Math::Pure(MathElement::VariantChar {
        class,
        big: false,
        style: Box::new(style),
    })))
}

fn prim_math_paren_v006(interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
    let m = args.pop().unwrap();
    let paren_r = args.pop().unwrap();
    let paren_l = args.pop().unwrap();
    let inner = as_math(interp, m)?;
    Ok(single_math(Math::Paren(
        Box::new(paren_l),
        Box::new(paren_r),
        (*inner).clone(),
    )))
}

/// `math-paren : context -> paren -> paren -> math-boxes -> math-boxes`
/// (vminst.ml:279).
fn prim_math_paren_v01(_interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
    let m = args.pop().unwrap();
    let paren_r = args.pop().unwrap();
    let paren_l = args.pop().unwrap();
    let _ctx = as_context(args.pop().unwrap())?;
    let inner = as_math_boxes(m)?;
    Ok(single_math_boxes(Math::Paren(
        Box::new(paren_l),
        Box::new(paren_r),
        (*inner).clone(),
    )))
}

fn prim_math_paren_with_middle_v006(
    interp: &mut Interp,
    mut args: Vec<Value>,
) -> Result<Value, EvalError> {
    let mlst = args.pop().unwrap();
    let middle = args.pop().unwrap();
    let paren_r = args.pop().unwrap();
    let paren_l = args.pop().unwrap();
    let items = as_list(mlst)?;
    let mut mlstlst = Vec::with_capacity(items.len());
    for it in items {
        mlstlst.push((*as_math(interp, it)?).clone());
    }
    Ok(single_math(Math::ParenWithMiddle(
        Box::new(paren_l),
        Box::new(paren_r),
        Box::new(middle),
        mlstlst,
    )))
}

/// `math-paren-with-middle : context -> paren -> paren -> paren -> list
/// math-boxes -> math-boxes` (vminst.ml:297).
fn prim_math_paren_with_middle_v01(
    _interp: &mut Interp,
    mut args: Vec<Value>,
) -> Result<Value, EvalError> {
    let mlst = args.pop().unwrap();
    let middle = args.pop().unwrap();
    let paren_r = args.pop().unwrap();
    let paren_l = args.pop().unwrap();
    let _ctx = as_context(args.pop().unwrap())?;
    let items = as_list(mlst)?;
    let mut mlstlst = Vec::with_capacity(items.len());
    for it in items {
        mlstlst.push((*as_math_boxes(it)?).clone());
    }
    Ok(single_math_boxes(Math::ParenWithMiddle(
        Box::new(paren_l),
        Box::new(paren_r),
        Box::new(middle),
        mlstlst,
    )))
}

fn prim_text_in_math(interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
    let body = args.pop().unwrap();
    let class = as_math_kind(args.pop().unwrap())?;
    let _ = interp;
    Ok(single_math(Math::Pure(MathElement::EmbeddedText {
        class,
        body: Box::new(body),
    })))
}

/// `convert-string-for-math : context -> math-char-class -> string ->
/// string` (`vminstdef.yaml` `PrimitiveConvertStringForMath`). Faithful to
/// upstream: it overrides the context's `math_char_class` with the passed
/// `mccls`, then runs `MathContext.convert_math_variant_char`
/// (`types.cppo.ml:1602`) over the whole string —
///  1. if the WHOLE string is a key of the (token-level) `math_class_map`
///     (`default_math_class_map`, e.g. `"-"` → `"−"` U+2212), return its
///     replacement codepoints; else
///  2. remap each char via the runtime `math_variant_char_map`
///     (`set-math-variant-char` overrides, keyed by `(char, mccls)`) first,
///     then the built-in `default_math_variant_char` table (the
///     Mathematical-Alphanumeric-Symbols remap), keeping any char with no
///     mapping.
/// Unlike the *rendering*-path `resolve_variant_char`, this string primitive
/// does NOT gate on font glyph availability (upstream's
/// `convert_math_variant_char` never does — it returns codepoints, not
/// glyphs), so `abc` under `MathItalic` yields U+1D44E/44F/450 regardless of
/// the active font.
fn prim_convert_string_for_math(
    _interp: &mut Interp,
    mut args: Vec<Value>,
) -> Result<Value, EvalError> {
    let s = as_str(args.pop().unwrap())?;
    let class = as_math_char_class(args.pop().unwrap())?;
    let ctx = as_context(args.pop().unwrap())?;
    // (1) whole-token class-map hit -> its replacement codepoints verbatim.
    if let Some((target, _mk)) = ctx.math_class_map.get(&s) {
        return Ok(Value::Str(target.clone()));
    }
    // (2) per-char variant remap under the PASSED class (which upstream
    // installs as the effective `math_char_class` before converting).
    let mut out = String::with_capacity(s.len());
    for ch in s.chars() {
        let mapped = ctx
            .math_variant_char_map
            .get(&(ch, class))
            .copied()
            .or_else(|| default_math_variant_char(class, ch))
            .unwrap_or(ch);
        out.push(mapped);
    }
    Ok(Value::Str(out))
}

/// `set-math-variant-char : math-char-class -> int -> int -> context ->
/// context` — FAITHFUL: installs a per-`(source char, style)`
/// override into `Context::math_variant_char_map`, consulted by
/// `resolve_variant_char` BEFORE the built-in `default_math_variant_char`
/// table. `Arc::make_mut` copy-on-writes the map so contexts that never
/// call this keep sharing one `Arc`-refcounted empty table.
fn prim_set_math_variant_char_v006(
    _interp: &mut Interp,
    mut args: Vec<Value>,
) -> Result<Value, EvalError> {
    let mut ctx = as_context(args.pop().unwrap())?;
    let cpto = as_int(args.pop().unwrap())?;
    let cpfrom = as_int(args.pop().unwrap())?;
    let cls = as_math_char_class(args.pop().unwrap())?;
    let from = u32::try_from(cpfrom)
        .ok()
        .and_then(char::from_u32)
        .ok_or_else(|| EvalError {
            span: None,
            msg: format!("set-math-variant-char: {cpfrom} is not a valid Unicode codepoint"),
        })?;
    let to = u32::try_from(cpto)
        .ok()
        .and_then(char::from_u32)
        .ok_or_else(|| EvalError {
            span: None,
            msg: format!("set-math-variant-char: {cpto} is not a valid Unicode codepoint"),
        })?;
    Arc::make_mut(&mut ctx.math_variant_char_map).insert((from, cls), to);
    Ok(Value::Context(Box::new(ctx)))
}

/// `set-math-variant-char : int -> (math-char-class -> int) -> context ->
/// context` (vminst.ml:36) — the v01 body applies the selector once per
/// each of the 9 `MathCharClass` values and inserts into `math_variant_
/// char_map` (an eager materialization of upstream's stored selector
/// closure; the observable map is the same either way).
fn prim_set_math_variant_char_v01(
    interp: &mut Interp,
    mut args: Vec<Value>,
) -> Result<Value, EvalError> {
    let mut ctx = as_context(args.pop().unwrap())?;
    let selector = args.pop().unwrap();
    let cpfrom = as_int(args.pop().unwrap())?;
    let from = u32::try_from(cpfrom)
        .ok()
        .and_then(char::from_u32)
        .ok_or_else(|| EvalError {
            span: None,
            msg: format!("set-math-variant-char: {cpfrom} is not a valid Unicode codepoint"),
        })?;
    const CLASSES: [MathCharClass; 9] = [
        MathCharClass::Italic,
        MathCharClass::BoldItalic,
        MathCharClass::Roman,
        MathCharClass::BoldRoman,
        MathCharClass::Script,
        MathCharClass::BoldScript,
        MathCharClass::Fraktur,
        MathCharClass::BoldFraktur,
        MathCharClass::DoubleStruck,
    ];
    for cls in CLASSES {
        let cpto_v = interp.apply(selector.clone(), math_char_class_value(cls))?;
        let cpto = as_int(cpto_v)?;
        let to = u32::try_from(cpto)
            .ok()
            .and_then(char::from_u32)
            .ok_or_else(|| EvalError {
                span: None,
                msg: format!("set-math-variant-char: {cpto} is not a valid Unicode codepoint"),
            })?;
        Arc::make_mut(&mut ctx.math_variant_char_map).insert((from, cls), to);
    }
    Ok(Value::Context(Box::new(ctx)))
}

/// The `MathKind` one `MathElement` atom presents as its own boundary class
/// — `Char`/`CharWithKern`/`EmbeddedText`/`VariantChar` carry an explicit
/// `class` field; `VariantCharPending` (not yet resolved to a class
/// at this point in the tree) consults `ctx.math_class_map` the same way
/// `layout_math_atom`'s own arm does, defaulting to `Ord` when the token
/// isn't a whole-token class-map entry (mirrors `layout_math_atom`'s
/// fallback path, whose per-char variant remap never changes the class).
fn math_element_kind(ctx: &Context, me: &MathElement) -> MathKind {
    match me {
        MathElement::Char { class, .. }
        | MathElement::CharWithKern { class, .. }
        | MathElement::EmbeddedText { class, .. }
        | MathElement::VariantChar { class, .. }
        | MathElement::EmbeddedBoxes { class, .. } => *class,
        MathElement::VariantCharPending(s) => ctx
            .math_class_map
            .get(s.as_str())
            .map(|(_, kind)| *kind)
            .unwrap_or(MathKind::Ord),
    }
}

/// Upstream `get_left_math_kind`/`get_right_math_kind` (math.ml:481-524),
/// fused into one direction-parameterized walk over a `&[Math]` list's
/// FIRST (`left = true`) or LAST (`left = false`) element: `Pure` atoms
/// report their own class (`math_element_kind`); `Group`/`PullInScripts`
/// present an explicit, possibly-asymmetric left/right pair; `Sup`/`Sub`/
/// `UpperLimit`/`LowerLimit` recurse into their `base`; `Fraction`/
/// `Radical` are always `Inner`; `Paren`/`ParenWithMiddle` are always
/// `Open`/`Close`; `ChangeColor`/`ChangeCharClass` recurse into `inner`; an
/// empty list is the synthetic `End` boundary sentinel (`MathKind::End`,
/// `horzBox.ml:134`) — `make_math_class_option_value` maps that to `None`,
/// same as upstream's own list-boundary handling.
fn boundary_math_kind(ctx: &Context, ms: &[Math], left: bool) -> MathKind {
    let m = if left { ms.first() } else { ms.last() };
    let Some(m) = m else {
        return MathKind::End;
    };
    match m {
        Math::Pure(me) => math_element_kind(ctx, me),
        Math::Group(cls1, cls2, _) => {
            if left {
                *cls1
            } else {
                *cls2
            }
        }
        Math::PullInScripts(cls1, cls2, _) => {
            if left {
                *cls1
            } else {
                *cls2
            }
        }
        Math::Sup(base, _)
        | Math::Sub(base, _)
        | Math::UpperLimit(base, _)
        | Math::LowerLimit(base, _) => boundary_math_kind(ctx, base, left),
        Math::Fraction(..) | Math::Radical(..) => MathKind::Inner,
        Math::Paren(..) | Math::ParenWithMiddle(..) => {
            if left {
                MathKind::Open
            } else {
                MathKind::Close
            }
        }
        Math::ChangeColor(_, inner) | Math::ChangeCharClass(_, inner) => {
            boundary_math_kind(ctx, inner, left)
        }
        // V0_1 only (`read-math`): the boundary class is a property of the
        // wrapped content, not of which context laid it out under, so
        // recurse into `inner` with the SAME probing `ctx` (mirrors the
        // `ChangeColor`/`ChangeCharClass` arms above, which also recurse
        // with the ambient `ctx` rather than switching to their own stored
        // state).
        Math::WithContext(_, inner) => boundary_math_kind(ctx, inner, left),
    }
}

fn left_math_kind(ctx: &Context, ms: &[Math]) -> MathKind {
    boundary_math_kind(ctx, ms, true)
}

fn right_math_kind(ctx: &Context, ms: &[Math]) -> MathKind {
    boundary_math_kind(ctx, ms, false)
}

/// `math-class option` — `MathKind::End` (the empty-list sentinel) becomes
/// `None`; every real class becomes `Some(<ctor>)`, round-tripping exactly
/// with `as_math_kind`'s ctor names.
fn make_math_class_option_value(mk: MathKind) -> Value {
    let name = match mk {
        MathKind::Ord => "MathOrd",
        MathKind::Bin => "MathBin",
        MathKind::Rel => "MathRel",
        MathKind::Op => "MathOp",
        MathKind::Punct => "MathPunct",
        MathKind::Open => "MathOpen",
        MathKind::Close => "MathClose",
        MathKind::Prefix => "MathPrefix",
        MathKind::Inner => "MathInner",
        MathKind::End => return Value::Ctor("None".to_string(), None),
    };
    Value::Ctor(
        "Some".to_string(),
        Some(Box::new(Value::Ctor(name.to_string(), None))),
    )
}

/// `get-left-math-class : context -> math -> math-class option`.
fn prim_get_left_math_class_v006(
    interp: &mut Interp,
    mut args: Vec<Value>,
) -> Result<Value, EvalError> {
    let m = as_math(interp, args.pop().unwrap())?;
    let ctx = as_context(args.pop().unwrap())?;
    Ok(make_math_class_option_value(left_math_kind(&ctx, &m)))
}

/// `get-left-math-class : math-boxes -> math-class option` (vminst.ml:128)
/// — ctx DROPPED (matches upstream, which takes no context at all here).
/// The boundary-class probe still needs SOME `Context` to resolve an
/// unresolved `VariantCharPending` token's whole-token class map
/// (`math_element_kind`) — this port's own deferred-resolution design, not
/// upstream's, since upstream's `math` atoms already carry a resolved
/// class — so a bare default context stands in.
fn prim_get_left_math_class_v01(
    _interp: &mut Interp,
    mut args: Vec<Value>,
) -> Result<Value, EvalError> {
    let m = as_math_boxes(args.pop().unwrap())?;
    let ctx = Context::initial(Length::ZERO);
    Ok(make_math_class_option_value(left_math_kind(&ctx, &m)))
}

/// `get-right-math-class : context -> math -> math-class option`.
fn prim_get_right_math_class_v006(
    interp: &mut Interp,
    mut args: Vec<Value>,
) -> Result<Value, EvalError> {
    let m = as_math(interp, args.pop().unwrap())?;
    let ctx = as_context(args.pop().unwrap())?;
    Ok(make_math_class_option_value(right_math_kind(&ctx, &m)))
}

/// `get-right-math-class : math-boxes -> math-class option` (vminst.ml:146)
/// — same fork as `get-left-math-class`.
fn prim_get_right_math_class_v01(
    _interp: &mut Interp,
    mut args: Vec<Value>,
) -> Result<Value, EvalError> {
    let m = as_math_boxes(args.pop().unwrap())?;
    let ctx = Context::initial(Length::ZERO);
    Ok(make_math_class_option_value(right_math_kind(&ctx, &m)))
}

/// `set-math-command : [math] inline-cmd -> context -> context`
/// FAITHFUL: installs the command `read_inline`'s `EmbedMath` arm applies
/// to bare `${…}`.
fn prim_set_math_command(interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
    let mut ctx = as_context(args.pop().unwrap())?;
    let cmd = args.pop().unwrap();
    ctx.math_command = Some(interp.register_math_command(cmd));
    Ok(Value::Context(Box::new(ctx)))
}

/// Resolve a font abbrev to one of the 3 base faces by name heuristic — the
/// only font-name resolution this port has. Shared by set-font/set-math-font.
fn resolve_font_abbrev(abbrev: &str) -> FontKey {
    let lower = abbrev.to_ascii_lowercase();
    if lower.contains("bold") {
        FONT_BOLD
    } else if lower.contains("it") || lower.contains("obl") || lower.contains("slant") {
        FONT_OBLIQUE
    } else {
        FONT_REGULAR
    }
}

/// `set-math-font : string -> context -> context` (0.0.6
/// `vminstdef.yaml:1364`) — `abbrev` resolves through the font metrics
/// provider's registry first (the same upgrade as `set-font`), falling back
/// to the 3-face name heuristic, so a math OTF configured under
/// any abbrev (not just the CLI regular face) can be selected.
fn prim_set_math_font_v006(interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
    let ctx = as_context(args.pop().unwrap())?;
    let abbrev = as_str(args.pop().unwrap())?;
    let math_font = interp
        .metrics
        .resolve_font_abbrev(&abbrev)
        .unwrap_or_else(|| resolve_font_abbrev(&abbrev));
    Ok(Value::Context(Box::new(Context { math_font, ..ctx })))
}

/// `set-math-font : font -> context -> context` (saphe-split
/// `tools/gencode/vminst.ml:1462`, whose body is
/// `ctx with math_font_key = Some(mathkey)`) — the 0.1 arm takes the opaque
/// handle, so there is no abbrev left to resolve. The bundled 0.1 corpus
/// already calls it that way (`std-ja.satyh`'s `set-math-font
/// FontLatinModernMath.main`).
fn prim_set_math_font_v01(_interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
    let ctx = as_context(args.pop().unwrap())?;
    let math_font = as_font_key(args.pop().unwrap())?;
    Ok(Value::Context(Box::new(Context { math_font, ..ctx })))
}

/// `load-single-font : string -> font` — LOCAL, non-upstream, V0_1-only.
///
/// Upstream has no surface name for this: `envelopeChecker.ml`'s
/// `check_font_envelope` synthesizes one binding per `files[]` row of a font
/// ENVELOPE, typed `BaseType(FontType)`, whose right-hand side is the
/// internal `LoadSingleFont{ path; used_as_math_font }` node — and
/// `evaluator.cppo.ml:427-434` evaluates that to `BaseConstant(BCFontKey
/// (FontInfo.add_single path))`. This port's bundled 0.1 font envelopes are
/// ordinary `.satyh` stand-ins (`dist-v01/packages/font-*.satyh`) rather
/// than envelopes the loader synthesizes bindings from, so they need a
/// spelling for the same step; this is it. Same LOCAL-primitive precedent as
/// `set-font-key`.
///
/// The argument stands in for upstream's font-file PATH: it is the port's
/// font-store key, resolved here through exactly the ladder `set-font` used
/// to run per call — the metrics provider's registry
/// (`FontMetrics::resolve_font_abbrev`, a real `TtfFontStore` built from
/// `fonts.satysfi-hash`), falling back to the 3-face name heuristic. Doing
/// it HERE rather than at `set-font` time is what makes the resulting `font`
/// a genuine handle: resolution is a pure function of the abbrev and the
/// provider (`&self`, no interior mutation), so moving it earlier is
/// observationally identical.
fn prim_load_single_font(interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
    let abbrev = as_str(args.pop().unwrap())?;
    let key = interp
        .metrics
        .resolve_font_abbrev(&abbrev)
        .unwrap_or_else(|| resolve_font_abbrev(&abbrev));
    Ok(Value::Font(key))
}

/// `space-between-maths : context -> math -> math -> inline-boxes option`
/// (vminst.ml:173) — STAND-IN: the real inter-atom glue is the full
/// `space_between_math_kinds` table (`math.ml:319-410`); always returns
/// `None` (no extra glue), used by `math.satyh`'s
/// `+align` — never invoked eagerly (that binding is a `let-block` closure).
fn prim_space_between_maths_v006(
    _interp: &mut Interp,
    mut args: Vec<Value>,
) -> Result<Value, EvalError> {
    let _m2 = args.pop().unwrap();
    let _m1 = args.pop().unwrap();
    let _ctx = as_context(args.pop().unwrap())?;
    Ok(Value::Ctor("None".to_string(), None))
}

/// `space-between-maths : context -> math-boxes -> math-boxes -> inline-
/// boxes option` (vminst.ml:164) — shared STAND-IN body, only the extractor
/// forks (`as_math_boxes` vs `as_math`).
fn prim_space_between_maths_v01(
    _interp: &mut Interp,
    mut args: Vec<Value>,
) -> Result<Value, EvalError> {
    let _m2 = as_math_boxes(args.pop().unwrap())?;
    let _m1 = as_math_boxes(args.pop().unwrap())?;
    let _ctx = as_context(args.pop().unwrap())?;
    Ok(Value::Ctor("None".to_string(), None))
}

/// `raise-inline : length -> inline-boxes -> inline-boxes` — STAND-IN: the
/// line model has no per-box vertical-offset wrapper outside
/// `PureHorzBox::Math`'s own per-glyph `dy` ("structural difference"
/// note); returns the boxes unshifted (used by `math.satyh`'s `\cases`,
/// never invoked eagerly).
fn prim_raise_inline(_interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
    let ib = as_inline_boxes(args.pop().unwrap())?;
    let _len = as_length(args.pop().unwrap())?;
    Ok(Value::InlineBoxes(ib))
}

/// `embed-block-breakable : context -> block-boxes -> inline-boxes`
/// (vminst.ml:973; upstream `HorzEmbeddedVertBreakable`) — a MANDATORY
/// break on both sides: upstream's `LBEmbeddedVertBreakable` resets the
/// width map to this breakpoint alone (`lineBreak.ml:1076-1087`), flushes
/// the accumulated line, emits the block as its own vertical item, then
/// starts a fresh line (`lineBreak.ml:809-818`).
///
/// Modelled here as a forced `Discretionary` either side of the block —
/// without them the block was just an inline box, so latexcmds'
/// `\linebreak` (`inline-fil ++ embed-block-breakable ctx (block-skip
/// gap)`, `latexcmds.satyh:150`) never broke: the `inline-fil` swallowed
/// the line's whole slack and shoved everything after it off the page
/// edge, silently losing it (`このように`/`使い`/`すぎると`/`読みにくく`
/// all vanished from the render).
fn prim_embed_block_breakable(
    _interp: &mut Interp,
    mut args: Vec<Value>,
) -> Result<Value, EvalError> {
    let bb = as_block_boxes(args.pop().unwrap())?;
    let ctx = as_context(args.pop().unwrap())?;
    // Embed the block inline, top-anchored (the block's FIRST line sits on the
    // surrounding text baseline — same as `embed-block-top`).
    // `make_embedded_block` splits the box's height/depth around the first line
    // so the pager accounts for the embedded figure's extent.
    let block = match make_embedded_block(ctx.paragraph_width, bb, false, true) {
        Value::InlineBoxes(boxes) => boxes,
        other => return Ok(other),
    };
    let forced = || {
        HorzBox::Pure(PureHorzBox::Discretionary {
            penalty: FORCED_BREAK_PENALTY,
            pre_break: Vec::new(),
            post_break: Vec::new(),
            no_break: Vec::new(),
        })
    };
    let mut out = vec![forced()];
    out.extend(block);
    out.push(forced());
    Ok(Value::InlineBoxes(out))
}

/// `unite-path : path -> path -> path` — FAITHFUL: `path` is upstream's
/// `path list` (a list of independently-closed subpaths — see
/// `graphics.rs`'s `Path` doc comment), so uniting two is a plain
/// subpath-list append. Used by `math.satyh`'s `\norm` (two parallel bars).
fn prim_unite_path(_interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
    let p2 = as_path(args.pop().unwrap())?;
    let p1 = as_path(args.pop().unwrap())?;
    let mut subpaths = p1.subpaths;
    subpaths.extend(p2.subpaths);
    Ok(Value::Path(Path { subpaths }))
}

/// `set-min-gap-of-lines : length -> context -> context` (vminst.ml:1291) —
/// STAND-IN: no separate `min_gap_of_lines` field on `Context` yet (see
/// `set-leading`'s own comment on why IT, not this, is the baseline-distance
/// setter); accepted and dropped. Used by `math.satyh`'s `+math-list`, never
/// invoked eagerly.
fn prim_set_min_gap_of_lines(
    _interp: &mut Interp,
    mut args: Vec<Value>,
) -> Result<Value, EvalError> {
    let ctx = as_context(args.pop().unwrap())?;
    let _len = as_length(args.pop().unwrap())?;
    Ok(Value::Context(Box::new(ctx)))
}

/// `embed-math : context -> math -> inline-boxes` (vminst.ml:520) — the
/// bridge to the page: the faithful, primitive-driven analog of `read_math`,
/// operating on a `Value::Math` tree instead. FAITHFUL for the atoms
/// `read_math` already draws (plain/kerned/variant chars, groups, sup/sub);
/// the structural forms (fraction/radical/paren/limits/pull-in-scripts/
/// embedded-text) get a deliberately cheap, documented stand-in rendering
/// rather than an error, so `${…}`-shaped math built through these
/// primitives is never *unusable*, just not yet typographically faithful.
fn prim_embed_math_v006(interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
    let m = args.pop().unwrap();
    let ctx = as_context(args.pop().unwrap())?;
    let elems = as_math(interp, m)?;
    let boxed = layout_math_value(interp, &ctx, &elems)?;
    Ok(Value::InlineBoxes(vec![HorzBox::Pure(boxed)]))
}

/// `embed-math : context -> math-boxes -> inline-boxes` (vminst.ml:472) —
/// `as_math_boxes` then the SAME `layout_math_value` (:5165 below) — the
/// whole MATH-engine reuse in one primitive.
fn prim_embed_math_v01(interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
    let m = args.pop().unwrap();
    let ctx = as_context(args.pop().unwrap())?;
    let elems = as_math_boxes(m)?;
    let boxed = layout_math_value(interp, &ctx, &elems)?;
    Ok(Value::InlineBoxes(vec![HorzBox::Pure(boxed)]))
}

/// Lay out a faithful `&[Math]` run into one `PureHorzBox::Math`, mirroring
/// `read_math`'s glyph-emission shape (fixed-constant super/subscript
/// shift/scale, the same minimal `Bin`/`Rel` spacer) but keyed on each
/// atom's own EXPLICIT class (from `math-char`/`math-group`/…) rather than
/// `ascii_math_kind`'s inference.
fn layout_math_value(
    interp: &mut Interp,
    ctx: &Context,
    elems: &[Math],
) -> Result<PureHorzBox, EvalError> {
    let (glyphs, rules, width, _left, _right) =
        layout_math_list(interp, ctx, elems, ctx.font_size)?;
    let mut height = Length::ZERO;
    let mut depth = Length::ZERO;
    for g in &glyphs {
        height = height.max(g.dy + g.height);
        depth = depth.max(g.depth - g.dy);
    }
    // A fraction bar/radical sign is a `Fill` with no `MathGlyph` backing it
    // at all, so the glyph-only aggregation above would silently undercount
    // a run whose bar/sign extends above every glyph's own ink (e.g.
    // `${\sqrt{2}}`'s `l_extra` ascender). Fold every rule's own (y-up,
    // box-local — same frame as `MathGlyph::dy`) bounding box in too.
    for r in &rules {
        // `graphics_bbox` -> `Option`; a `None` rule (unreachable here
        // under 0.0.6 math rules) contributes nothing.
        if let Some(((_, min_y), (_, max_y))) = graphics_bbox(r) {
            height = height.max(max_y);
            depth = depth.max(-min_y);
        }
    }
    Ok(PureHorzBox::Math {
        width,
        height,
        depth,
        glyphs,
        rules,
    })
}

/// Lay out a flat `&[Math]` list at `size`, threading inter-atom spacing
/// (`space_before`, a minimal spacer) and returning the glyphs (at
/// LOCAL coordinates starting at `x = 0`), any graphics `rules` an atom
/// pushed (shifted horizontally by the same running `x` a glyph gets
/// — `layout_math_list` never shifts an atom vertically, only
/// `shift_and_append`'s callers do), the total width, and the boundary
/// classes on either end (needed by a `Group` ancestor, which can present
/// different left/right classes — see `Math::Group`'s doc comment).
fn layout_math_list(
    interp: &mut Interp,
    ctx: &Context,
    elems: &[Math],
    size: Length,
) -> Result<
    (
        Vec<MathGlyph>,
        Vec<GraphicsElem>,
        Length,
        MathKind,
        MathKind,
    ),
    EvalError,
> {
    // Lay every atom out FIRST, because `normalize_math_kind` below needs each
    // one's NEIGHBOURS' raw classes — upstream's `convert_to_low` passes
    // `mkprev`/`mknext` into `convert_to_low_single` for exactly this
    // (`math.ml:753-765`, via `get_right_math_kind`/`get_left_math_kind`).
    // The layout of an atom does not depend on its class, only the SPACING
    // between atoms does, so splitting the walk in two moves no glyph.
    let mut laid: Vec<(
        Vec<MathGlyph>,
        Vec<GraphicsElem>,
        Length,
        MathKind,
        MathKind,
    )> = Vec::with_capacity(elems.len());
    for atom in elems {
        laid.push(layout_math_atom(interp, ctx, atom, size)?);
    }

    let mut glyphs = Vec::new();
    let mut rules = Vec::new();
    let mut x = Length::ZERO;
    let mut last_kind: Option<MathKind> = None;
    let mut first_kind: Option<MathKind> = None;
    let in_script = math_in_script(ctx, size);
    for (i, (atom_glyphs, atom_rules, atom_width, left_raw, right_raw)) in
        laid.iter().cloned().enumerate()
    {
        // `mkprev`/`mknext` are the neighbours' RAW classes (upstream never
        // feeds a normalized class back in), and the ends of the list are
        // `MathEnd` — `math.ml:1270`'s `convert_to_low mathctx MathEnd MathEnd`.
        let prev_raw = if i == 0 { MathKind::End } else { laid[i - 1].4 };
        let next_raw = laid.get(i + 1).map_or(MathKind::End, |a| a.3);
        let left = normalize_math_kind(prev_raw, next_raw, left_raw);
        let right = normalize_math_kind(prev_raw, next_raw, right_raw);
        if let Some(prev) = last_kind {
            x += space_before(prev, left, in_script, size);
        }
        first_kind.get_or_insert(left);
        let base_x = x;
        for mut g in atom_glyphs {
            g.dx = base_x + g.dx;
            glyphs.push(g);
        }
        for r in &atom_rules {
            rules.push(shift_graphics((base_x, Length::ZERO), r));
        }
        x = base_x + atom_width;
        last_kind = Some(right);
    }
    let left = first_kind.unwrap_or(MathKind::Ord);
    let right = last_kind.unwrap_or(MathKind::Ord);
    Ok((glyphs, rules, x, left, right))
}

/// Upstream `check_subscript` (math.ml:682-699): if a superscript base's
/// LAST element is itself a `Sub`, strip it — returning `(subscript script,
/// new base)` where the new base is the preceding elements followed by the
/// inner `Sub`'s own base, so `{x_1}^2` becomes one base carrying both a
/// sub and a sup. Recurses through `ChangeColor`/`ChangeCharClass`.
fn check_subscript(base: &[Math]) -> Option<(Vec<Math>, Vec<Math>)> {
    let (last, head) = base.split_last()?;
    match last {
        Math::Sub(inner_base, sub_script) => {
            let mut new_base = head.to_vec();
            new_base.extend(inner_base.iter().cloned());
            Some((sub_script.clone(), new_base))
        }
        Math::ChangeColor(color, inner) => {
            let (sub_script, inner_new) = check_subscript(inner)?;
            let mut new_base = head.to_vec();
            new_base.push(Math::ChangeColor(color.clone(), inner_new));
            Some((vec![Math::ChangeColor(color.clone(), sub_script)], new_base))
        }
        Math::ChangeCharClass(cls, inner) => {
            let (sub_script, inner_new) = check_subscript(inner)?;
            let mut new_base = head.to_vec();
            new_base.push(Math::ChangeCharClass(cls.clone(), inner_new));
            Some((
                vec![Math::ChangeCharClass(cls.clone(), sub_script)],
                new_base,
            ))
        }
        _ => None,
    }
}

/// Upstream `invoke_pull_in_scripts` (math.ml:957-966): call a
/// `math-pull-in-scripts` resolver with the actual pulled-in scripts —
/// `resolver : math option -> math option -> math`, SUBSCRIPT option first,
/// SUPERSCRIPT second — then splice the returned math after the remaining
/// base as ONE `Group(cls1, cls2, …)` atom and lay the whole list out.
#[allow(clippy::too_many_arguments)]
fn layout_pull_in_scripts(
    interp: &mut Interp,
    ctx: &Context,
    head: &[Math],
    cls1: MathKind,
    cls2: MathKind,
    resolver: &Value,
    sub: Option<&[Math]>,
    sup: Option<&[Math]>,
    size: Length,
) -> Result<
    (
        Vec<MathGlyph>,
        Vec<GraphicsElem>,
        Length,
        MathKind,
        MathKind,
    ),
    EvalError,
> {
    let opt_math = |o: Option<&[Math]>| match o {
        Some(m) => Value::Ctor(
            "Some".to_string(),
            Some(Box::new(Value::Math(Rc::new(m.to_vec())))),
        ),
        None => Value::Ctor("None".to_string(), None),
    };
    let partial = interp.apply(resolver.clone(), opt_math(sub))?;
    let result = interp.apply(partial, opt_math(sup))?;
    let resolved = as_math(interp, result)?;
    let mut items: Vec<Math> = head.to_vec();
    items.push(Math::Group(cls1, cls2, (*resolved).clone()));
    layout_math_list(interp, ctx, &items, size)
}

/// The metrics-probe fallback policy: resolve `c` under `ctx`'s current
/// `math_char_class` (checking the runtime override map first, then the
/// built-in `default_math_variant_char` table), but only actually EMIT the
/// remapped codepoint if the current font can render it
/// (`interp.metrics.advance` returns `Some`) — otherwise fall back to the
/// source char `c` (its class, from `Context::math_class_map`/
/// `ascii_math_kind`-style inference, is kept regardless). This is what
/// keeps base-14/WinAnsi documents byte-identical (`Base14Metrics` returns
/// `None` outside ASCII 32-126) while a math-capable TTF, or a permissive
/// test stub, gets the real Mathematical-Alphanumeric glyph automatically.
fn resolve_variant_char(interp: &Interp, ctx: &Context, c: char, size: Length) -> char {
    let mapped = ctx
        .math_variant_char_map
        .get(&(c, ctx.math_char_class))
        .copied()
        .or_else(|| default_math_variant_char(ctx.math_char_class, c));
    match mapped {
        Some(m) if math_char_available(interp, ctx, m, size) => m,
        _ => c,
    }
}

/// Invoke ONE `paren` closure (`math.satyh`'s `paren-left`/
/// `paren-right`/`abs-left`/`brace-left`/…) exactly the way upstream's
/// `make_paren` does (`math.ml:644-649`): 5 CURRIED args in order — inner
/// height `h_in` (≥0), inner depth SIGNED (≤0, hence `-d_in` — this port
/// carries depths as non-negative magnitudes, see this function's `d_in`
/// param doc below), the axis height at the local size, the local
/// (script-scaled) size, and the current text color — then unpack the
/// returned `(inline-boxes, length -> length)` 2-tuple and harvest the
/// boxes' glyphs/rules/width via `math_boxes_of_inline_boxes` (the
/// graphics-harvesting sibling of `math_glyphs_of_inline_boxes`, since a
/// closure's delimiter is drawn `Fill`/`Stroke` ink via `inline-graphics`,
/// not a font glyph). The kernf itself is returned un-invoked (callers
/// re-derive/discard it as `math.ml:923` does for `ParenWithMiddle`'s own
/// middle).
///
/// `d_in`: this port's non-negative ink-depth MAGNITUDE (`inner_ink_extent`'s
/// second component). Upstream's own box depths are non-positive internally
/// (`convert_to_low`'s `dC` folds via `Length.min`, always ≤ `Length.zero`),
/// and `half-length` (`math.satyh:1023-1026`) computes the below-axis need
/// as `hgtaxis +' dpt` on that SIGNED value — so passing the magnitude
/// directly would OVERSIZE every delimiter below the axis (double-counts
/// the depth on the wrong side). Negating here is what keeps the closure's
/// own arithmetic faithful without changing this port's magnitude
/// convention everywhere else.
fn make_paren_run(
    interp: &mut Interp,
    ctx: &Context,
    paren: &Value,
    h_in: Length,
    d_in: Length,
    axis: Length,
    size: Length,
) -> Result<(Vec<MathGlyph>, Vec<GraphicsElem>, Length, Value), EvalError> {
    let mut v = paren.clone();
    if interp.version.math_is_split() {
        // 0.1 protocol (math.ml:640-642): `paren h d ictx` — (height, SIGNED
        // depth, context). The closure extracts fontsize / axis-ratio (via
        // `get-math-axis-height-ratio`) / color FROM the context instead of
        // receiving them as separate explicit arguments (the 0.0.6→0.1
        // delta, `t_paren`'s doc comment). Upstream's `ictx` is already
        // scaled to the local (script-level) size at this call site; this
        // port threads `size` as a separate parameter, so clone-and-set —
        // BIGGEST RISK: forgetting this silently
        // oversizes script-level delimiters (the closure would read the
        // OUTER context's font_size instead of the local scaled one).
        let mut c2 = ctx.clone();
        c2.font_size = size;
        let args = [
            Value::Length(h_in),
            Value::Length(-d_in),
            Value::Context(Box::new(c2)),
        ];
        for a in args {
            v = interp.apply(v, a)?;
        }
    } else {
        // 0.0.6 protocol.
        let args = [
            Value::Length(h_in),
            Value::Length(-d_in),
            Value::Length(axis),
            Value::Length(size),
            make_color_value(ctx.text_color),
        ];
        for a in args {
            v = interp.apply(v, a)?;
        }
    }
    let (boxes_v, kernf) = match v {
        Value::Tuple(mut items) if items.len() == 2 => {
            let kernf = items.pop().unwrap();
            (items.pop().unwrap(), kernf)
        }
        other => {
            return eval_error(format!(
                "math-paren: a paren closure must return (inline-boxes, length -> length), got {}",
                other.type_name()
            ))
        }
    };
    let boxes = as_inline_boxes(boxes_v)?;
    let (glyphs, rules, width) = math_boxes_of_inline_boxes(&boxes);
    Ok((glyphs, rules, width, kernf))
}

/// The original MATH-native stretchy-delimiter body, extracted verbatim as
/// the fallback `Math::Paren`/`Math::ParenWithMiddle` now take when the
/// closure route (`make_paren_run`, primary — upstream-faithful) errors:
/// every delimiter renders as a correctly-SIZED `(`/`)`/`|` regardless of
/// the requested paren kind (identity-wrong, but usable, for any closure
/// that can't be run — a synthetic/ill-shaped test closure, or a real error
/// from a malformed user-supplied one).
fn paren_variant_fallback(
    interp: &mut Interp,
    ctx: &Context,
    parts: Vec<(Vec<MathGlyph>, Vec<GraphicsElem>, Length)>,
    h_in: Length,
    d_in: Length,
    axis: Length,
    size: Length,
) -> Result<
    (
        Vec<MathGlyph>,
        Vec<GraphicsElem>,
        Length,
        MathKind,
        MathKind,
    ),
    EvalError,
> {
    let target = (h_in - axis).max(axis + d_in) * 2.0;
    let mut glyphs = Vec::new();
    let mut rules = Vec::new();
    let mut x = Length::ZERO;
    push_delimiter_glyph(interp, ctx, '(', size, target, axis, &mut glyphs, &mut x)?;
    for (i, (pg, pr, pw)) in parts.into_iter().enumerate() {
        if i > 0 {
            push_delimiter_glyph(interp, ctx, '|', size, target, axis, &mut glyphs, &mut x)?;
        }
        append_at(&mut glyphs, &mut rules, &mut x, pg, pr, pw);
    }
    push_delimiter_glyph(interp, ctx, ')', size, target, axis, &mut glyphs, &mut x)?;
    Ok((glyphs, rules, x, MathKind::Open, MathKind::Close))
}

/// Re-derive a paren base's TRAILING (right) delimiter's dense math
/// kern function by re-invoking its closure at the script-attachment site
/// (`superscript_kern`'s glyph-corner sampling doesn't apply to a paren
/// base — it has no single "last glyph" to sample italic-correction/corner
/// kerns off; the closure itself IS the source of truth for how much a
/// script should tuck into it, exactly upstream's `lp_math_kern_scheme`,
/// `math.ml:906`/`922`). Closures are pure (`math.satyh`'s bundled ones
/// have no side effects), so re-invoking with the SAME `(h_in, d_in, axis,
/// size)` the original `Math::Paren`/`ParenWithMiddle` layout used yields
/// the identical `kernf` value. Returns `None` when `base`'s last atom
/// isn't a paren, or when re-running its closure(s) errors (the delimiter
/// fallback path carries no math-kern scheme at all — `dense_kern`'s
/// caller then falls back to zero, matching that stand-in's own
/// `kerninfo _ = 0pt` shape).
fn paren_trailing_kernf(
    interp: &mut Interp,
    ctx: &Context,
    base: &[Math],
    size: Length,
) -> Option<Value> {
    let (r, h_in, d_in) = match base.last()? {
        Math::Paren(_, r, inner) => {
            let (g, ru, ..) = layout_math_list(interp, ctx, inner, size).ok()?;
            let (h, d) = inner_ink_extent(&g, &ru);
            (r, h, d)
        }
        Math::ParenWithMiddle(_, r, _, parts) => {
            let mut h = Length::ZERO;
            let mut d = Length::ZERO;
            for p in parts {
                let (g, ru, ..) = layout_math_list(interp, ctx, p, size).ok()?;
                let (ph, pd) = inner_ink_extent(&g, &ru);
                h = h.max(ph);
                d = d.max(pd);
            }
            (r, h, d)
        }
        _ => return None,
    };
    let mc = MathC::of(interp, ctx);
    let axis = mc.axis(size);
    let (_, _, _, kernf) = make_paren_run(interp, ctx, r, h_in, d_in, axis, size).ok()?;
    Some(kernf)
}

/// `fontInfo.ml:361`'s `DenseMathKern` branch: `Length.negate (kernf
/// corrhgt)` — the closure returns a POSITIVE tuck amount (how far to slide
/// the script INTO the delimiter's hollow), and the engine negates it into
/// a kern (negative = closer to the previous glyph, `get_math_kern`'s own
/// doc comment). Any failure (wrong-shaped return, closure error) collapses
/// to `Length::ZERO` — no kern, not a layout error; matches
/// `paren_trailing_kernf`'s own `None`-on-error contract.
fn dense_kern(interp: &mut Interp, kernf: &Value, corrhgt: Length) -> Length {
    match interp.apply(kernf.clone(), Value::Length(corrhgt)) {
        Ok(Value::Length(l)) => -l,
        _ => Length::ZERO,
    }
}

/// Lay out one `Math` atom at `size` (LOCAL coordinates, `x` starting at
/// 0), returning its glyphs, any graphics `rules` it pushed (only the
/// `Fraction`/`Radical` arms produce any; every other arm forwards its
/// children's), width, and left/right boundary class.
fn layout_math_atom(
    interp: &mut Interp,
    ctx: &Context,
    atom: &Math,
    size: Length,
) -> Result<
    (
        Vec<MathGlyph>,
        Vec<GraphicsElem>,
        Length,
        MathKind,
        MathKind,
    ),
    EvalError,
> {
    match atom {
        Math::Pure(MathElement::Char { class, big, chars })
        | Math::Pure(MathElement::CharWithKern {
            class, big, chars, ..
        }) => {
            let mut glyphs = Vec::new();
            let mut x = Length::ZERO;
            for c in chars.chars() {
                if *big {
                    push_big_char_glyph(interp, ctx, c, size, &mut glyphs, &mut x)?;
                } else {
                    push_char_glyph(interp, ctx, c, size, &mut glyphs, &mut x)?;
                }
            }
            Ok((glyphs, Vec::new(), x, *class, *class))
        }
        Math::Pure(MathElement::VariantChar { class, style, .. }) => {
            // Select the target codepoints by the CURRENT restyling
            // (`Context::math_char_class`, set by `ChangeCharClass`'s
            // layout arm below) rather than always `style.italic` — these
            // are explicit per-style codepoints the caller built
            // (`math-variant-char`), so no metrics-probe fallback (unlike
            // `resolve_variant_char`): `push_char_glyph` errors like any
            // other explicit-codepoint atom if the font can't render it.
            let text = match ctx.math_char_class {
                MathCharClass::Italic => &style.italic,
                MathCharClass::BoldItalic => &style.bold_italic,
                MathCharClass::Roman => &style.roman,
                MathCharClass::BoldRoman => &style.bold_roman,
                MathCharClass::Script => &style.script,
                MathCharClass::BoldScript => &style.bold_script,
                MathCharClass::Fraktur => &style.fraktur,
                MathCharClass::BoldFraktur => &style.bold_fraktur,
                MathCharClass::DoubleStruck => &style.double_struck,
                // `MathVariantStyle` (this
                // 9-field record) is deliberately NOT widened to 14 fields
                // — it models the 0.0.6 `math-variant-char` prim's record
                // shape, which upstream itself never grew sans-
                // serif/typewriter fields for either (only `math-char-class`
                // itself widened, `horzBox.ml:98-113`). This arm is
                // unreachable in practice: `math-variant-char`/
                // `MathElement::VariantChar` is a V0_0-only prim
                // (registered `v006` only, `primitives.rs`'s prim table),
                // and the 5 new `MathCharClass` ctors are V0_1-only
                // (`prim_types.rs::math_char_class_decl`) — the two can
                // never co-occur. Closest-analog fallback, purely to keep
                // the match exhaustive.
                MathCharClass::SansSerif | MathCharClass::Typewriter => &style.roman,
                MathCharClass::ItalicSansSerif => &style.italic,
                MathCharClass::BoldSansSerif => &style.bold_roman,
                MathCharClass::BoldItalicSansSerif => &style.bold_italic,
            };
            let mut glyphs = Vec::new();
            let mut x = Length::ZERO;
            for c in text.chars() {
                push_char_glyph(interp, ctx, c, size, &mut glyphs, &mut x)?;
            }
            Ok((glyphs, Vec::new(), x, *class, *class))
        }
        Math::Pure(MathElement::VariantCharPending(s)) => {
            // One MATHCHAR token, resolved now that `ctx` (font +
            // math_char_class + both override maps) is available: first
            // try the whole-TOKEN class map (`=`, `-`, `,`, … ->
            // (replacement, MathKind)); if the token isn't there, fall back
            // to a per-char variant remap (the metrics-probe policy)
            // with `MathKind::Ord`.
            let mut glyphs = Vec::new();
            let mut x = Length::ZERO;
            if let Some((target, kind)) = ctx.math_class_map.get(s.as_str()) {
                let kind = *kind;
                let all_renderable = target
                    .chars()
                    .all(|c| math_char_available(interp, ctx, c, size));
                let chosen = if all_renderable {
                    target.clone()
                } else {
                    s.clone()
                };
                for c in chosen.chars() {
                    push_char_glyph(interp, ctx, c, size, &mut glyphs, &mut x)?;
                }
                return Ok((glyphs, Vec::new(), x, kind, kind));
            }
            for c in s.chars() {
                let chosen = resolve_variant_char(interp, ctx, c, size);
                push_char_glyph(interp, ctx, chosen, size, &mut glyphs, &mut x)?;
            }
            Ok((glyphs, Vec::new(), x, MathKind::Ord, MathKind::Ord))
        }
        Math::Pure(MathElement::EmbeddedText { class, body }) => {
            let v = interp.apply((**body).clone(), Value::Context(Box::new(ctx.clone())))?;
            let boxes = as_inline_boxes(v)?;
            // `math_boxes_of_inline_boxes`, not the glyphs-only walk: embedded
            // inline content can carry its ink as GRAPHICS rather than glyphs.
            // latexcmds' `\underset`/`\overset` are exactly that — they reduce
            // to `text-in-math (… \normal-underset …)`, which draws through
            // `inline-graphics` + `draw-text`. Harvesting glyphs alone kept the
            // box's WIDTH and threw the drawing away, so the Schrödinger-equation
            // example rendered as `[−     + V(x)]Ψ`: a correctly-sized hole where
            // the fraction and its under-text should be.
            let (glyphs, rules, width) = math_boxes_of_inline_boxes(&boxes);
            Ok((glyphs, rules, width, *class, *class))
        }
        Math::Pure(MathElement::EmbeddedBoxes { class, boxes }) => {
            // V0_1 `embed-inline-to-math`: eager, already-materialized
            // boxes, so no closure application (contrast `EmbeddedText`
            // above) — but the same graphics-bearing content is possible.
            let (glyphs, rules, width) = math_boxes_of_inline_boxes(boxes);
            Ok((glyphs, rules, width, *class, *class))
        }
        Math::Group(cls1, cls2, inner) => {
            let (glyphs, rules, width, _, _) = layout_math_list(interp, ctx, inner, size)?;
            Ok((glyphs, rules, width, *cls1, *cls2))
        }
        Math::Sup(base, script) => {
            // Upstream MathSuperscript: (1) check_subscript merges a
            // base-tail `Sub` into one base + (sub, sup) pair;
            // (2) check_pull_in hands the script(s) to a base-tail
            // `PullInScripts` resolver.
            if let Some((sub_script, new_base)) = check_subscript(base) {
                if let Some((Math::PullInScripts(cls1, cls2, resolver), head)) =
                    new_base.split_last()
                {
                    return layout_pull_in_scripts(
                        interp,
                        ctx,
                        head,
                        *cls1,
                        *cls2,
                        resolver,
                        Some(&sub_script),
                        Some(script),
                        size,
                    );
                }
                // No pull-in (`{x_1}^2`): one sub+sup pair on the same base.
                let (mut glyphs, mut rules, base_width, left, _) =
                    layout_math_list(interp, ctx, &new_base, size)?;
                let mc = MathC::of(interp, ctx);
                let script_size = size * mc.script_scale();
                // Re-derive ONCE (a paren base's dense math
                // kern function, if `new_base`'s trailing atom is a paren —
                // `paren_trailing_kernf`'s doc comment) and reuse it for
                // BOTH the sup and sub kerns below, mirroring
                // `lp_math_kern_scheme`'s single scheme feeding both corner
                // attachments upstream.
                let paren_kernf = paren_trailing_kernf(interp, ctx, &new_base, size);
                // Subscripts are always cramped; the superscript inherits
                // the ambient cramped state unchanged (do NOT flip/reset it
                // here).
                let sub_ctx = Context {
                    math_cramped: true,
                    ..ctx.clone()
                };
                let (sub_glyphs, sub_rules, sub_width, _, _) =
                    layout_math_list(interp, &sub_ctx, &sub_script, script_size)?;
                let (sup_glyphs, sup_rules, sup_width, _, _) =
                    layout_math_list(interp, ctx, script, script_size)?;
                let (h_base, d_base) = inner_ink_extent(&glyphs, &rules);
                let (_, d_sup) = inner_ink_extent(&sup_glyphs, &sup_rules);
                let (h_sub, _) = inner_ink_extent(&sub_glyphs, &sub_rules);
                let sup_shift_raw = mc.sup_shift_clamped(ctx.font_size, h_base, d_sup);
                let sub_shift_raw = mc.sub_shift_clamped(ctx.font_size, d_base, h_sub);
                let (sup_shift, sub_shift) = mc.correct_script_gap(
                    ctx.font_size,
                    d_sup,
                    h_sub,
                    sup_shift_raw,
                    sub_shift_raw,
                );
                let kern = match &paren_kernf {
                    Some(kf) => dense_kern(interp, kf, sup_shift - d_sup),
                    None => superscript_kern(
                        interp,
                        ctx,
                        size,
                        script_size,
                        &glyphs,
                        &sup_glyphs,
                        sup_shift,
                        h_base,
                        d_sup,
                    ),
                };
                let sub_kern = paren_kernf
                    .as_ref()
                    .map(|kf| dense_kern(interp, kf, h_sub - d_base))
                    .unwrap_or(Length::ZERO);
                shift_and_append(
                    &mut glyphs,
                    &mut rules,
                    sub_glyphs,
                    sub_rules,
                    base_width + sub_kern,
                    -sub_shift,
                );
                shift_and_append(
                    &mut glyphs,
                    &mut rules,
                    sup_glyphs,
                    sup_rules,
                    base_width + kern,
                    sup_shift,
                );
                return Ok((
                    glyphs,
                    rules,
                    base_width + (sub_kern + sub_width).max(kern + sup_width),
                    left,
                    MathKind::Ord,
                ));
            }
            if let Some((Math::PullInScripts(cls1, cls2, resolver), head)) = base.split_last() {
                return layout_pull_in_scripts(
                    interp,
                    ctx,
                    head,
                    *cls1,
                    *cls2,
                    resolver,
                    None,
                    Some(script),
                    size,
                );
            }
            let (mut glyphs, mut rules, base_width, left, _) =
                layout_math_list(interp, ctx, base, size)?;
            let mc = MathC::of(interp, ctx);
            let script_size = size * mc.script_scale();
            let (script_glyphs, script_rules, script_width, _, _) =
                layout_math_list(interp, ctx, script, script_size)?;
            let (h_base, _) = inner_ink_extent(&glyphs, &rules);
            let (_, d_sup) = inner_ink_extent(&script_glyphs, &script_rules);
            let sup_shift = mc.sup_shift_clamped(ctx.font_size, h_base, d_sup);
            // A paren base has no italic correction / glyph
            // corner kern to sample (`superscript_kern`'s own last-glyph
            // sampling would hit the INNER run's last glyph, not the
            // delimiter) — its closure's dense kern REPLACES
            // `superscript_kern` outright rather than adding to it.
            let kern = match paren_trailing_kernf(interp, ctx, base, size) {
                Some(kf) => dense_kern(interp, &kf, sup_shift - d_sup),
                None => superscript_kern(
                    interp,
                    ctx,
                    size,
                    script_size,
                    &glyphs,
                    &script_glyphs,
                    sup_shift,
                    h_base,
                    d_sup,
                ),
            };
            shift_and_append(
                &mut glyphs,
                &mut rules,
                script_glyphs,
                script_rules,
                base_width + kern,
                sup_shift,
            );
            Ok((
                glyphs,
                rules,
                base_width + kern + script_width,
                left,
                MathKind::Ord,
            ))
        }
        Math::Sub(base, script) => {
            // Upstream MathSubscript: a `PullInScripts` at the base list's
            // TAIL receives the subscript itself instead of a corner script.
            if let Some((Math::PullInScripts(cls1, cls2, resolver), head)) = base.split_last() {
                return layout_pull_in_scripts(
                    interp,
                    ctx,
                    head,
                    *cls1,
                    *cls2,
                    resolver,
                    Some(script),
                    None,
                    size,
                );
            }
            let (mut glyphs, mut rules, base_width, left, _) =
                layout_math_list(interp, ctx, base, size)?;
            let mc = MathC::of(interp, ctx);
            let script_size = size * mc.script_scale();
            // Subscripts are always cramped.
            let sub_ctx = Context {
                math_cramped: true,
                ..ctx.clone()
            };
            let (script_glyphs, script_rules, script_width, _, _) =
                layout_math_list(interp, &sub_ctx, script, script_size)?;
            let (_, d_base) = inner_ink_extent(&glyphs, &rules);
            let (h_sub, _) = inner_ink_extent(&script_glyphs, &script_rules);
            let sub_shift = mc.sub_shift_clamped(ctx.font_size, d_base, h_sub);
            // Non-paren subscripts carry no kern (`kern = Length::ZERO`); a
            // paren base's closure supplies one via `paren_trailing_kernf`'s
            // `Some` arm.
            let kern = match paren_trailing_kernf(interp, ctx, base, size) {
                Some(kf) => dense_kern(interp, &kf, h_sub - d_base),
                None => Length::ZERO,
            };
            shift_and_append(
                &mut glyphs,
                &mut rules,
                script_glyphs,
                script_rules,
                base_width + kern,
                -sub_shift,
            );
            Ok((
                glyphs,
                rules,
                base_width + kern + script_width,
                left,
                MathKind::Ord,
            ))
        }
        Math::ChangeColor(_, inner) => {
            // STAND-IN: color restyling doesn't affect glyph rendering yet
            // — just render the content.
            let (glyphs, rules, width, left, right) = layout_math_list(interp, ctx, inner, size)?;
            Ok((glyphs, rules, width, left, right))
        }
        Math::ChangeCharClass(cls, inner) => {
            // Lay `inner` out under a
            // context with `math_char_class` set to `cls`, which is what
            // `VariantCharPending`/`VariantChar`'s arms above consult.
            let ctx2 = Context {
                math_char_class: *cls,
                ..ctx.clone()
            };
            let (glyphs, rules, width, left, right) = layout_math_list(interp, &ctx2, inner, size)?;
            Ok((glyphs, rules, width, left, right))
        }
        Math::Fraction(num, den) => {
            // Real numerator/denominator placement (`math.ml:574-594`
            // `numerator_baseline_height`/ `denominator_baseline_depth`)
            // plus a bar `Fill` — replaces the ASCII "num / den" stand-in.
            // `num`/`den` are laid out at the SAME `size` as this atom (no
            // script-scale reduction — a fraction's own
            // numerator/denominator aren't scripts, matching upstream's
            // `convert_to_low` call with the ambient `mathctx` unchanged).
            let (num_glyphs, num_rules, num_w, ..) = layout_math_list(interp, ctx, num, size)?;
            // The denominator is always cramped; the numerator inherits the
            // ambient cramped state unchanged.
            let den_ctx = Context {
                math_cramped: true,
                ..ctx.clone()
            };
            let (den_glyphs, den_rules, den_w, ..) = layout_math_list(interp, &den_ctx, den, size)?;
            let w = num_w.max(den_w);
            // Center the narrower of the two over/under the wider
            // (`math.ml:1140-1155`'s symmetric padding).
            let num_dx = (w - num_w) * 0.5;
            let den_dx = (w - den_w) * 0.5;
            let (_, d_numer) = inner_ink_extent(&num_glyphs, &num_rules);
            let (h_denom, _) = inner_ink_extent(&den_glyphs, &den_rules);
            let mc = MathC::of(interp, ctx);
            let numer_shift = mc.frac_numer_shift(size, d_numer);
            let denom_shift = mc.frac_denom_shift(size, h_denom);
            let axis = mc.axis(size);
            let rule = mc.frac_rule(size);
            let mut glyphs = Vec::new();
            let mut rules = Vec::new();
            // `num dy>0` (raised above the axis), `den dy<0` (`frac_denom_
            // shift` is already signed negative — see that method's doc
            // comment) — both applied via the SAME up-positive `dy_shift`
            // `shift_and_append` uses for Sup/Sub.
            shift_and_append(
                &mut glyphs,
                &mut rules,
                num_glyphs,
                num_rules,
                num_dx,
                numer_shift,
            );
            shift_and_append(
                &mut glyphs,
                &mut rules,
                den_glyphs,
                den_rules,
                den_dx,
                denom_shift,
            );
            // The bar itself: `rect x∈[0,w], y∈[axis·s, axis·s+rule·s]`
            // (a deliberate simplification of
            // upstream's own `Rectangle((xpos, ypos+h_bar+t_bar/2), (wid,
            // t_bar))`, which centers the rule on its OWN half-thickness
            // rather than sitting flush on the axis; this port picks the
            // simpler flush-on-axis placement instead).
            rules.push(GraphicsElem::Fill(
                ctx.text_color,
                rect_path((Length::ZERO, axis), (w, rule)),
            ));
            Ok((glyphs, rules, w, MathKind::Inner, MathKind::Inner))
        }
        Math::Radical(_degree, inner) => {
            // Real bar metrics (`math.ml:620-626` `radical_bar_
            // metrics`) plus a ported `default_radical` checkmark `Fill`
            // (`primitives.cppo.ml:311-355`) and an overbar rect `Fill` —
            // replaces the U+221A stand-in. `RadicalWithDegree` (`_degree =
            // Some(..)`, `\sqrt[n]{..}`) stays unimplemented — the degree is
            // carried faithfully in the
            // `Math` value but silently NOT drawn, matching upstream's own
            // parity note (`math.ml:886-899`'s `failwith "unsupported"` is
            // upstream's harder failure mode; this port's own stand-in
            // policy already chose "render the radicand
            // without the degree" over erroring, unchanged since).
            // The radicand is always cramped.
            let radicand_ctx = Context {
                math_cramped: true,
                ..ctx.clone()
            };
            let (inner_glyphs, inner_rules, inner_w, ..) =
                layout_math_list(interp, &radicand_ctx, inner, size)?;
            let (h_cont, d_cont) = inner_ink_extent(&inner_glyphs, &inner_rules);
            let mc = MathC::of(interp, ctx);
            let (h_bar, t_bar, l_extra) = mc.radical_bar_metrics(size, h_cont);
            // `_nonnegdpt` (the sign's own, slightly deeper, ink extent —
            // `default_radical`'s downward checkmark stroke pads `d_cont` by
            // `size*0.1`, upstream's own `nonnegdpt`) isn't threaded into
            // this atom's reported `depth` directly: unlike upstream's own
            // `d_whole = d_cont` (`math.ml:884`, a "temporary" simplification
            // per its own comment there), this port's `layout_math_value`
            // folds every rule's `graphics_bbox` into the OUTER box's
            // height/depth (a correctness fix, `PureHorzBox::Math`'s doc
            // comment), so the sign's real ink depth reaches the top-level
            // box automatically THROUGH the drawn `Fill` — no separate
            // manual accounting needed here.
            let (sign_path, sign_w, _nonnegdpt) = radical_sign_geometry(size, h_bar, t_bar, d_cont);
            let mut rules = vec![GraphicsElem::Fill(ctx.text_color, sign_path)];
            // Overbar + radicand share the same x-range right after the
            // sign (`math.ml:1163-1176`'s `hbbar`/`hbback`/`hblstC`); the
            // radicand itself stays at `dy = 0` (its own baseline), exactly
            // upstream — `h_bar` already clears it via the vertical-gap add
            // in `radical_bar_metrics`, so no raise is needed here.
            rules.push(GraphicsElem::Fill(
                ctx.text_color,
                rect_path((sign_w, h_bar), (inner_w, t_bar)),
            ));
            // `l_extra`: the extra ascender ABOVE the bar this run reports
            // to its container (upstream `h_whole = h_rad +% l_extra`,
            // `math.ml:882`) — no ink of its own, just headroom, so there's
            // no glyph/fill shape to naturally carry it. A single-point
            // "extent marker" `Fill` (a subpath with a `move_to` and no
            // further segments paints nothing — PDF's `f` on a degenerate
            // zero-length path is a no-op) reports it through the SAME
            // `graphics_bbox` fold `layout_math_value` already does for
            // every rule, without adding a new return channel just for this
            // one field.
            rules.push(GraphicsElem::Fill(
                ctx.text_color,
                Path {
                    subpaths: vec![Subpath {
                        start: (Length::ZERO, h_bar + t_bar + l_extra),
                        segs: Vec::new(),
                        closing: Closing::Open,
                    }],
                },
            ));
            let mut glyphs = Vec::new();
            for mut g in inner_glyphs {
                g.dx = sign_w + g.dx;
                glyphs.push(g);
            }
            for r in &inner_rules {
                rules.push(shift_graphics((sign_w, Length::ZERO), r));
            }
            Ok((
                glyphs,
                rules,
                sign_w + inner_w,
                MathKind::Inner,
                MathKind::Inner,
            ))
        }
        Math::Paren(l, r, inner) => {
            // PRIMARY route is upstream's own `make_paren` closure
            // invocation (`math.ml:644-649`, `make_paren_run` above) —
            // identity (a `\paren` drawing round parens vs. an `\abs`
            // drawing vertical bars, etc.) lives ENTIRELY in the `l`/`r`
            // closures (`math.satyh`'s `paren-left`/`abs-left`/…), so
            // running them is what makes different delimiter kinds actually
            // look different. Falls back to the MATH-native
            // stretchy-variant stand-in (`paren_variant_fallback`) only if
            // either closure errors (synthetic/ill-shaped test closures, or
            // a real user error) — that fallback's own delimiter kind is
            // always `(`/`)` regardless of what was requested. Inner is laid
            // out OUTSIDE the closure
            // route so an inner layout error still propagates normally
            // (only closure-route errors trigger the fallback); splice
            // order `lg ++ inner ++ rg` matches upstream's own
            // `LowMathParen(lpL, lpR, lmC)` (`math.ml:909`).
            let (inner_glyphs, inner_rules, inner_w, ..) =
                layout_math_list(interp, ctx, inner, size)?;
            let (h_in, d_in) = inner_ink_extent(&inner_glyphs, &inner_rules);
            let mc = MathC::of(interp, ctx);
            let axis = mc.axis(size);
            let closure_route =
                make_paren_run(interp, ctx, l, h_in, d_in, axis, size).and_then(|left| {
                    let right = make_paren_run(interp, ctx, r, h_in, d_in, axis, size)?;
                    Ok((left, right))
                });
            match closure_route {
                Ok(((lg, lr, lw, _), (rg, rr, rw, _))) => {
                    let mut glyphs = Vec::new();
                    let mut rules = Vec::new();
                    let mut x = Length::ZERO;
                    append_at(&mut glyphs, &mut rules, &mut x, lg, lr, lw);
                    append_at(
                        &mut glyphs,
                        &mut rules,
                        &mut x,
                        inner_glyphs,
                        inner_rules,
                        inner_w,
                    );
                    append_at(&mut glyphs, &mut rules, &mut x, rg, rr, rw);
                    Ok((glyphs, rules, x, MathKind::Open, MathKind::Close))
                }
                Err(_) => paren_variant_fallback(
                    interp,
                    ctx,
                    vec![(inner_glyphs, inner_rules, inner_w)],
                    h_in,
                    d_in,
                    axis,
                    size,
                ),
            }
        }
        Math::ParenWithMiddle(l, r, m, mlstlst) => {
            // Same closure-primary/fallback policy as `Math::Paren`,
            // but ONE shared `(h_in, d_in)` over every part (the tallest
            // part's ink drives the size of every delimiter, including the
            // middle separator(s)) — mirrors upstream's own
            // `MathParenWithMiddle` fold (`math.ml:912-916`). The middle
            // closure's own kernf is DISCARDED (`math.ml:923`: `let
            // (hblstmiddle, _) = make_paren mathctx middle hC dC in ...`) —
            // a separator never tucks a script into itself.
            let mut parts = Vec::with_capacity(mlstlst.len());
            let mut h_in = Length::ZERO;
            let mut d_in = Length::ZERO;
            for part in mlstlst {
                let (part_glyphs, part_rules, part_w, ..) =
                    layout_math_list(interp, ctx, part, size)?;
                let (h, d) = inner_ink_extent(&part_glyphs, &part_rules);
                h_in = h_in.max(h);
                d_in = d_in.max(d);
                parts.push((part_glyphs, part_rules, part_w));
            }
            let mc = MathC::of(interp, ctx);
            let axis = mc.axis(size);
            let closure_route =
                make_paren_run(interp, ctx, l, h_in, d_in, axis, size).and_then(|left| {
                    let right = make_paren_run(interp, ctx, r, h_in, d_in, axis, size)?;
                    let middle = make_paren_run(interp, ctx, m, h_in, d_in, axis, size)?;
                    Ok((left, right, middle))
                });
            match closure_route {
                Ok(((lg, lr, lw, _), (rg, rr, rw, _), (mg, mr, mw, _))) => {
                    let mut glyphs = Vec::new();
                    let mut rules = Vec::new();
                    let mut x = Length::ZERO;
                    append_at(&mut glyphs, &mut rules, &mut x, lg, lr, lw);
                    for (i, (part_glyphs, part_rules, part_w)) in parts.into_iter().enumerate() {
                        if i > 0 {
                            append_at(&mut glyphs, &mut rules, &mut x, mg.clone(), mr.clone(), mw);
                        }
                        append_at(
                            &mut glyphs,
                            &mut rules,
                            &mut x,
                            part_glyphs,
                            part_rules,
                            part_w,
                        );
                    }
                    append_at(&mut glyphs, &mut rules, &mut x, rg, rr, rw);
                    Ok((glyphs, rules, x, MathKind::Open, MathKind::Close))
                }
                Err(_) => paren_variant_fallback(interp, ctx, parts, h_in, d_in, axis, size),
            }
        }
        Math::UpperLimit(base, upper) => {
            let (mut glyphs, mut rules, base_width, left, right) =
                layout_math_list(interp, ctx, base, size)?;
            let mc = MathC::of(interp, ctx);
            let script_size = size * mc.script_scale();
            let (script_glyphs, script_rules, script_width, _, _) =
                layout_math_list(interp, ctx, upper, script_size)?;
            let (h_base, _) = inner_ink_extent(&glyphs, &rules);
            let (_, d_up) = inner_ink_extent(&script_glyphs, &script_rules);
            let up_shift = mc.upper_limit_shift(ctx.font_size, h_base, d_up);
            // A LIMIT is CENTERED over its base, not set beside it
            // (`math.ml:1219-1231`: upstream pads the narrower of the two with
            // half the difference on each side, so the whole is
            // `max(w_base, w_up)` wide). Placing it at `base_width` — i.e. to
            // the right, widening the box to the SUM — set `\sum_a^b`'s limits
            // off the operator's shoulder instead of above and below it.
            let (base_dx, script_dx) = center_offsets(base_width, script_width);
            shift_existing(&mut glyphs, &mut rules, base_dx);
            shift_and_append(
                &mut glyphs,
                &mut rules,
                script_glyphs,
                script_rules,
                script_dx,
                up_shift,
            );
            Ok((glyphs, rules, base_width.max(script_width), left, right))
        }
        Math::LowerLimit(base, lower) => {
            let (mut glyphs, mut rules, base_width, left, right) =
                layout_math_list(interp, ctx, base, size)?;
            let mc = MathC::of(interp, ctx);
            let script_size = size * mc.script_scale();
            let (script_glyphs, script_rules, script_width, _, _) =
                layout_math_list(interp, ctx, lower, script_size)?;
            let (_, d_base) = inner_ink_extent(&glyphs, &rules);
            let (h_low, _) = inner_ink_extent(&script_glyphs, &script_rules);
            let low_shift = mc.lower_limit_shift(ctx.font_size, d_base, h_low);
            // Centered under the base — see the `UpperLimit` arm above.
            let (base_dx, script_dx) = center_offsets(base_width, script_width);
            shift_existing(&mut glyphs, &mut rules, base_dx);
            shift_and_append(
                &mut glyphs,
                &mut rules,
                script_glyphs,
                script_rules,
                script_dx,
                -low_shift,
            );
            Ok((glyphs, rules, base_width.max(script_width), left, right))
        }
        Math::PullInScripts(cls1, cls2, resolver) => {
            // Not consumed by an enclosing Sub/Sup (bare `\sum` with no
            // scripts): resolver gets (None, None).
            layout_pull_in_scripts(interp, ctx, &[], *cls1, *cls2, resolver, None, None, size)
        }
        // V0_1 only (`read-math`): lay `inner` out
        // with ambient context = the STORED context, and size = the
        // stored context's OWN `font_size` — an ABSOLUTE override, not a
        // further multiply of the caller's `size`. This is deliberate: a
        // `WithContext` built under an `enter_script`-shrunk context
        // already carries the script-shrunk `font_size` in `stored`, so
        // laying it out at `stored.font_size` (rather than at this call's
        // `size`) means the engine's own Sup/Sub shrink is never applied a
        // second time on top of it.
        Math::WithContext(stored, inner) => {
            layout_math_list(interp, stored, inner, stored.font_size)
        }
    }
}

/// Append `glyphs`/`rules` (already at LOCAL coordinates relative to their
/// own run) onto `out_glyphs`/`out_rules` at the running `*x`, advancing `*x`
/// past them — the no-spacing-adjustment sibling of `layout_math_list`'s
/// per-atom loop, used by the structural stand-ins above (paren) that
/// concatenate sub-runs directly rather than through the spacing table.
/// `rules` shifts horizontally only (`shift_graphics` with a zero `dy` —
/// `append_at`'s callers never raise/lower a sub-run, only `dx`-place it;
/// contrast `shift_and_append` below, which does both).
fn append_at(
    out_glyphs: &mut Vec<MathGlyph>,
    out_rules: &mut Vec<GraphicsElem>,
    x: &mut Length,
    glyphs: Vec<MathGlyph>,
    rules: Vec<GraphicsElem>,
    width: Length,
) {
    let base_x = *x;
    for mut g in glyphs {
        g.dx = base_x + g.dx;
        out_glyphs.push(g);
    }
    for r in &rules {
        out_rules.push(shift_graphics((base_x, Length::ZERO), r));
    }
    *x = base_x + width;
}

/// Horizontal offsets that CENTER a limit against its base: half the width
/// difference goes to whichever of the two is narrower, so the pair occupies
/// `max(base, script)` (upstream `math.ml:1219-1231`).
fn center_offsets(base_width: Length, script_width: Length) -> (Length, Length) {
    if base_width < script_width {
        ((script_width - base_width) * 0.5, Length::ZERO)
    } else {
        (Length::ZERO, (base_width - script_width) * 0.5)
    }
}

/// Slide already-emitted glyphs/rules right by `dx` — used when a limit is
/// WIDER than its base, so the base itself has to move to stay centered.
fn shift_existing(glyphs: &mut [MathGlyph], rules: &mut [GraphicsElem], dx: Length) {
    if dx == Length::ZERO {
        return;
    }
    for g in glyphs.iter_mut() {
        g.dx = g.dx + dx;
    }
    for r in rules.iter_mut() {
        *r = shift_graphics((dx, Length::ZERO), r);
    }
}

/// Append `glyphs`/`rules` (LOCAL coordinates, from an isolated
/// `layout_math_list` call) onto `out_glyphs`/`out_rules`, shifting every
/// glyph/rule right by `dx_shift` (its base's own width — placing the
/// script/numerator/denominator/radicand right after the preceding content)
/// and up/down by `dy_shift` (`> 0` raises, `< 0` lowers) — the `Math`-atom
/// analog of `place_script`, which instead threads a single
/// running `x` across a flat `MathElem` list. `rules` go through the SAME
/// `shift_graphics` a standalone `inline-graphics` box's `shift-graphics`
/// primitive uses — box-local, y-**up** coordinates, exactly
/// `MathGlyph::dy`'s sign convention (a critical correctness note: get
/// this sign wrong and a fraction bar/ radical mirrors instead of landing
/// at the axis).
fn shift_and_append(
    out_glyphs: &mut Vec<MathGlyph>,
    out_rules: &mut Vec<GraphicsElem>,
    glyphs: Vec<MathGlyph>,
    rules: Vec<GraphicsElem>,
    dx_shift: Length,
    dy_shift: Length,
) {
    for mut g in glyphs {
        g.dx = dx_shift + g.dx;
        g.dy = g.dy + dy_shift;
        out_glyphs.push(g);
    }
    for r in &rules {
        out_rules.push(shift_graphics((dx_shift, dy_shift), r));
    }
}

/// An axis-aligned rectangle `Fill` path, box-local (y-**up**): bottom-left
/// corner `origin`, extending `size.0` right and `size.1` up. Shared by the
/// fraction bar and the radical overbar — both are exactly this
/// shape, just at different `y`/width.
fn rect_path(origin: Point, size: (Length, Length)) -> Path {
    let (x, y) = origin;
    let (w, h) = size;
    Path {
        subpaths: vec![Subpath {
            start: (x, y),
            segs: vec![
                PathSeg::Line((x + w, y)),
                PathSeg::Line((x + w, y + h)),
                PathSeg::Line((x, y + h)),
            ],
            closing: Closing::Line,
        }],
    }
}

/// Port of `default_radical` (`primitives.cppo.ml:311-355`): the radical
/// checkmark's `GeneralPath`, plus its own natural advance (`wid`, upstream's
/// `PHGFixedGraphics`'s declared width) and `nonnegdpt` (its own depth
/// extent, upstream's declared `depth` — returned for completeness though
/// The overall `Math::Radical` depth uses `d_cont` directly, matching
/// upstream's own "temporary" simplification, see that arm's call site).
/// `size` is the ambient LOCAL nesting size (upstream `fontsize`); `hgt_bar`/
/// `t_bar` come from `MathC::radical_bar_metrics`; `dpt` is the radicand's
/// own depth (a NON-NEGATIVE magnitude, this port's convention — see
/// `sup_shift_clamped`'s doc comment; upstream's signed `Length.negate dpt`
/// becomes a plain ADD of `dpt` here).
///
/// Box-local origin `(0, 0)` = this atom's own baseline-left corner (where
/// upstream's `graphics (xpos, ypos)` closure is finally called with the
/// box's placed anchor — every point below is relative to that same origin,
/// matching `PathSeg`/`Subpath`'s y-**up** convention).
fn radical_sign_geometry(
    size: Length,
    hgt_bar: Length,
    t_bar: Length,
    dpt: Length,
) -> (Path, Length, Length) {
    let w_m = size * 0.02;
    let w1 = size * 0.1;
    let w2 = size * 0.15;
    let w3 = size * 0.4;
    let w_a = size * 0.18;
    let h1 = size * 0.3;
    let h2 = size * 0.375;

    let nonnegdpt = dpt + size * 0.1;
    let l_r = hgt_bar + nonnegdpt;

    let wid = w_m + w1 + w2 + w3;
    let a1 = (h2 - h1) / w1;
    let a2 = h2 / w2;
    let a3 = l_r / w3;
    let t1 = t_bar * (1.0 + a1 * a1).sqrt();
    let t3 = t_bar * (((1.0 + a3 * a3).sqrt() - 1.0) / a3);
    let h_a = h1 + t1 + w_a * a1;
    let w_b = (l_r + t_bar - h_a - (w1 + w2 + w3 - t3 - w_a) * a3) * (-1.0 / (a2 + a3));
    let h_b = h_a - w_b * a2;

    let path = Path {
        subpaths: vec![Subpath {
            start: (wid, hgt_bar),
            segs: vec![
                PathSeg::Line((w_m + w1 + w2, -nonnegdpt)),
                PathSeg::Line((w_m + w1, -nonnegdpt + h2)),
                PathSeg::Line((w_m, -nonnegdpt + h1)),
                PathSeg::Line((w_m, -nonnegdpt + h1 + t1)),
                PathSeg::Line((w_m + w_a, -nonnegdpt + h_a)),
                PathSeg::Line((w_m + w_a + w_b, -nonnegdpt + h_b)),
                PathSeg::Line((wid - t3, hgt_bar + t_bar)),
                PathSeg::Line((wid, hgt_bar + t_bar)),
            ],
            closing: Closing::Line,
        }],
    };
    (path, wid, nonnegdpt)
}

/// Flatten `text-in-math`'s embedded `inline-boxes` (already laid out
/// by `read_inline` against the math atom's own context) into `MathGlyph`s
/// nestable in a math run — the box-in-math bridge `layout_math_atom`'s
/// `EmbeddedText` arm needs. Mirrors `linebreak.rs`'s `natural_metrics`
/// exhaustive `PureHorzBox` walk EXACTLY (same variant list, same "what
/// advances `x`" choice per variant) so an added/renamed `PureHorzBox`
/// variant can't silently drop content here without also breaking that
/// walk. Caveats (faithful to what's actually renderable here): only
/// `InnerString`/nested `Math` boxes contribute real glyphs (hence height/
/// depth, computed by the caller from the returned glyphs); every other
/// box kind (`Image`/`Graphics`/`Tabular`/`EmbeddedBlock`/…) keeps its
/// horizontal space but contributes no ink; text run at full (non-script)
/// size regardless of the math run's own `size` (upstream-faithful — a
/// `text-in-math` body is laid out once, by `read_inline`, before this
/// function ever sees it).
// UNWIRED. `layout_script` builds the same `(Vec<MathGlyph>, Length)` on the
// live path, so nothing calls this. Kept rather than deleted because
// `math_boxes_of_inline_boxes` below is documented as its sibling, and
// because it is the upstream-faithful flattening a `text-in-math` body needs
// if that path is ever wired back up.
#[allow(dead_code)]
fn math_glyphs_of_inline_boxes(boxes: &[HorzBox]) -> (Vec<MathGlyph>, Length) {
    fn go(pure: &PureHorzBox, out: &mut Vec<MathGlyph>, x: &mut Length) {
        match pure {
            PureHorzBox::InnerString {
                info,
                text,
                width,
                height,
                depth,
            } => {
                out.push(MathGlyph {
                    info: info.clone(),
                    text: text.clone(),
                    gid: None,
                    dx: *x,
                    dy: Length::ZERO,
                    width: *width,
                    height: *height,
                    depth: *depth,
                });
                *x += *width;
            }
            PureHorzBox::OuterEmpty { natural, .. } => *x += *natural,
            PureHorzBox::OuterFil => {}
            PureHorzBox::FixedEmpty { width } => *x += *width,
            PureHorzBox::Image { width, .. } => *x += *width,
            PureHorzBox::Discretionary { no_break, .. } => {
                for p in no_break {
                    go(p, out, x);
                }
            }
            PureHorzBox::Graphics { width, .. } => *x += *width,
            // An unresolved `inline-graphics-outer` marker has zero width
            // (fil semantics, see the variant's doc comment) and no glyph
            // representation this walk can extract — advance past it like
            // `Image`/`Tabular` (a resolved one is an ordinary `Graphics`,
            // handled by the arm above).
            PureHorzBox::GraphicsOuter { width, .. } => *x += *width,
            PureHorzBox::Math { width, glyphs, .. } => {
                for g in glyphs {
                    let mut g = g.clone();
                    g.dx = *x + g.dx;
                    out.push(g);
                }
                *x += *width;
            }
            PureHorzBox::HookPageBreak { .. } => {}
            PureHorzBox::Tabular(tab) => *x += tab.width,
            PureHorzBox::EmbeddedBlock { width, .. } => *x += *width,
            // A frame in a math context has no glyph representation this
            // walk can extract — advance past it like `Image`/`Tabular`.
            PureHorzBox::Frame { width, .. } => *x += *width,
            PureHorzBox::FrameMarker { .. } => {}
            // Zero-width bracket; its contents are spliced siblings, already
            // walked by this same loop.
            PureHorzBox::InlineFrameMarker { .. } => {}
            // Zero-width marker; no glyph representation. Same treatment
            // as `HookPageBreak`.
            PureHorzBox::Footnote { .. } => {}
            // inert reflow marker, no glyph representation — same
            // treatment as `HookPageBreak`/`FrameMarker`/`Footnote`
            // above.
            PureHorzBox::InlineMark(_) => {}
        }
    }
    let mut glyphs = Vec::new();
    let mut x = Length::ZERO;
    for HorzBox::Pure(p) in boxes {
        go(p, &mut glyphs, &mut x);
    }
    (glyphs, x)
}

/// `math_glyphs_of_inline_boxes`'s graphics-harvesting sibling — the
/// shape a `make_paren` closure's result needs, since a delimiter drawn via
/// `inline-graphics` (`math.satyh`'s `paren-left`/`abs-left`/…, `fill`/
/// `stroke` a path) carries its ink as a `PureHorzBox::Graphics` box, not a
/// `MathGlyph`. The same exhaustive `PureHorzBox` variant list as
/// `math_glyphs_of_inline_boxes` (do NOT modify that function — every OTHER
/// caller still wants glyphs-only, e.g. `EmbeddedText`), but additionally
/// harvests `Graphics::elems` (`dx`-shifted via `shift_graphics`, the box's
/// own local-origin convention — see `PureHorzBox::Graphics`'s doc comment)
/// and forwards BOTH the glyphs AND `rules` out of any nested
/// `PureHorzBox::Math` box (a paren closure could, in principle, embed one
/// via `text-in-math`/`embed-math`).
///
/// ONE arm diverges from that sibling and makes this walk VERTICAL too: `dy`
/// (y-up, box-local — `MathGlyph::dy`'s own frame) carries the offset of the
/// stacked line a nested `EmbeddedBlock`'s content sits on. `Frame` and
/// `Tabular` still contribute width alone; they could be descended into the
/// same way, but nothing in the corpus puts either inside a `text-in-math`
/// body, so neither has a measured shape to be faithful to.
fn math_boxes_of_inline_boxes(boxes: &[HorzBox]) -> (Vec<MathGlyph>, Vec<GraphicsElem>, Length) {
    fn go(
        pure: &PureHorzBox,
        out: &mut Vec<MathGlyph>,
        rules: &mut Vec<GraphicsElem>,
        x: &mut Length,
        dy: Length,
    ) {
        match pure {
            PureHorzBox::InnerString {
                info,
                text,
                width,
                height,
                depth,
            } => {
                out.push(MathGlyph {
                    info: info.clone(),
                    text: text.clone(),
                    gid: None,
                    dx: *x,
                    dy,
                    width: *width,
                    height: *height,
                    depth: *depth,
                });
                *x += *width;
            }
            PureHorzBox::OuterEmpty { natural, .. } => *x += *natural,
            PureHorzBox::OuterFil => {}
            PureHorzBox::FixedEmpty { width } => *x += *width,
            PureHorzBox::Image { width, .. } => *x += *width,
            PureHorzBox::Discretionary { no_break, .. } => {
                for p in no_break {
                    go(p, out, rules, x, dy);
                }
            }
            PureHorzBox::Graphics { width, elems, .. } => {
                for e in elems {
                    rules.push(shift_graphics((*x, dy), e));
                }
                *x += *width;
            }
            // See `math_glyphs_of_inline_boxes`'s matching arm.
            PureHorzBox::GraphicsOuter { width, .. } => *x += *width,
            PureHorzBox::Math {
                width,
                glyphs,
                rules: inner_rules,
                ..
            } => {
                for g in glyphs {
                    let mut g = g.clone();
                    g.dx = *x + g.dx;
                    g.dy += dy;
                    out.push(g);
                }
                for r in inner_rules {
                    rules.push(shift_graphics((*x, dy), r));
                }
                *x += *width;
            }
            PureHorzBox::HookPageBreak { .. } => {}
            PureHorzBox::Tabular(tab) => *x += tab.width,
            // A `line-stack-top`/`-bottom` (or `embed-block-top`/`-bottom`) box
            // handed BACK to math through `text-in-math` — azmath's
            // `\overbrace`/`\underbrace` (`parens.satyh:533`/`:561`) stack the
            // brace over the braced formula this way. Placed with
            // `place_embedded_block`'s (rustyfi-pdf) geometry but in this walk's
            // y-UP frame: `place_block_at` seats the stack at a page-y-DOWN
            // origin, the anchored line lands on the math baseline
            // (`anchor_last`: the LAST for `-bottom`, the FIRST for `-top` —
            // upstream's `adjust_to_last_line`/`adjust_to_first_line`), and
            // every other line is offset by the NEGATED difference of their
            // placed baselines. That is the same split `make_embedded_block`
            // measured the box's own height/depth from, so what
            // `layout_math_value` folds back up agrees with the box metrics the
            // rest of the pipeline already saw.
            PureHorzBox::EmbeddedBlock {
                width,
                block,
                anchor_last,
                ..
            } => {
                let placed = place_block_at((Length::ZERO, Length::ZERO), block.clone());
                let anchor = if *anchor_last {
                    placed.last()
                } else {
                    placed.first()
                };
                if let Some(anchor) = anchor {
                    let anchor_y = anchor.baseline_y;
                    for line in &placed {
                        let line_dy = dy - (line.baseline_y - anchor_y);
                        for (cdx, cbx) in &line.contents {
                            // Each stacked line has its own horizontal origin,
                            // and must not advance the OUTER run's pen — the
                            // block's own `width` accounts for that once below.
                            let mut cx = *x + line.x + *cdx;
                            go(cbx, out, rules, &mut cx, line_dy);
                        }
                    }
                }
                *x += *width;
            }
            // See `math_glyphs_of_inline_boxes`'s matching arm.
            PureHorzBox::Frame { width, .. } => *x += *width,
            PureHorzBox::FrameMarker { .. } => {}
            // See `math_glyphs_of_inline_boxes`'s matching arm.
            PureHorzBox::InlineFrameMarker { .. } => {}
            // See `math_glyphs_of_inline_boxes`'s matching arm.
            PureHorzBox::Footnote { .. } => {}
            // See `math_glyphs_of_inline_boxes`'s matching arm.
            PureHorzBox::InlineMark(_) => {}
        }
    }
    let mut glyphs = Vec::new();
    let mut rules = Vec::new();
    let mut x = Length::ZERO;
    for HorzBox::Pure(p) in boxes {
        go(p, &mut glyphs, &mut rules, &mut x, Length::ZERO);
    }
    (glyphs, rules, x)
}

// ============================================================================
// ---- context-setter + box-combinator prims `code.satyh`/`itemize.satyh`
// need. ------------------------------------------------------------------
// ============================================================================

/// The inverse of `as_color` (mirrors `evalUtil.ml:124`'s `get_color` the
/// other way) — `get-text-color`'s result, which `itemize.satyh` feeds
/// straight into `fill`, so the tag/payload shape must match `as_color`
/// exactly (see that primitive's doc comment).
fn make_color_value(c: Color) -> Value {
    match c {
        Color::Gray(g) => Value::Ctor("Gray".to_string(), Some(Box::new(Value::Float(g)))),
        Color::Rgb(r, g, b) => Value::Ctor(
            "RGB".to_string(),
            Some(Box::new(Value::Tuple(vec![
                Value::Float(r),
                Value::Float(g),
                Value::Float(b),
            ]))),
        ),
        Color::Cmyk(c, m, y, k) => Value::Ctor(
            "CMYK".to_string(),
            Some(Box::new(Value::Tuple(vec![
                Value::Float(c),
                Value::Float(m),
                Value::Float(y),
                Value::Float(k),
            ]))),
        ),
    }
}

/// `font` = `Value::Tuple([string, float, float])` in `(abbrev, size_ratio,
/// rising_ratio)` order (vminst.ml's `tFONT`) — `set-font`'s second argument.
fn as_font(v: Value) -> Result<(String, f64, f64), EvalError> {
    match v {
        Value::Tuple(vs) if vs.len() == 3 => {
            let mut it = vs.into_iter();
            let abbrev = as_str(it.next().unwrap())?;
            let size_ratio = as_float(it.next().unwrap())?;
            let rising_ratio = as_float(it.next().unwrap())?;
            Ok((abbrev, size_ratio, rising_ratio))
        }
        other => eval_error(format!(
            "expected a font (string * float * float), got {}",
            other.type_name()
        )),
    }
}

/// [`as_font`]'s V0_1 twin — saphe-split's `tFONTWR = font * float * float`,
/// whose head is the opaque handle rather than an abbrev.
fn as_font_with_ratio(v: Value) -> Result<(FontKey, f64, f64), EvalError> {
    match v {
        Value::Tuple(vs) if vs.len() == 3 => {
            let mut it = vs.into_iter();
            let key = as_font_key(it.next().unwrap())?;
            let size_ratio = as_float(it.next().unwrap())?;
            let rising_ratio = as_float(it.next().unwrap())?;
            Ok((key, size_ratio, rising_ratio))
        }
        other => eval_error(format!(
            "expected a font (font * float * float), got {}",
            other.type_name()
        )),
    }
}

/// The opaque V0_1 `font` handle (upstream's `BCFontKey of FontKey.t`).
fn as_font_key(v: Value) -> Result<FontKey, EvalError> {
    match v {
        Value::Font(key) => Ok(key),
        other => eval_error(format!("expected a font, got {}", other.type_name())),
    }
}

/// `set-text-color : color -> context -> context` (vminst.ml:1603) —
/// FAITHFUL store (`Context::text_color`, the `set-font-size` shape); it
/// rides on every `HorzStringInfo` and both PDF writers emit `rg`/`g`
/// before `Tj` for a non-black run.
fn prim_set_text_color(_interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
    let ctx = as_context(args.pop().unwrap())?;
    let color = as_color(args.pop().unwrap())?;
    Ok(Value::Context(Box::new(Context {
        text_color: color,
        ..ctx
    })))
}

/// `get-text-color : context -> color` (vminst.ml:1618) — FAITHFUL and
/// load-bearing: `itemize.satyh`'s `make-bullet` feeds this straight into
/// `fill color (Gr.circle …)`, so it must round-trip exactly what
/// `set-text-color` stored (see `make_color_value`'s doc comment).
fn prim_get_text_color(_interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
    let ctx = as_context(args.pop().unwrap())?;
    Ok(make_color_value(ctx.text_color))
}

/// `set-hyphen-penalty : int -> context -> context` (vminst.ml:1692) —
/// FAITHFUL store (`Context::hyphen_badness`), now a real consumer:
/// `text_to_boxes`'s `flush_word` uses this as each injected
/// `Discretionary`'s `penalty`, but only when a dictionary is installed via
/// `set-hyphenation-dictionary` — with no dictionary installed (the
/// default), this is stored but has no layout effect, same as before.
/// `code.satyh`'s `set-hyphen-penalty 100000` still works as "disable
/// hyphenation" (huge positive penalty, DP avoids it).
fn prim_set_hyphen_penalty(_interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
    let ctx = as_context(args.pop().unwrap())?;
    let n = as_int(args.pop().unwrap())?;
    Ok(Value::Context(Box::new(Context {
        hyphen_badness: n,
        ..ctx
    })))
}

/// `set-hyphen-min : int -> int -> context -> context` (upstream
/// `vminstdef.yaml:1163-1177`) — writes
/// `Context::left_hyphen_min`/`right_hyphen_min`, each clamped to `>= 0`
/// (mirrors `set-space-ratio`'s `.max(0.0)` clamping style; a negative
/// minimum would be meaningless to the min-fragment filter in
/// `crate::hyphenation::hyphenate_word`).
fn prim_set_hyphen_min(_interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
    let ctx = as_context(args.pop().unwrap())?;
    let right = as_int(args.pop().unwrap())?.max(0);
    let left = as_int(args.pop().unwrap())?.max(0);
    Ok(Value::Context(Box::new(Context {
        left_hyphen_min: left,
        right_hyphen_min: right,
        ..ctx
    })))
}

/// `set-space-ratio : float -> float -> float -> context -> context`
/// (vminst.ml:1309), params `(natural, shrink, stretch)` — FAITHFUL store
/// (`Context::space_natural`/`space_shrink`/`space_stretch`, clamped to
/// `>= 0.0` like upstream), read by `text_to_boxes`'s interword-glue
/// computation.
fn prim_set_space_ratio(_interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
    let ctx = as_context(args.pop().unwrap())?;
    let stretch = as_float(args.pop().unwrap())?.max(0.0);
    let shrink = as_float(args.pop().unwrap())?.max(0.0);
    let natural = as_float(args.pop().unwrap())?.max(0.0);
    Ok(Value::Context(Box::new(Context {
        space_natural: natural,
        space_shrink: shrink,
        space_stretch: stretch,
        ..ctx
    })))
}

/// `set-space-ratio-between-scripts : float -> float -> float -> script ->
/// script -> context -> context` (`vminstdef.yaml:1230-1250`) — writes one
/// ordered script pair's entry of `ctx.script_space_map`
/// (`convertText.ml:34-50` reads it back).
///
/// Only the NATURAL ratio is stored. The other two arguments are accepted and
/// dropped, because upstream drops them too: `pure_space_between_scripts`
/// misplaces them into `LBAtom`'s height and depth slots, so no
/// `set-space-ratio-between-scripts` call in any document has ever been able
/// to give this glue stretch or shrink. See [`interscript_glue`].
///
/// This was a STAND-IN that ignored all three, on the reasoning that slydifi
/// only ever calls it with `0. 0. 0.` to SUPPRESS the spacing and the port
/// inserted none anyway. The port has inserted Latin↔CJK glue for some time
/// now, so ignoring the call left slydifi with a 0.24em space at every
/// Japanese/Latin junction that upstream does not set.
fn prim_set_space_ratio_between_scripts(
    _interp: &mut Interp,
    mut args: Vec<Value>,
) -> Result<Value, EvalError> {
    let ctx = as_context(args.pop().unwrap())?;
    let script2 = as_script(args.pop().unwrap())?;
    let script1 = as_script(args.pop().unwrap())?;
    let _stretch = as_float(args.pop().unwrap())?;
    let _shrink = as_float(args.pop().unwrap())?;
    // `max 0.`, as `vminstdef.yaml`'s own `set_space_ratio_between_scripts`
    // clamps each ratio before storing it.
    let natural = as_float(args.pop().unwrap())?.max(0.0);
    let mut script_space_map = ctx.script_space_map;
    script_space_map[script1 as usize][script2 as usize] = natural;
    Ok(Value::Context(Box::new(Context {
        script_space_map,
        ..ctx
    })))
}

/// `split-into-lines : string -> (int * string) list` (vminst.ml:2269) —
/// FAITHFUL: splits on `'\n'` and, per line, counts the leading ASCII spaces
/// `i` and returns `(i, rest_after_indent)` — exactly `evalUtil.ml:36`'s
/// `chop_space_indent`. Pure string op: no context, no box, no new type.
fn prim_split_into_lines(_interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
    let s = as_str(args.pop().unwrap())?;
    let mut out = Vec::new();
    for line in s.split('\n') {
        let indent = line.chars().take_while(|c| *c == ' ').count();
        let rest: String = line.chars().skip(indent).collect();
        out.push(Value::Tuple(vec![
            Value::Int(indent as i64),
            Value::Str(rest),
        ]));
    }
    Ok(Value::List(out))
}

/// Shift every content box in `block`'s `Line`s right by `pad_l`
/// (`block-frame-breakable`'s left-indent, point 4) — the simplest of the
/// two options that section names: adjusting each box's own `x` offset
/// directly rather than prepending an extra `FixedEmpty` box (`Skip`s carry
/// no `x` offsets to shift, so they pass through unchanged).
fn indent_left(block: Vec<VertBox>, pad_l: Length) -> Vec<VertBox> {
    block
        .into_iter()
        .map(|vb| match vb {
            VertBox::Line {
                height,
                depth,
                leading,
                contents,
            } => VertBox::Line {
                height,
                depth,
                leading,
                contents: contents
                    .into_iter()
                    .map(|(x, bx)| (x + pad_l, bx))
                    .collect(),
            },
            // `Skip`/`ClearPage`/`HookPageBreak` carry no `x` offsets to shift.
            other => other,
        })
        .collect()
}

/// `block-frame-breakable : context -> paddings -> deco-set -> (context ->
/// block-boxes) -> block-boxes` (vminst.ml:1090) — the `inline-frame-outer`
/// playbook, one dimension up:
/// `paddingL`/`paddingR` shrink the inner `reducef` closure's context width,
/// and the result is indented and top/bottom-padded with plain `Skip`s,
/// bracketed by a `FrameStart(id)`/`FrameEnd(id)` marker pair — the frame's
/// pads/width/deco-set are interned into `interp.decos` under `id`
/// (`DecoEntry::Block`), and `fire_hooks`'s block-fragment pass fires
/// `decoS` once the frame's whole single-page fragment is placed (the first
/// cut: multi-page fragments/`decoH`/`decoM`/`decoT` are a documented
/// follow-up, see `fire_hooks`'s doc comment).
/// Drop the margin boxes at either END of a `block-frame-breakable`'s body —
/// the first inner block's top margin and the last inner block's bottom
/// margin, which upstream's `normalize` never produces for a frame's contents
/// (`pageBreak.ml:664` and `:582-585`; see the call site). Margins in the
/// MIDDLE of the body are untouched: those are real inter-block gaps, squashed
/// there exactly as they are outside a frame.
fn strip_outer_margins(body: &mut Vec<VertBox>) {
    let is_margin = |vb: &VertBox| matches!(vb, VertBox::Skip(_) | VertBox::ParagTop(_));
    if body.first().is_some_and(is_margin) {
        body.remove(0);
    }
    if body.last().is_some_and(is_margin) {
        body.pop();
    }
}

fn prim_block_frame_breakable(
    interp: &mut Interp,
    version: RustyfiVersion,
    mut args: Vec<Value>,
) -> Result<Value, EvalError> {
    let k = args.pop().unwrap();
    let decoset = as_decoset(args.pop().unwrap())?;
    let (pad_l, pad_r, pad_t, pad_b) = as_paddings(args.pop().unwrap())?;
    let ctx = as_context(args.pop().unwrap())?;
    let id = DecoId(interp.decos.len());
    interp.decos.push(DecoEntry::Block {
        pads: Paddings {
            l: pad_l,
            r: pad_r,
            t: pad_t,
            b: pad_b,
        },
        width: ctx.paragraph_width,
        decoset,
        // See `make_inline_frame`'s identical capture.
        version,
    });
    let inner_ctx = Context {
        paragraph_width: ctx.paragraph_width - pad_l - pad_r,
        ..ctx
    };
    let inner = as_block_boxes(interp.apply(k, Value::Context(Box::new(inner_ctx)))?)?;
    let mut indented = indent_left(inner, pad_l);
    // THE FRAME CARRIES THE MARGINS, ITS BODY DOES NOT. Upstream normalizes a
    // frame's contents STANDALONE — `aux None TopMarginProhibited Alist.empty
    // vblstsub` (`pageBreak.ml:664`) — so the first inner block's `margin_top`
    // is never appended, and the last inner block's `margin_bottom` goes
    // through `squash_margins _ []`, whose empty-list arm (`:582-585`) emits
    // no skip at all. What surrounds the frame instead is the frame's OWN
    // `margins`, taken from the OUTER context (`vminstdef.yaml`'s
    // `BackendVertFrame`: `margin_top = ctx.paragraph_top`, `margin_bottom =
    // ctx.paragraph_bottom`), which `squash_margins` max-collapses against the
    // neighbouring blocks' margins exactly as `chop_page` collapses adjacent
    // `Skip`s.
    //
    // The distinction is not cosmetic: the body's `ParagTop` carries
    // `min_first_line_ascender` folded in (`prim_line_break`,
    // `lineBreak.ml:855-857`), and the frame's margin does NOT. Keeping the
    // body's made the advance INTO a frame a constant — `max(0, 9pt - hgt)`
    // cancels the first line's own height — where upstream's tracks the ink:
    // measured on `layout-tests/probes/code_line_height.saty` against real
    // SATySFi 0.0.11, `+code(`ooo`)` / `lll` / `ggg` advance 29.114 / 31.166 /
    // 29.138pt upstream and a flat 32.835pt here.
    strip_outer_margins(&mut indented);
    let mut out = Vec::with_capacity(indented.len() + 6);
    out.push(VertBox::Skip(ctx.paragraph_top));
    out.push(VertBox::FrameStart(id));
    out.push(VertBox::FramePad(pad_t));
    out.extend(indented);
    out.push(VertBox::FramePad(pad_b));
    out.push(VertBox::FrameEnd(id));
    out.push(VertBox::Skip(ctx.paragraph_bottom));
    Ok(Value::BlockBoxes(out))
}

/// Build the `PureHorzBox::EmbeddedBlock` shared by `embed-block-top`
/// (vminst.ml:1145) and `embed-block-bottom` (vminst.ml:1185). FAITHFUL:
/// `anchor_last` selects which of `block`'s lines lands on the surrounding
/// text baseline — the FIRST for top (upstream's `adjust_to_first_line`) or
/// the LAST for bottom (`adjust_to_last_line`) — computed by placing the
/// block once (`place_block_at`) to find where each line's baseline falls,
/// then splitting the box's total vertical extent around the anchored line:
/// around the first line for TOP, so the box hangs DOWN from the baseline;
/// around the last line for BOTTOM, so it hangs UP. A degenerate line-less
/// block (only skips, no baseline to anchor) falls back to
/// `measure_block`'s skip-as-height sum for both.
fn make_embedded_block(
    width: Length,
    block: Vec<VertBox>,
    anchor_last: bool,
    breakable: bool,
) -> Value {
    let first_line_height = block.iter().find_map(|vb| match vb {
        VertBox::Line { height, .. } => Some(*height),
        _ => None,
    });
    let last_line_depth = block.iter().rev().find_map(|vb| match vb {
        VertBox::Line { depth, .. } => Some(*depth),
        _ => None,
    });
    let (height, depth) = match (first_line_height, last_line_depth) {
        // Place once to learn each line's baseline, then split the box's
        // total vertical extent around the anchored line: `place_block_at`
        // seats the first baseline at `first_h` (origin 0), so the block
        // spans `[0, last_baseline + last_d]`.
        (Some(first_h), Some(last_d)) => {
            let placed = place_block_at((Length::ZERO, Length::ZERO), block.clone());
            let last_baseline = placed.last().map(|l| l.baseline_y).unwrap_or(first_h);
            let bottom_edge = last_baseline + last_d;
            if anchor_last {
                (last_baseline, last_d)
            } else {
                (first_h, bottom_edge - first_h)
            }
        }
        // A degenerate line-less block (only skips — no baseline to anchor):
        // keep `measure_block` (its skip-as-height fallback is right there).
        _ => measure_block(&block),
    };
    Value::InlineBoxes(vec![HorzBox::Pure(PureHorzBox::EmbeddedBlock {
        width,
        height,
        depth,
        block,
        anchor_last,
        breakable,
    })])
}

/// `embed-block-top : context -> length -> (context -> block-boxes) ->
/// inline-boxes` (vminst.ml:1145) — see [`make_embedded_block`].
fn prim_embed_block_top(interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
    let k = args.pop().unwrap();
    let wid = as_length(args.pop().unwrap())?;
    let ctx = as_context(args.pop().unwrap())?;
    let inner_ctx = Context {
        paragraph_width: wid,
        ..ctx
    };
    let block = as_block_boxes(interp.apply(k, Value::Context(Box::new(inner_ctx)))?)?;
    Ok(make_embedded_block(wid, block, false, false))
}

/// `embed-block-bottom : context -> length -> (context -> block-boxes) ->
/// inline-boxes` (vminst.ml:1185) — see [`make_embedded_block`]; anchors the
/// LAST line, used by latexcmds' `\parbox?:(Bottom)`.
fn prim_embed_block_bottom(interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
    let k = args.pop().unwrap();
    let wid = as_length(args.pop().unwrap())?;
    let ctx = as_context(args.pop().unwrap())?;
    let inner_ctx = Context {
        paragraph_width: wid,
        ..ctx
    };
    let block = as_block_boxes(interp.apply(k, Value::Context(Box::new(inner_ctx)))?)?;
    Ok(make_embedded_block(wid, block, true, false))
}

/// `line-stack-bottom : inline-boxes list -> inline-boxes` (vminst.ml:1229,
/// `evalUtil.ml`'s `make_line_stack`) — FAITHFUL: each `inline-boxes` in the
/// list becomes exactly one line, fit (not broken) to the widest line's
/// natural width via `fit_cell` (this port's `LineBreak.fit`, already used
/// by the tabular grid solver — same "no `Context`, `natural_metrics`
/// height/depth" fallback upstream's `make_line_stack` needs since it too
/// has no context to lean on). Lines are stacked with zero extra margin
/// (upstream's `VertParagraph`s all have `margin_top`/`margin_bottom =
/// None`): each line's `leading` is set to the previous line's depth plus
/// this line's height, so consecutive baselines sit exactly
/// `prev_depth + this_height` apart (see `pagebreak.rs`'s
/// `leading.max(height)` placement formula — this choice makes that `max`
/// always resolve to our computed `leading`). See `line_stack` for the
/// shared body and [`prim_line_stack_top`] for the other half.
fn prim_line_stack_bottom(_interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
    line_stack(args.pop().unwrap(), true)
}

/// `line-stack-top : inline-boxes list -> inline-boxes`
/// (vminstdef.yaml:1109 `BackendLineStackTop`) — FAITHFUL: the same
/// `make_line_stack` construction as [`prim_line_stack_bottom`], differing
/// only in which stacked line's baseline becomes the result's — one shared
/// body and one flag rather than two copies that could drift.
///
/// `ruby` calls this to sit its annotation above the base run.
fn prim_line_stack_top(_interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
    line_stack(args.pop().unwrap(), false)
}

/// `evalUtil.ml`'s `make_line_stack` — shared body of the two `line-stack-*`
/// prims; `anchor_last` picks upstream's `adjust_to_last_line` (`true`) or
/// `adjust_to_first_line` (`false`).
fn line_stack(arg: Value, anchor_last: bool) -> Result<Value, EvalError> {
    let hblstlst = as_list(arg)?
        .into_iter()
        .map(as_inline_boxes)
        .collect::<Result<Vec<_>, _>>()?;
    let wid = hblstlst
        .iter()
        .map(|hbs| natural_metrics(hbs).0)
        .fold(Length::ZERO, |acc, w| if w > acc { w } else { acc });
    let mut block = Vec::with_capacity(hblstlst.len());
    let mut prev_depth = Length::ZERO;
    for (idx, hbs) in hblstlst.into_iter().enumerate() {
        let (contents, height, depth) = fit_cell(hbs, wid);
        let leading = if idx == 0 {
            height + depth
        } else {
            prev_depth + height
        };
        block.push(VertBox::Line {
            height,
            depth,
            leading,
            contents,
        });
        prev_depth = depth;
    }
    // `anchor_last` IS upstream's `adjust_to_last_line`/`adjust_to_first_line`
    // choice: `line-stack-bottom` is BOTTOM-anchored (SATySFi vminst.ml:1229 —
    // the result baseline is the LAST stacked line's baseline), so the box's
    // height spans everything above that last line and its depth is the last
    // line's depth. Top-anchoring it instead put the baseline at the FIRST
    // line, which dropped the whole stack below the baseline — e.g. figbox's
    // `margin`/`hvmargin` (a `line-stack-bottom` of [top-mgn; content;
    // bot-mgn]) had its content rendered below its frame (the E=mc² bug). For
    // `line-stack-top` the first line IS the right anchor, which is the whole
    // difference between the two prims.
    Ok(make_embedded_block(wid, block, anchor_last, false))
}

/// `add-footnote : block-boxes -> inline-boxes` (vminst.ml:1130
/// `BackendAddFootnote`) — FAITHFUL: wraps the block in a zero-metric
/// `PureHorzBox::Footnote` marker (upstream `PHGFootnote`,
/// vminstdef.yaml:1034-1044; the upstream body's `PageBreak.solidify` is a
/// no-op here because this port's block-boxes are already solid
/// `Vec<VertBox>`). `chop_page` (rustyfi-backend) extracts the marker when
/// its line is committed to a page, reserves the stack's height at the
/// column bottom, and places the block bottom-aligned there — see that
/// function's doc comment. The cross-trial `changed`-flag protocol
/// `footnote-scheme.satyh` layers on top rides the crossref fixpoint.
fn prim_add_footnote(_interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
    let block = as_block_boxes(args.pop().unwrap())?;
    Ok(Value::InlineBoxes(vec![HorzBox::Pure(
        PureHorzBox::Footnote { block },
    )]))
}

/// `set-font : script -> string * float * float -> context -> context`
/// (0.0.6 `vminstdef.yaml:1335`, `tFONT` head) — real per-script wiring.
/// `abbrev` resolves through the font metrics
/// provider's registry first (`FontMetrics::resolve_font_abbrev` — a real
/// `TtfFontStore` built from `fonts.satysfi-hash`), falling back to
/// the 3-face name heuristic (`resolve_font_abbrev` free fn)
/// when the provider has no registry entry for it (an abbrev the config
/// doesn't name) — never an error, matching this
/// port's existing accept-and-degrade stance on unresolvable font names.
///
/// **Resolution rule (back-compat critical).** `Latin`-script text keeps
/// reading `Context::font` directly rather than `font_scheme[Latin]` (see
/// that field's doc comment) — `set-font Latin f` therefore writes BOTH so
/// the two stay in sync, but `set-font` on any OTHER script only touches
/// `font_scheme`, leaving `ctx.font` (and hence `set-font-key`/`\bold`/
/// `\emph`, which only ever read `ctx.font`) untouched.
fn prim_set_font_v006(interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
    let mut ctx = as_context(args.pop().unwrap())?;
    let (abbrev, size_ratio, rising_ratio) = as_font(args.pop().unwrap())?;
    let script = as_script(args.pop().unwrap())?;
    let font = interp
        .metrics
        .resolve_font_abbrev(&abbrev)
        .unwrap_or_else(|| resolve_font_abbrev(&abbrev));
    install_script_font(&mut ctx, script, font, size_ratio, rising_ratio);
    Ok(Value::Context(Box::new(ctx)))
}

/// `set-font : script -> font * float * float -> context -> context`
/// (saphe-split `tools/gencode/vminst.ml:1433`, `tFONTWR` head). Identical
/// to [`prim_set_font_v006`] except that the triple's head is ALREADY a
/// resolved handle — 0.1 has no abbrev at this point and nothing to resolve;
/// `load-single-font` did that when the font envelope's member was minted.
fn prim_set_font_v01(_interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
    let mut ctx = as_context(args.pop().unwrap())?;
    let (font, size_ratio, rising_ratio) = as_font_with_ratio(args.pop().unwrap())?;
    let script = as_script(args.pop().unwrap())?;
    install_script_font(&mut ctx, script, font, size_ratio, rising_ratio);
    Ok(Value::Context(Box::new(ctx)))
}

/// `get-font : script -> context -> string * float * float`
/// (vminstdef.yaml:1350 `PrimitiveGetFont`) — FAITHFUL: `script_font` IS
/// upstream's `get_font_with_ratio` (normalize the script, then read the
/// scheme slot), and the triple is `evalUtil.ml:196`'s `make_font_value`.
///
/// The head is a font ABBREV. Upstream's `font_scheme` stores abbrevs and
/// resolves them to files only at render time; this port resolves eagerly in
/// [`prim_set_font_v006`] and stores a `FontKey`, so the name comes back from
/// the store that minted it (`FontMetrics::font_abbrev`) and is `""` when the
/// key was never named by a registry — see that method for exactly when, and
/// why the corpus does not care (every caller in it, and upstream's own
/// `convertText.ml:78`, writes `let (_, ratio, _) =` and uses the RATIO,
/// which is exact).
///
/// This is what `ruby` and `quotation` need: the CJK face's size ratio, so a
/// ruby annotation or a two-em Japanese indent scales with the face rather
/// than with the Latin `get-font-size`.
fn prim_get_font_v006(interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
    let ctx = as_context(args.pop().unwrap())?;
    let script = as_script(args.pop().unwrap())?;
    let sf = script_font(&ctx, script);
    let abbrev = interp.metrics.font_abbrev(sf.font).unwrap_or_default();
    Ok(Value::Tuple(vec![
        Value::Str(abbrev),
        Value::Float(sf.ratio),
        Value::Float(sf.rising),
    ]))
}

/// `get-font : script -> context -> font * float * float` — the 0.1 arm,
/// mirroring [`prim_set_font_v006`]/[`prim_set_font_v01`]'s split. 0.1's
/// `font` IS the opaque handle this port already stores, so unlike the 0.0.6
/// arm there is nothing to recover: the value round-trips exactly.
fn prim_get_font_v01(_interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
    let ctx = as_context(args.pop().unwrap())?;
    let script = as_script(args.pop().unwrap())?;
    let sf = script_font(&ctx, script);
    Ok(Value::Tuple(vec![
        Value::Font(sf.font),
        Value::Float(sf.ratio),
        Value::Float(sf.rising),
    ]))
}

/// The half of `set-font` that is NOT version-forked — the `Context` write
/// both arms end at, kept in one place so the 0.0.6 behaviour cannot drift
/// when the 0.1 one changes. See `prim_set_font_v006`'s "Resolution rule".
fn install_script_font(ctx: &mut Context, script: Script, font: FontKey, ratio: f64, rising: f64) {
    ctx.font_scheme[script as usize] = ScriptFont {
        font,
        ratio,
        rising,
    };
    if script == Script::Latin {
        ctx.font = font;
    }
}

/// `set-code-text-command : [string] inline-cmd -> context -> context`
/// (`stdja:116`; no vminst.ml entry to cite). STAND-IN, same
/// shape as `set-math-command`/`set-math-font` above: `(command \cmd)`
/// means a real program CAN build a `[string]
/// inline-cmd` value to pass here — but `Context` (`rustyfi-backend`) still
/// cannot hold an arbitrary lang-side `Value` without a reverse crate
/// dependency, and the one seam this codebase uses for that indirection
/// (`Interp::hooks`'s ID-table, `eval.rs`) sits outside this file's
/// boundary — so the command argument is accepted (to keep the
/// arity/signature faithful) and dropped.
fn prim_set_code_text_command(
    interp: &mut Interp,
    mut args: Vec<Value>,
) -> Result<Value, EvalError> {
    let mut ctx = as_context(args.pop().unwrap())?;
    let cmd = args.pop().unwrap();
    ctx.code_text_command = Some(interp.register_math_command(cmd));
    Ok(Value::Context(Box::new(ctx)))
}

/// `get-natural-length : block-boxes -> length` (vminst.ml:2040) —
/// FAITHFUL: `get-natural-width`'s block sibling (`get-natural-width` itself
/// is a `pervasives.satyh` wrapper over `get-natural-metrics`, not a
/// primitive). A block's own "natural length" is its total vertical extent
/// — `measure_block`'s two components (height above the nominal top, depth
/// of the last line) summed into one length.
fn prim_get_natural_length(_interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
    let bb = as_block_boxes(args.pop().unwrap())?;
    let (height, depth) = measure_block(&bb);
    Ok(Value::Length(height + depth))
}

/// `set-dominant-wide-script : script -> context -> context`
/// (vminst.ml:1511 `PrimitiveSetDominantWideScript`) — FAITHFUL store,
/// consumed by `get-dominant-wide-script` now, by CJK script normalization
/// later.
fn prim_set_dominant_wide_script(
    _interp: &mut Interp,
    mut args: Vec<Value>,
) -> Result<Value, EvalError> {
    let ctx = as_context(args.pop().unwrap())?;
    let dominant_wide_script = as_script(args.pop().unwrap())?;
    Ok(Value::Context(Box::new(Context {
        dominant_wide_script,
        ..ctx
    })))
}

/// `set-dominant-narrow-script : script -> context -> context`
/// (vminst.ml:1539) — FAITHFUL store, mirror of the wide setter.
fn prim_set_dominant_narrow_script(
    _interp: &mut Interp,
    mut args: Vec<Value>,
) -> Result<Value, EvalError> {
    let ctx = as_context(args.pop().unwrap())?;
    let dominant_narrow_script = as_script(args.pop().unwrap())?;
    Ok(Value::Context(Box::new(Context {
        dominant_narrow_script,
        ..ctx
    })))
}

/// `set-language : script -> language -> context -> context`
/// (vminst.ml:1568 `PrimitiveSetLangSys`) — FAITHFUL per-script map insert
/// (`langsys_scheme |> ScriptSchemeMap.add script langsys` upstream; a
/// 4-slot array write here).
fn prim_set_language(_interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
    let ctx = as_context(args.pop().unwrap())?;
    let langsys = as_language(args.pop().unwrap())?;
    let script = as_script(args.pop().unwrap())?;
    let mut langsys_scheme = ctx.langsys_scheme;
    langsys_scheme[script as usize] = langsys;
    Ok(Value::Context(Box::new(Context {
        langsys_scheme,
        ..ctx
    })))
}

/// `get-dominant-wide-script : context -> script` (vminst.ml:1526) — FAITHFUL.
fn prim_get_dominant_wide_script(
    _interp: &mut Interp,
    mut args: Vec<Value>,
) -> Result<Value, EvalError> {
    let ctx = as_context(args.pop().unwrap())?;
    Ok(make_script_value(ctx.dominant_wide_script))
}

/// `get-dominant-narrow-script : context -> script` (vminst.ml:1555) — FAITHFUL.
fn prim_get_dominant_narrow_script(
    _interp: &mut Interp,
    mut args: Vec<Value>,
) -> Result<Value, EvalError> {
    let ctx = as_context(args.pop().unwrap())?;
    Ok(make_script_value(ctx.dominant_narrow_script))
}

/// `get-language : script -> context -> language` (vminst.ml:1587
/// `PrimitiveGetLangSys`) — FAITHFUL. Upstream routes through
/// `get_language_system`, whose `normalize_script` step is the identity on
/// every script a VALUE can carry (only the char-decoder-internal
/// CommonNarrow/CommonWide/Inherited normalize, horzBox.ml:470-479), so
/// this is a plain indexed read; absent-entry default `NoLanguageSystem`
/// is baked into the array's initial value.
fn prim_get_language(_interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
    let ctx = as_context(args.pop().unwrap())?;
    let script = as_script(args.pop().unwrap())?;
    Ok(make_language_value(ctx.langsys_scheme[script as usize]))
}

/// `set-every-word-break : inline-boxes -> inline-boxes -> context -> context`
/// (vminst.ml:3007 `PrimitiveSetEveryWordBreak`) — sets the inline-boxes
/// inserted before/after every inter-word break (mdja.satyh uses it for a
/// CJK word-break strut). STAND-IN: accepted and dropped (no per-context
/// every-word-break state yet), same pattern as `prim_set_language` above.
fn prim_set_every_word_break(
    _interp: &mut Interp,
    mut args: Vec<Value>,
) -> Result<Value, EvalError> {
    let ctx = as_context(args.pop().unwrap())?;
    let _after = args.pop().unwrap();
    let _before = args.pop().unwrap();
    Ok(Value::Context(Box::new(ctx)))
}

/// `register-outline : (int * string * string * bool) list -> unit`
/// (vminstdef.yaml:2794 `BackendRegisterOutline`) — FAITHFUL: upstream
/// REPLACES the whole registered list (`outline.ml`: `registered_outline :=
/// ol`), it does not append; and it is callable anywhere (no
/// during-page-break gate — upstream's `Outline.register` has no `State`
/// check). Keys resolve through [`Interp::dest_name`] (upstream
/// `make_entry`'s `NamedDest.get key`).
fn prim_register_outline(interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
    let entries = as_list(args.pop().unwrap())?;
    let mut out = Vec::with_capacity(entries.len());
    for e in entries {
        let Value::Tuple(vs) = e else {
            return eval_error("register-outline expects a list of (int * string * string * bool)");
        };
        if vs.len() != 4 {
            return eval_error("register-outline expects 4-tuples (level, text, key, is-open)");
        }
        let mut it = vs.into_iter();
        let level = as_int(it.next().unwrap())?;
        let text = as_str(it.next().unwrap())?;
        let key = as_str(it.next().unwrap())?;
        let is_open = as_bool(it.next().unwrap())?;
        let dest_name = interp.dest_name(&key);
        out.push(OutlineEntry {
            level,
            text,
            dest_name,
            is_open,
        });
    }
    interp.outline = out; // replace, not extend
    Ok(Value::Unit)
}

/// Recursive `extract_one` helper for [`prim_extract_string`] — mirrors
/// `horzBox.ml`'s `extract_string`'s `extract_one`: an `InnerString`
/// contributes its own text, a `Discretionary` recurses into `no_break`
/// (the "not yet broken" reading), every other box contributes nothing.
/// This port's box vocabulary has no separate Rising/Frame/ScriptGuard
/// wrapper (`inline-frame-breakable` et al. already flatten their padding
/// into the same flat `Vec<HorzBox>` — see `prim_inline_frame_breakable`),
/// so there is nothing else to recurse into.
fn extract_string_pure_one(phb: &PureHorzBox) -> String {
    match phb {
        PureHorzBox::InnerString { text, .. } => text.clone(),
        PureHorzBox::Discretionary { no_break, .. } => {
            no_break.iter().map(extract_string_pure_one).collect()
        }
        // Upstream `extract_string` recurses into frames.
        PureHorzBox::Frame { contents, .. } => contents
            .iter()
            .map(|(_, b)| extract_string_pure_one(b))
            .collect(),
        _ => String::new(),
    }
}

fn extract_string_one(hb: &HorzBox) -> String {
    match hb {
        HorzBox::Pure(phb) => extract_string_pure_one(phb),
    }
}

/// `extract-string : inline-boxes -> string` (vminstdef.yaml:1565
/// `PrimitiveExtract`) — FAITHFUL (see [`extract_string_one`]).
fn prim_extract_string(_interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
    let boxes = as_inline_boxes(args.pop().unwrap())?;
    let s: String = boxes.iter().map(extract_string_one).collect();
    Ok(Value::Str(s))
}

/// `get-initial-text-info : unit -> text-info` (v0.0.6 vminst.ml:953
/// `TextGetInitialTextModeContext`) — FAITHFUL:
/// `TextBackend.get_initial_text_mode_context` is `{ indent = 0;
/// escape_list = [] }` (textBackend.ml:9-12); escape_list is omitted from
/// the port's `TextInfo` (see its doc comment). The v0.0.6 fork side.
fn prim_get_initial_text_info_v006(
    _interp: &mut Interp,
    mut args: Vec<Value>,
) -> Result<Value, EvalError> {
    let _unit = args.pop().unwrap();
    Ok(Value::TextInfo(TextInfo { indent: 0 }))
}

/// `get-initial-text-info : inline [math-text] -> (string -> option string
/// -> option string -> string) -> text-info` (dev-0-1-0 vminst.ml:904-925)
/// — the v0.1 fork side. STAND-IN: pops and
/// drops both new arguments (the text-mode default math command and the
/// math-scripts stringifier) — this port's `TextInfo` carries no text-mode
/// command state, same degenerate policy as `stringify-math`. Returns the
/// same `TextInfo{indent: 0}` as the v0.0.6 side.
fn prim_get_initial_text_info_v01(
    _interp: &mut Interp,
    mut args: Vec<Value>,
) -> Result<Value, EvalError> {
    let _stringifier = args.pop().unwrap();
    let _default_math_cmd = args.pop().unwrap();
    Ok(Value::TextInfo(TextInfo { indent: 0 }))
}

/// `deepen-indent : int -> text-info -> text-info` (vminst.ml:921
/// `TextDeepenIndent`) — FAITHFUL: `indent + max i 0`
/// (`TextBackend.deepen_indent`, textBackend.ml:15-16 — the INCREMENT is
/// clamped, not the total).
fn prim_deepen_indent(_interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
    let tinfo = as_text_info(args.pop().unwrap())?;
    let i = as_int(args.pop().unwrap())?;
    Ok(Value::TextInfo(TextInfo {
        indent: tinfo.indent + i.max(0),
    }))
}

/// `break : text-info -> string` (vminst.ml:935 `TextBreak`) — FAITHFUL:
/// `"\n" ^ String.make indent ' '` (`TextBackend.get_indent`).
fn prim_break(_interp: &mut Interp, mut args: Vec<Value>) -> Result<Value, EvalError> {
    let tinfo = as_text_info(args.pop().unwrap())?;
    let mut s = String::with_capacity(1 + tinfo.indent as usize);
    s.push('\n');
    for _ in 0..tinfo.indent {
        s.push(' ');
    }
    Ok(Value::Str(s))
}

// ============================================================================
// unit tests: `as_page` (every paper-size ctor),
// `read_content_scheme`/`read_parts_scheme` (field extraction +
// missing-field errors). These extractors are private, so the tests live
// in-module rather than in `tests/`, same pattern as `crossref.rs`'s own
// `#[cfg(test)] mod tests`.
// ============================================================================
#[cfg(test)]
mod page_model_tests {
    use super::*;

    #[test]
    fn as_page_maps_every_nullary_ctor_to_the_right_paper_size() {
        let cases: &[(&str, PaperSize)] = &[
            ("A0Paper", PaperSize::A0),
            ("A1Paper", PaperSize::A1),
            ("A2Paper", PaperSize::A2),
            ("A3Paper", PaperSize::A3),
            ("A4Paper", PaperSize::A4),
            ("A5Paper", PaperSize::A5),
            ("USLetter", PaperSize::USLetter),
            ("USLegal", PaperSize::USLegal),
        ];
        for (name, expected) in cases {
            let v = Value::Ctor((*name).to_string(), None);
            assert_eq!(as_page(v).unwrap(), *expected, "ctor {name}");
        }
    }

    #[test]
    fn as_page_unwraps_user_defined_papers_tuple_payload() {
        let v = Value::Ctor(
            "UserDefinedPaper".to_string(),
            Some(Box::new(Value::Tuple(vec![
                Value::Length(Length::pt(100.0)),
                Value::Length(Length::pt(200.0)),
            ]))),
        );
        assert_eq!(
            as_page(v).unwrap(),
            PaperSize::UserDefined(Length::pt(100.0), Length::pt(200.0))
        );
    }

    #[test]
    fn a4_paper_dims_are_595_by_842_points() {
        let (w, h) = PaperSize::A4.dims();
        assert!((w.0 - 595.0).abs() < 1.0, "width: {}", w.0);
        assert!((h.0 - 842.0).abs() < 1.0, "height: {}", h.0);
    }

    #[test]
    fn read_content_scheme_extracts_origin_and_height() {
        let mut fields = BTreeMap::new();
        fields.insert(
            "text-origin".to_string(),
            Value::Tuple(vec![
                Value::Length(Length::pt(10.0)),
                Value::Length(Length::pt(20.0)),
            ]),
        );
        fields.insert("text-height".to_string(), Value::Length(Length::pt(300.0)));
        let (origin, height) = read_content_scheme(Value::Record(fields)).unwrap();
        assert_eq!(origin, (Length::pt(10.0), Length::pt(20.0)));
        assert_eq!(height, Length::pt(300.0));
    }

    #[test]
    fn read_content_scheme_errors_on_a_missing_field() {
        let mut fields = BTreeMap::new();
        fields.insert(
            "text-origin".to_string(),
            Value::Tuple(vec![
                Value::Length(Length::ZERO),
                Value::Length(Length::ZERO),
            ]),
        );
        let err = read_content_scheme(Value::Record(fields)).unwrap_err();
        assert!(
            err.msg.contains("text-height"),
            "error should name the missing field: {}",
            err.msg
        );
    }

    #[test]
    fn read_parts_scheme_extracts_all_four_fields() {
        let mut fields = BTreeMap::new();
        fields.insert(
            "header-origin".to_string(),
            Value::Tuple(vec![
                Value::Length(Length::ZERO),
                Value::Length(Length::ZERO),
            ]),
        );
        fields.insert("header-content".to_string(), Value::BlockBoxes(Vec::new()));
        fields.insert(
            "footer-origin".to_string(),
            Value::Tuple(vec![
                Value::Length(Length::pt(1.0)),
                Value::Length(Length::pt(2.0)),
            ]),
        );
        fields.insert("footer-content".to_string(), Value::BlockBoxes(Vec::new()));
        let (horg, hbb, forg, fbb) = read_parts_scheme(Value::Record(fields)).unwrap();
        assert_eq!(horg, (Length::ZERO, Length::ZERO));
        assert!(hbb.is_empty());
        assert_eq!(forg, (Length::pt(1.0), Length::pt(2.0)));
        assert!(fbb.is_empty());
    }

    #[test]
    fn read_parts_scheme_errors_on_a_missing_field() {
        let err = read_parts_scheme(Value::Record(BTreeMap::new())).unwrap_err();
        assert!(
            err.msg.contains("header-origin"),
            "error should name the missing field: {}",
            err.msg
        );
    }
}

/// `enter_script_scales_and_saturates`:
/// `enter_script` is crate-private, so this lives here rather than in the
/// external `tests/v01_math.rs` integration suite, which can only reach
/// `pub` items.
#[cfg(test)]
mod math_split_tests {
    use super::*;
    use rustyfi_backend::FontMetrics;

    /// A `FontMetrics` stub with NO MATH table (`math_constants` defaults
    /// to `None`) — exercises `enter_script`'s documented fallback
    /// constants (`0.7`, `5.0/7.0`), the shape every other base-14 fixture
    /// in this crate already relies on.
    struct NoMath;
    impl FontMetrics for NoMath {
        fn advance(&self, _f: FontKey, c: char, size: Length) -> Option<Length> {
            if c.is_ascii() {
                Some(size * 0.5)
            } else {
                None
            }
        }
        fn ascender(&self, _f: FontKey, size: Length) -> Length {
            size * 0.75
        }
        fn descender(&self, _f: FontKey, size: Length) -> Length {
            size * 0.25
        }
    }

    #[test]
    fn enter_script_scales_and_saturates() {
        let metrics = NoMath;
        let interp = Interp::new(&metrics);
        let ctx = Context::initial(Length::pt(400.0));
        assert_eq!(ctx.math_script_level, MathScriptLevel::Base);
        assert_eq!(ctx.font_size, Length::pt(12.0));

        // Base -> Script: font_size * script_scale_down (fallback 0.7).
        let s1 = enter_script(&interp, &ctx);
        assert_eq!(s1.math_script_level, MathScriptLevel::Script);
        assert!(
            (s1.font_size.0 - ctx.font_size.0 * 0.7).abs() < 1e-9,
            "expected {} * 0.7, got {}",
            ctx.font_size.0,
            s1.font_size.0
        );

        // Script -> ScriptScript: font_size * (script_script_scale_down /
        // script_scale_down) (fallback 5.0/7.0).
        let s2 = enter_script(&interp, &s1);
        assert_eq!(s2.math_script_level, MathScriptLevel::ScriptScript);
        assert!(
            (s2.font_size.0 - s1.font_size.0 * (5.0 / 7.0)).abs() < 1e-9,
            "expected {} * 5/7, got {}",
            s1.font_size.0,
            s2.font_size.0
        );

        // ScriptScript saturates: no further shrink, level stays put.
        let s3 = enter_script(&interp, &s2);
        assert_eq!(s3.math_script_level, MathScriptLevel::ScriptScript);
        assert_eq!(s3.font_size, s2.font_size);
    }
}