retex_lua/

nodelib.rs

//! The `node` library (LuaTeX manual §10.5) and `node.direct`.
//!
//! Node userdata ([`LNode`]) and direct integers both refer to nodes in the
//! engine's arena. Type ids, subtypes and field names come from the data
//! recorded from LuaTeX's own `node` library
//! ([`retex_engine::nodes::LUATEX_NODE_TYPES`]).

use std::collections::HashMap;
use std::sync::OnceLock;

use mlua::{Lua, MetaMethod, MultiValue, Table, UserData, UserDataMethods, Value};
use retex_engine::Engine;
use retex_engine::nodes::{NodeData, NodeRef, id, noad_opt};

use crate::with_engine;

/// Node type information parsed from LuaTeX's API dump.
struct TypeInfo {
    names: HashMap<u8, String>,
    ids: HashMap<String, u8>,
    fields: HashMap<u8, Vec<(i32, String)>>,
    subtypes: HashMap<u8, Vec<(i32, String)>>,
    whatsits: Vec<(u16, String)>,
    whatsit_fields: HashMap<u16, Vec<(i32, String)>>,
}

fn info() -> &'static TypeInfo {
    static T: OnceLock<TypeInfo> = OnceLock::new();
    T.get_or_init(|| {
        let data = retex_engine::nodes::LUATEX_NODE_TYPES;
        let mut ti = TypeInfo {
            names: HashMap::new(),
            ids: HashMap::new(),
            fields: HashMap::new(),
            subtypes: HashMap::new(),
            whatsits: Vec::new(),
            whatsit_fields: HashMap::new(),
        };
        let pairs = |s: &str| -> Vec<(i32, String)> {
            s.split_whitespace()
                .filter_map(|kv| {
                    let (k, v) = kv.split_once('=')?;
                    Some((k.parse().ok()?, v.to_owned()))
                })
                .collect()
        };
        let mut cur: u8 = 0;
        for line in data.lines() {
            let l = line.trim_start();
            if let Some(rest) = line.strip_prefix("type ") {
                let mut it = rest.split_whitespace();
                let i: u8 = it.next().and_then(|x| x.parse().ok()).unwrap_or(0);
                let name = it.next().unwrap_or("").to_owned();
                ti.names.insert(i, name.clone());
                ti.ids.insert(name, i);
                cur = i;
            } else if let Some(rest) = l.strip_prefix("fields ") {
                ti.fields.insert(cur, pairs(rest));
            } else if let Some(rest) = l.strip_prefix("subtypes ") {
                ti.subtypes.insert(cur, pairs(rest));
            } else if let Some(rest) = line.strip_prefix("whatsits ") {
                ti.whatsits = pairs(rest)
                    .into_iter()
                    .map(|(k, v)| (k as u16, v))
                    .collect();
            } else if let Some(rest) = l.strip_prefix("whatsit ") {
                let mut it = rest.splitn(4, ' ');
                let _name = it.next();
                let n: u16 = it.next().and_then(|x| x.parse().ok()).unwrap_or(0);
                let _ = it.next();
                ti.whatsit_fields.insert(n, pairs(it.next().unwrap_or("")));
            }
        }
        ti
    })
}

/// A node userdata.
#[derive(Clone, Copy, Debug, PartialEq, Eq)]
pub struct LNode(pub u32);

impl UserData for LNode {
    fn add_methods<M: UserDataMethods<Self>>(m: &mut M) {
        m.add_meta_method(MetaMethod::Index, |lua, this, key: String| {
            get_field(lua, NodeRef(this.0), &key)
        });
        m.add_meta_method(
            MetaMethod::NewIndex,
            |lua, this, (key, v): (String, Value)| set_field(lua, NodeRef(this.0), &key, v),
        );
        m.add_meta_method(MetaMethod::Eq, |_, this, other: mlua::AnyUserData| {
            Ok(other
                .borrow::<LNode>()
                .map(|o| o.0 == this.0)
                .unwrap_or(false))
        });
        m.add_meta_method(MetaMethod::ToString, |lua, this, ()| {
            let p = NodeRef(this.0);
            let (t, sub, prev, next) = with_engine(lua, |e| {
                (
                    e.nodes.id(p),
                    e.nodes.subtype(p),
                    e.nodes.prev(p),
                    e.nodes.next(p),
                )
            })?;
            let name = info().names.get(&t).cloned().unwrap_or_default();
            // As LuaTeX: `<node prev < this > next : type subtype>`.
            let num = |q: NodeRef| {
                if q.is_null() {
                    "nil".to_owned()
                } else {
                    q.0.to_string()
                }
            };
            Ok(format!(
                "<node {:>6} < {:>6} > {:>6} : {name} {sub}>",
                num(prev),
                this.0,
                num(next)
            ))
        });
    }
}

/// The Lua name of node type `t` (`glyph`).
pub(crate) fn type_name(t: u8) -> String {
    info().names.get(&t).cloned().unwrap_or_default()
}

pub(crate) fn to_ref(v: &Value) -> Option<NodeRef> {
    match v {
        Value::UserData(u) => u.borrow::<LNode>().ok().map(|n| NodeRef(n.0)),
        Value::Integer(n) if *n > 0 => Some(NodeRef(*n as u32)),
        _ => None,
    }
}

pub(crate) fn wrap(lua: &Lua, p: NodeRef, direct: bool) -> mlua::Result<Value> {
    if p.is_null() {
        return Ok(Value::Nil);
    }
    if direct {
        Ok(Value::Integer(i64::from(p.0)))
    } else {
        Ok(Value::UserData(lua.create_userdata(LNode(p.0))?))
    }
}

/// An attribute list as Lua sees it (`n.attr`, `node.current_attr`): a
/// value that can be given to other nodes, compared, and traversed. LuaTeX
/// returns an `attribute_list` node (id 40), followed by an `attribute`
/// node (id 38) per attribute set; here only `id` and `subtype` are
/// fields, and [`attr_entries`] is what `node.traverse` yields.
#[derive(Clone, Debug)]
pub struct LAttr(pub retex_engine::nodes::AttrList);

impl UserData for LAttr {
    fn add_methods<M: UserDataMethods<Self>>(m: &mut M) {
        m.add_meta_method(MetaMethod::Eq, |_, this, other: mlua::AnyUserData| {
            Ok(other
                .borrow::<LAttr>()
                .map(|o| o.0 == this.0)
                .unwrap_or(false))
        });
        m.add_meta_method(MetaMethod::Index, |_, _, key: Value| {
            Ok(match &key {
                Value::String(k) if k.as_bytes().as_ref() == b"id" => Value::Integer(40),
                Value::String(k) if k.as_bytes().as_ref() == b"subtype" => Value::Integer(0),
                _ => Value::Nil,
            })
        });
        m.add_meta_method(MetaMethod::ToString, |_, _, ()| {
            Ok("<node attribute_list>".to_string())
        });
    }
}

/// One `attribute` node of a traversed attribute list: its number and
/// value.
#[derive(Clone, Copy, Debug)]
struct LAttrEntry(u32, i32);

impl UserData for LAttrEntry {
    fn add_methods<M: UserDataMethods<Self>>(m: &mut M) {
        m.add_meta_method(MetaMethod::Index, |_, this, key: Value| {
            let Value::String(k) = &key else {
                return Ok(Value::Nil);
            };
            Ok(match k.as_bytes().as_ref() {
                b"id" => Value::Integer(38),
                b"subtype" => Value::Integer(0),
                b"number" => Value::Integer(i64::from(this.0)),
                b"value" => Value::Integer(i64::from(this.1)),
                _ => Value::Nil,
            })
        });
        m.add_meta_method(MetaMethod::ToString, |_, _, ()| {
            Ok("<node attribute>".to_string())
        });
    }
}

/// What `node.traverse` yields for an attribute list: the list itself,
/// then each attribute (node, id and subtype).
fn attr_entries(lua: &Lua, list: &mlua::AnyUserData) -> mlua::Result<Vec<[Value; 3]>> {
    let a = list.borrow::<LAttr>()?.0.clone();
    let mut out = vec![[
        Value::UserData(list.clone()),
        Value::Integer(40),
        Value::Integer(0),
    ]];
    for &(n, v) in a.iter() {
        out.push([
            Value::UserData(lua.create_userdata(LAttrEntry(n, v))?),
            Value::Integer(38),
            Value::Integer(0),
        ]);
    }
    Ok(out)
}

/// `n.attr`: nil for a node without attributes.
fn attr_value(lua: &Lua, p: NodeRef) -> mlua::Result<Value> {
    match with_engine(lua, |e| e.nodes.attr(p).cloned())? {
        Some(a) => Ok(Value::UserData(lua.create_userdata(LAttr(a))?)),
        None => Ok(Value::Nil),
    }
}

/// `n.attr = v`: another node's list, or nil.
fn set_attr_value(lua: &Lua, p: NodeRef, v: &Value) -> mlua::Result<()> {
    let a = match v {
        Value::UserData(u) => match u.borrow::<LAttr>() {
            Ok(a) => Some(a.0.clone()),
            Err(_) => return Ok(()),
        },
        Value::Nil => None,
        _ => return Ok(()),
    };
    with_engine(lua, |e| e.nodes.set_attr(p, a))
}

/// Default data for a new node of type `t`.
fn new_data(t: u8) -> NodeData {
    use retex_engine::glue::Glue;
    match t {
        id::HLIST | id::VLIST => NodeData::Box(Box::default()),
        id::RULE => NodeData::Rule {
            width: retex_engine::nodes::RUNNING,
            depth: retex_engine::nodes::RUNNING,
            height: retex_engine::nodes::RUNNING,
            dir: 0,
            index: 0,
            left: 0,
            right: 0,
        },
        id::GLUE | id::GLUE_SPEC => NodeData::Glue {
            spec: Glue::ZERO,
            leader: NodeRef::NULL,
        },
        id::KERN => NodeData::Kern {
            kern: 0,
            expansion_factor: 0,
        },
        id::PENALTY => NodeData::Penalty { penalty: 0 },
        id::MARGIN_KERN => NodeData::MarginKern {
            width: 0,
            glyph: NodeRef::NULL,
        },
        id::GLYPH => NodeData::Glyph(Default::default()),
        id::DISC => NodeData::Disc {
            pre: NodeRef::NULL,
            post: NodeRef::NULL,
            replace: NodeRef::NULL,
            penalty: 0,
        },
        id::BOUNDARY => NodeData::Boundary { value: 0 },
        id::MATH => NodeData::Math {
            surround: 0,
            glue: Glue::ZERO,
        },
        id::ADJUST => NodeData::Adjust {
            head: NodeRef::NULL,
        },
        id::MARK => NodeData::Mark {
            class: 0,
            mark: retex_engine::token::empty_list(),
        },
        id::DIR => NodeData::Dir { dir: 0, level: 0 },
        id::STYLE => NodeData::Style { style: 0 },
        id::LOCAL_PAR => NodeData::LocalPar {
            pen_inter: 0,
            pen_broken: 0,
            dir: 0,
            box_left: NodeRef::NULL,
            box_left_width: 0,
            box_right: NodeRef::NULL,
            box_right_width: 0,
        },
        id::WHATSIT => NodeData::Whatsit(Box::new(retex_engine::nodes::Whatsit::Other {
            fields: Vec::new(),
            data: Vec::new(),
        })),
        _ => NodeData::Temp,
    }
}

fn int(v: &Value) -> i64 {
    match v {
        Value::Integer(n) => *n,
        Value::Number(n) => n.round() as i64,
        Value::Boolean(b) => i64::from(*b),
        _ => 0,
    }
}

/// Reads field `key` of node `p`.
fn get_field(lua: &Lua, p: NodeRef, key: &str) -> mlua::Result<Value> {
    // Observed: nodes of the types without subtypes read their subtype
    // field as nil (getsubtype, getfield and traverse give 0).
    if key == "subtype"
        && matches!(with_engine(lua, |e| e.nodes.id(p))?, 9 | 30..=32 | 35..=37 | 39 | 41..=49)
    {
        return Ok(Value::Nil);
    }
    get_field_impl(lua, p, key, false)
}

/// A field value read under the engine borrow.
enum R {
    I(i64),
    N(NodeRef),
    F(f64),
    S(Vec<u8>),
    /// A Lua value kept by reference (see [`lua_ref`]).
    L(i32),
    Nil,
}

fn get_field_impl(lua: &Lua, p: NodeRef, key: &str, direct: bool) -> mlua::Result<Value> {
    if key == "attr" {
        return attr_value(lua, p);
    }
    let r = with_engine(lua, |e| -> R {
        let n = e.nodes.get(p);
        match key {
            "id" => return R::I(i64::from(n.id)),
            "subtype" => return R::I(i64::from(n.subtype)),
            "next" => return R::N(n.next),
            "prev" => return R::N(n.prev),
            _ => {}
        }
        match &n.data {
            NodeData::Box(b) | NodeData::Unset { b, .. } => match key {
                "width" => R::I(b.width.into()),
                "height" => R::I(b.height.into()),
                "depth" => R::I(b.depth.into()),
                "shift" => R::I(b.shift.into()),
                "dir" => R::S(dir_name(b.dir).into()),
                "direction" => R::I(b.dir.into()),
                "glue_order" => R::I(b.glue_order.into()),
                "glue_sign" => R::I(b.glue_sign.into()),
                "glue_set" => R::F(b.glue_set),
                "head" | "list" => R::N(b.head),
                _ => R::Nil,
            },
            NodeData::Glyph(g) => match key {
                "char" => R::I(g.chr.into()),
                "font" => R::I(g.font.into()),
                "lang" => R::I(g.lang.into()),
                "left" => R::I(g.left.into()),
                "right" => R::I(g.right.into()),
                "uchyph" => R::I(i64::from(g.uchyph)),
                "components" => R::N(g.components),
                "xoffset" => R::I(g.xoffset.into()),
                "yoffset" => R::I(g.yoffset.into()),
                "expansion_factor" => R::I(g.expansion_factor.into()),
                "data" => R::I(g.data.into()),
                "width" => R::I(e.font_char_dimen(g.font, g.chr, 0).into()),
                "height" => R::I(e.font_char_dimen(g.font, g.chr, 1).into()),
                "depth" => R::I(e.font_char_dimen(g.font, g.chr, 2).into()),
                _ => R::Nil,
            },
            NodeData::Glue { spec, leader } => match key {
                "width" => R::I(spec.width.into()),
                "stretch" => R::I(spec.stretch.into()),
                "shrink" => R::I(spec.shrink.into()),
                "stretch_order" => R::I(spec.stretch_order.into()),
                "shrink_order" => R::I(spec.shrink_order.into()),
                "leader" => R::N(*leader),
                _ => R::Nil,
            },
            NodeData::Kern {
                kern,
                expansion_factor,
            } => match key {
                "kern" | "width" => R::I((*kern).into()),
                "expansion_factor" => R::I((*expansion_factor).into()),
                _ => R::Nil,
            },
            NodeData::Penalty { penalty } => match key {
                "penalty" => R::I((*penalty).into()),
                _ => R::Nil,
            },
            NodeData::MarginKern { width, glyph } => match key {
                "width" => R::I((*width).into()),
                "glyph" => R::N(*glyph),
                _ => R::Nil,
            },
            NodeData::Rule {
                width,
                depth,
                height,
                dir,
                index,
                left,
                right,
            } => match key {
                "width" => R::I((*width).into()),
                "depth" => R::I((*depth).into()),
                "height" => R::I((*height).into()),
                "dir" => R::S(dir_name(*dir).into()),
                "direction" => R::I((*dir).into()),
                "index" => R::I((*index).into()),
                "left" => R::I((*left).into()),
                "right" => R::I((*right).into()),
                _ => R::Nil,
            },
            NodeData::Disc {
                pre,
                post,
                replace,
                penalty,
            } => match key {
                "pre" => R::N(*pre),
                "post" => R::N(*post),
                "replace" => R::N(*replace),
                "penalty" => R::I((*penalty).into()),
                _ => R::Nil,
            },
            NodeData::Boundary { value } => match key {
                "value" => R::I((*value).into()),
                _ => R::Nil,
            },
            NodeData::Whatsit(w) => {
                let w = (**w).clone();
                whatsit_field(e, &w, key)
            }
            NodeData::Mark { class, mark } => match key {
                "class" => R::I((*class).into()),
                "mark" => {
                    let mark = mark.clone();
                    R::S(e.print_to_string(|e| e.show_token_list(&mark, 0, mark.len(), i64::MAX)))
                }
                _ => R::Nil,
            },
            NodeData::Ins {
                cost,
                depth,
                height,
                head,
                ..
            } => match key {
                "cost" => R::I((*cost).into()),
                "depth" => R::I((*depth).into()),
                "height" => R::I((*height).into()),
                "head" | "list" => R::N(*head),
                _ => R::Nil,
            },
            NodeData::Adjust { head } => match key {
                "head" | "list" => R::N(*head),
                _ => R::Nil,
            },
            // Observed: "+TRT" opens, "-TRT" (subtype 1) closes.
            NodeData::Dir { dir, level } => match key {
                "dir" => {
                    let sign = if n.subtype == 0 { "+" } else { "-" };
                    R::S(format!("{sign}{}", dir_name(*dir)).into_bytes())
                }
                "direction" => R::I((*dir).into()),
                "level" => R::I((*level).into()),
                _ => R::Nil,
            },
            NodeData::LocalPar { dir, .. } => match key {
                "dir" => R::S(dir_name(*dir).into()),
                "direction" => R::I((*dir).into()),
                _ => R::Nil,
            },
            NodeData::Math { surround, glue } => match key {
                "surround" => R::I((*surround).into()),
                "width" => R::I(glue.width.into()),
                "stretch" => R::I(glue.stretch.into()),
                "shrink" => R::I(glue.shrink.into()),
                "stretch_order" => R::I(glue.stretch_order.into()),
                "shrink_order" => R::I(glue.shrink_order.into()),
                _ => R::Nil,
            },
            NodeData::Noad(d) => match key {
                "nucleus" => R::N(d.nucleus),
                "sub" => R::N(d.sub),
                "sup" => R::N(d.sup),
                "options" => R::I(d.options.into()),
                "left" => R::N(d.left),
                "degree" => R::N(d.degree),
                "width" => R::I(d.width.into()),
                // Observed: top_accent is accent; an overlay accent
                // reads as overlay_accent only.
                "accent" | "top_accent" if d.options & noad_opt::OVERLAY == 0 => R::N(d.accent),
                "overlay_accent" if d.options & noad_opt::OVERLAY != 0 => R::N(d.accent),
                "bot_accent" => R::N(d.bot_accent),
                "fraction" => R::I(d.fraction.into()),
                _ => R::Nil,
            },
            NodeData::Fraction(d) => match key {
                "width" => R::I(d.thickness.into()),
                "num" => R::N(d.num),
                "denom" => R::N(d.denom),
                "left" => R::N(d.left),
                "right" => R::N(d.right),
                "middle" => R::N(d.middle),
                _ => R::Nil,
            },
            NodeData::Fence(d) => match key {
                "delim" => R::N(d.delim),
                "italic" => R::I(d.italic.into()),
                "height" => R::I(d.height.into()),
                "depth" => R::I(d.depth.into()),
                "options" => R::I(d.options.into()),
                "class" => R::I(d.class.into()),
                _ => R::Nil,
            },
            // Observed: the style of a style node reads as its name.
            NodeData::Style { style } => match key {
                "style" => R::S(
                    crate::texlib::MATH_STYLE_NAMES
                        .get(usize::from(*style))
                        .copied()
                        .unwrap_or("display")
                        .as_bytes()
                        .to_vec(),
                ),
                _ => R::Nil,
            },
            NodeData::Choice(c) => match key {
                "display" => R::N(c[0]),
                "text" => R::N(c[1]),
                "script" => R::N(c[2]),
                "scriptscript" => R::N(c[3]),
                _ => R::Nil,
            },
            NodeData::MathChar { fam, chr } => match key {
                "fam" => R::I((*fam).into()),
                "char" => R::I((*chr).into()),
                _ => R::Nil,
            },
            NodeData::SubList { head } => match key {
                "head" | "list" => R::N(*head),
                _ => R::Nil,
            },
            NodeData::Delim {
                small_fam,
                small_char,
                large_fam,
                large_char,
            } => match key {
                "small_fam" => R::I((*small_fam).into()),
                "small_char" => R::I((*small_char).into()),
                "large_fam" => R::I((*large_fam).into()),
                "large_char" => R::I((*large_char).into()),
                _ => R::Nil,
            },
            _ => R::Nil,
        }
    })?;
    Ok(match r {
        R::I(i) => Value::Integer(i),
        R::N(n) => wrap(lua, n, direct)?,
        R::F(f) => Value::Number(f),
        R::S(s) => Value::String(lua.create_string(&s)?),
        R::L(n) => lua_refs_synced(lua)?.raw_get(n)?,
        R::Nil => Value::Nil,
    })
}

/// The name of direction `d` (`TLT`, `TRT`, …).
fn dir_name(d: i8) -> &'static str {
    retex_engine::showbox::DIR_NAMES[i32::from(d).rem_euclid(4) as usize]
}

/// A direction given to a `dir` or `direction` field: a number, or a name
/// with an optional sign (`"-TRT"` closes a direction: `Some(true)`).
fn dir_value(v: &Value) -> (i8, Option<bool>) {
    match v {
        Value::String(s) => {
            let b = s.as_bytes();
            let (cancel, name) = match b.first() {
                Some(b'+') => (Some(false), &b[1..]),
                Some(b'-') => (Some(true), &b[1..]),
                _ => (None, &b[..]),
            };
            let d = retex_engine::showbox::DIR_NAMES
                .iter()
                .position(|n| n.as_bytes() == name)
                .unwrap_or(0);
            (d as i8, cancel)
        }
        _ => (int(v).clamp(0, 3) as i8, None),
    }
}

/// Writes field `key` of node `p`.
fn set_field(lua: &Lua, p: NodeRef, key: &str, v: Value) -> mlua::Result<()> {
    if !matches!(key, "next" | "prev" | "subtype" | "attr")
        && with_engine(lua, |e| e.nodes.id(p) == id::WHATSIT)?
    {
        return set_whatsit_field(lua, p, key, v);
    }
    if key == "attr" {
        return set_attr_value(lua, p, &v);
    }
    let r = to_ref(&v).unwrap_or(NodeRef::NULL);
    let i = int(&v);
    // A style is set by name or by number.
    let style_value = match &v {
        Value::String(name) => crate::texlib::MATH_STYLE_NAMES
            .iter()
            .position(|n| n.as_bytes() == name.as_bytes().as_ref())
            .unwrap_or(0) as i64,
        _ => i.clamp(0, 7),
    };
    let f = match &v {
        Value::Number(x) => *x,
        Value::Integer(x) => *x as f64,
        _ => 0.0,
    };
    with_engine(lua, |e| {
        let n = e.nodes.get_mut(p);
        match key {
            "next" => {
                n.next = r;
                return;
            }
            "prev" => {
                n.prev = r;
                return;
            }
            // Observed: a style node's subtype follows its style and
            // cannot be set.
            "subtype" if n.id == id::STYLE => return,
            "subtype" => {
                n.subtype = i as u16;
                return;
            }
            // A sign also sets whether the node opens or closes.
            "dir" | "direction" if n.id == id::DIR => {
                let (d, cancel) = dir_value(&v);
                if let Some(c) = cancel {
                    n.subtype = u16::from(c);
                }
                if let NodeData::Dir { dir, .. } = &mut n.data {
                    *dir = d;
                }
                return;
            }
            "dir" | "direction" if n.id == id::LOCAL_PAR => {
                if let NodeData::LocalPar { dir, .. } = &mut n.data {
                    *dir = dir_value(&v).0;
                }
                return;
            }
            _ => {}
        }
        match &mut n.data {
            NodeData::Box(b) | NodeData::Unset { b, .. } => match key {
                "width" => b.width = i as i32,
                "height" => b.height = i as i32,
                "depth" => b.depth = i as i32,
                "shift" => b.shift = i as i32,
                "dir" | "direction" => b.dir = dir_value(&v).0,
                "glue_order" => b.glue_order = i as u8,
                "glue_sign" => b.glue_sign = i as u8,
                "glue_set" => b.glue_set = f64::from(f as f32),
                "head" | "list" => b.head = r,
                _ => {}
            },
            NodeData::Glyph(g) => match key {
                "char" => g.chr = i as u32,
                "font" => g.font = i as u32,
                "lang" => g.lang = i as u16,
                "left" => g.left = i as u8,
                "right" => g.right = i as u8,
                "uchyph" => g.uchyph = i != 0,
                "components" => g.components = r,
                "xoffset" => g.xoffset = i as i32,
                "yoffset" => g.yoffset = i as i32,
                "expansion_factor" => g.expansion_factor = i as i32,
                "data" => g.data = i as i32,
                _ => {}
            },
            NodeData::Glue { spec, leader } => match key {
                "width" => spec.width = i as i32,
                "stretch" => spec.stretch = i as i32,
                "shrink" => spec.shrink = i as i32,
                "stretch_order" => spec.stretch_order = i as u8,
                "shrink_order" => spec.shrink_order = i as u8,
                "leader" => *leader = r,
                _ => {}
            },
            NodeData::Kern {
                kern,
                expansion_factor,
            } => {
                if key == "kern" || key == "width" {
                    *kern = i as i32;
                } else if key == "expansion_factor" {
                    *expansion_factor = i as i32;
                }
            }
            NodeData::MarginKern { width, glyph } => match key {
                "width" => *width = i as i32,
                "glyph" => *glyph = r,
                _ => {}
            },
            NodeData::Penalty { penalty } => {
                if key == "penalty" {
                    *penalty = i as i32;
                }
            }
            NodeData::Rule {
                width,
                depth,
                height,
                dir,
                ..
            } => match key {
                "dir" | "direction" => *dir = dir_value(&v).0,
                "width" => *width = i as i32,
                "depth" => *depth = i as i32,
                "height" => *height = i as i32,
                _ => {}
            },
            NodeData::Disc {
                pre,
                post,
                replace,
                penalty,
            } => match key {
                "pre" => *pre = r,
                "post" => *post = r,
                "replace" => *replace = r,
                "penalty" => *penalty = i as i32,
                _ => {}
            },
            NodeData::Boundary { value } => {
                if key == "value" {
                    *value = i as i32;
                }
            }
            NodeData::Mark { class, .. } => {
                if key == "class" {
                    *class = i as u32;
                }
            }
            NodeData::Noad(d) => match key {
                "nucleus" => d.nucleus = r,
                "sub" => d.sub = r,
                "sup" => d.sup = r,
                "options" => d.options = i as u32,
                "left" => d.left = r,
                "degree" => d.degree = r,
                "width" => d.width = i as i32,
                "accent" | "top_accent" => {
                    d.accent = r;
                    d.options &= !noad_opt::OVERLAY;
                }
                "overlay_accent" => {
                    d.accent = r;
                    d.options |= noad_opt::OVERLAY;
                }
                "bot_accent" => d.bot_accent = r,
                "fraction" => d.fraction = i as i32,
                _ => {}
            },
            NodeData::Fraction(d) => match key {
                "width" => d.thickness = i as i32,
                "num" => d.num = r,
                "denom" => d.denom = r,
                "left" => d.left = r,
                "right" => d.right = r,
                "middle" => d.middle = r,
                _ => {}
            },
            NodeData::Fence(d) => match key {
                "delim" => d.delim = r,
                "italic" => d.italic = i as i32,
                "height" => d.height = i as i32,
                "depth" => d.depth = i as i32,
                "options" => d.options = i as u32,
                "class" => d.class = i as i32,
                _ => {}
            },
            NodeData::Style { style } => {
                if key == "style" {
                    *style = style_value as u8;
                    n.subtype = u16::from(*style);
                }
            }
            NodeData::Choice(c) => match key {
                "display" => c[0] = r,
                "text" => c[1] = r,
                "script" => c[2] = r,
                "scriptscript" => c[3] = r,
                _ => {}
            },
            NodeData::MathChar { fam, chr } => match key {
                "fam" => *fam = i as u32,
                "char" => *chr = i as u32,
                _ => {}
            },
            NodeData::SubList { head } => {
                if key == "head" || key == "list" {
                    *head = r;
                }
            }
            NodeData::Delim {
                small_fam,
                small_char,
                large_fam,
                large_char,
            } => match key {
                "small_fam" => *small_fam = i as u32,
                "small_char" => *small_char = i as u32,
                "large_fam" => *large_fam = i as u32,
                "large_char" => *large_char = i as u32,
                _ => {}
            },
            NodeData::Ins { head, .. } | NodeData::Adjust { head } => {
                if key == "head" || key == "list" {
                    *head = r;
                }
            }
            NodeData::Math { surround, glue } => match key {
                "surround" => *surround = i as i32,
                "width" => glue.width = i as i32,
                "stretch" => glue.stretch = i as i32,
                "shrink" => glue.shrink = i as i32,
                "stretch_order" => glue.stretch_order = i as u8,
                "shrink_order" => glue.shrink_order = i as u8,
                _ => {}
            },
            _ => {}
        }
    })
}

/// Installs `node` and `node.direct`.
pub fn install(lua: &Lua) -> mlua::Result<()> {
    let node = lua.create_table()?;
    let direct = lua.create_table()?;
    for (t, is_direct) in [(&node, false), (&direct, true)] {
        install_common(lua, t, is_direct)?;
    }
    direct.set(
        "todirect",
        lua.create_function(|_, v: Value| Ok(to_ref(&v).map(|p| i64::from(p.0))))?,
    )?;
    direct.set(
        "tonode",
        lua.create_function(|lua, v: Value| match to_ref(&v) {
            Some(p) => wrap(lua, p, false),
            None => Ok(Value::Nil),
        })?,
    )?;
    install_properties(lua, &node, &direct)?;
    require_nodes(lua, &node)?;
    node.set("direct", direct)?;
    lua.globals().set("node", node)?;
    lua.load(ARGUMENT_COUNT_CHECKS)
        .set_name("=[retex node checks]")
        .exec()?;
    Ok(())
}

/// How a function of the `node` library treats its node argument when it
/// is missing, nil, or not a node (observed in LuaTeX; "fatal" is its
/// error "lua <node> expected, not an object with type ...").
#[derive(Clone, Copy)]
struct NodeArg {
    /// The argument's position (0-based).
    pos: usize,
    /// A missing argument is fine (the function returns nothing).
    absent_ok: bool,
    /// nil is fine.
    nil_ok: bool,
}

const STRICT: NodeArg = NodeArg {
    pos: 0,
    absent_ok: false,
    nil_ok: false,
};
const NIL_OK: NodeArg = NodeArg {
    pos: 0,
    absent_ok: false,
    nil_ok: true,
};
const ABSENT_OK: NodeArg = NodeArg {
    pos: 0,
    absent_ok: true,
    nil_ok: false,
};
const NOTHING_OK: NodeArg = NodeArg {
    pos: 0,
    absent_ok: true,
    nil_ok: true,
};

/// The functions of `node` (not `node.direct`) that check their node
/// argument. Before, such values were taken as no node and the run went
/// on where LuaTeX stops, or stopped where LuaTeX goes on.
const NODE_ARGUMENT: &[(&str, NodeArg)] = &[
    ("hpack", STRICT),
    ("vpack", STRICT),
    ("remove", STRICT),
    ("mlist_to_hlist", STRICT),
    ("has_attribute", STRICT),
    ("set_attribute", STRICT),
    ("unset_attribute", STRICT),
    ("protect_glyphs", STRICT),
    ("protect_glyph", STRICT),
    ("unprotect_glyphs", STRICT),
    ("unprotect_glyph", STRICT),
    ("flatten_discretionaries", STRICT),
    ("is_char", STRICT),
    ("is_glyph", STRICT),
    ("has_glyph", STRICT),
    ("getglue", STRICT),
    ("setglue", STRICT),
    ("is_zero_glue", STRICT),
    ("hyphenating", STRICT),
    ("write", ABSENT_OK),
    ("first_glyph", ABSENT_OK),
    ("kerning", ABSENT_OK),
    ("ligaturing", ABSENT_OK),
    ("copy", NIL_OK),
    ("copy_list", NIL_OK),
    ("tail", NIL_OK),
    ("length", NIL_OK),
    ("slide", NIL_OK),
    ("end_of_math", NIL_OK),
    ("traverse", NIL_OK),
    ("traverse_char", NIL_OK),
    ("traverse_glyph", NIL_OK),
    ("count", NodeArg { pos: 1, ..NIL_OK }),
    ("traverse_id", NodeArg { pos: 1, ..NIL_OK }),
    ("free", NOTHING_OK),
    ("flush_node", NOTHING_OK),
    ("flush_list", NOTHING_OK),
];

/// Lua errors (not fatal) of `node` functions called with too few
/// arguments, raised at the caller's position as LuaTeX does.
const ARGUMENT_COUNT_CHECKS: &str = r##"
local node, direct, select, error = node, node.direct, select, error
local function check(t, name, n, msg)
  local f = t[name]
  if f == nil then return end
  t[name] = function(...)
    if select("#", ...) < n then error(msg, 2) end
    return f(...)
  end
end
check(node, "remove", 2, "Not enough arguments for node.remove()")
check(node, "insert_after", 3, "Not enough arguments for node.insert_after()")
check(node, "insert_before", 3, "Not enough arguments for node.insert_before()")
check(node, "set_attribute", 3, "incorrect number of arguments")
check(node, "unset_attribute", 2,
  "bad argument #2 to 'unset_attribute' (number expected, got no value)")
do
  local f = node.unset_attribute
  node.unset_attribute = function(...)
    local id = select(2, ...)
    if select("#", ...) >= 2 and type(id) ~= "number" then
      error("bad argument #2 to 'unset_attribute' (number expected, got " .. type(id) .. ")", 2)
    end
    return f(...)
  end
end
check(node, "dimensions", 1, "missing argument to 'dimensions' (node expected)")
check(node, "rangedimensions", 2,
  "missing argument to 'rangedimensions' (2 or more nodes expected)")
check(direct, "dimensions", 1, "missing argument to 'dimensions' (direct node expected)")
check(direct, "rangedimensions", 2,
  "missing argument to 'rangedimensions' (2 or more direct nodes expected)")
"##;

/// Wraps the functions of [`NODE_ARGUMENT`].
fn require_nodes(lua: &Lua, node: &Table) -> mlua::Result<()> {
    for &(name, rule) in NODE_ARGUMENT {
        let Ok(f) = node.get::<mlua::Function>(name) else {
            continue;
        };
        let checked = lua.create_function(move |lua, args: MultiValue| {
            let arg = args.get(rule.pos).cloned();
            let fine = match &arg {
                None => rule.absent_ok,
                Some(Value::Nil) => rule.nil_ok,
                // Attribute lists are nodes too, for traversal.
                Some(Value::UserData(u)) => {
                    u.is::<LNode>() || (u.is::<LAttr>() && name.starts_with("traverse"))
                }
                Some(_) => false,
            };
            if !fine {
                return Err(match &arg {
                    None => {
                        let msg = "lua <node> expected, not an object with type no value";
                        match with_engine(lua, |e| e.luatex_fatal("node lib", msg)) {
                            Err(e) => e,
                        }
                    }
                    Some(v) => crate::texlib::not_a_node(lua, v),
                });
            }
            if arg.is_none() {
                // Observed: nil comes back.
                return Ok(MultiValue::from_iter([Value::Nil]));
            }
            f.call::<MultiValue>(args)
        })?;
        node.set(name, checked)?;
    }
    // node.dimensions and node.rangedimensions take glue settings or a
    // parent before the node: nil there is fatal.
    for name in ["dimensions", "rangedimensions"] {
        if let Ok(f) = node.get::<mlua::Function>(name) {
            let checked = lua.create_function(move |lua, args: MultiValue| {
                if let Some(v) = args.iter().find(|v| {
                    !matches!(v, Value::Integer(_) | Value::Number(_))
                        && !matches!(v, Value::UserData(u) if u.is::<LNode>())
                }) {
                    return Err(crate::texlib::not_a_node(lua, v));
                }
                f.call::<MultiValue>(args)
            })?;
            node.set(name, checked)?;
        }
    }
    Ok(())
}

/// Registry key of the table holding node properties by direct number.
const PROPERTIES_KEY: &str = "retex.node.properties";

/// The property store, with the engine's pending frees and copies of
/// nodes with properties applied (see [`retex_engine::nodes::Properties`]).
fn properties(lua: &Lua) -> mlua::Result<Table> {
    let store: Table = match lua.named_registry_value::<Value>(PROPERTIES_KEY)? {
        Value::Table(t) => t,
        _ => {
            let t = lua.create_table()?;
            lua.set_named_registry_value(PROPERTIES_KEY, &t)?;
            t
        }
    };
    let events = with_engine(lua, |e| std::mem::take(&mut e.nodes.props.events))?;
    for ev in events {
        match ev {
            retex_engine::nodes::PropEvent::Flush(n) => store.raw_set(n, Value::Nil)?,
            retex_engine::nodes::PropEvent::Copy(from, to) => {
                // Observed (properties mode copy): a table is inherited
                // through `__index`; other values are not copied.
                let v = match store.raw_get::<Value>(from)? {
                    Value::Table(t) => {
                        let copy = lua.create_table()?;
                        let mt = lua.create_table()?;
                        mt.set("__index", t)?;
                        copy.set_metatable(Some(mt))?;
                        Value::Table(copy)
                    }
                    _ => Value::Nil,
                };
                if v.is_nil() {
                    with_engine(lua, |e| e.nodes.props.nodes.remove(&to))?;
                }
                store.raw_set(to, v)?;
            }
        }
    }
    Ok(store)
}

fn set_property(lua: &Lua, p: NodeRef, v: Value) -> mlua::Result<()> {
    let store = properties(lua)?;
    with_engine(lua, |e| {
        let props = &mut e.nodes.props;
        if v.is_nil() {
            props.nodes.remove(&p.0);
        } else if props.flush || props.copy {
            props.nodes.insert(p.0);
        }
    })?;
    store.raw_set(p.0, v)
}

/// `get_properties_table`, `getproperty`, `setproperty`,
/// `flush_properties_table` and `set_properties_mode` (LuaTeX manual
/// §10.6.6). The tables returned by `get_properties_table` are proxies
/// indexed by node (`node`) or direct number (`node.direct`), so that
/// properties of freed nodes go away as in LuaTeX.
fn install_properties(lua: &Lua, node: &Table, direct: &Table) -> mlua::Result<()> {
    for t in [node, direct] {
        let proxy = lua.create_table()?;
        let mt = lua.create_table()?;
        mt.set(
            "__index",
            lua.create_function(|lua, (_t, k): (Value, Value)| match to_ref(&k) {
                Some(p) => properties(lua)?.raw_get::<Value>(p.0),
                None => Ok(Value::Nil),
            })?,
        )?;
        mt.set(
            "__newindex",
            lua.create_function(|lua, (_t, k, v): (Value, Value, Value)| match to_ref(&k) {
                Some(p) => set_property(lua, p, v),
                None => Ok(()),
            })?,
        )?;
        proxy.set_metatable(Some(mt))?;
        t.set(
            "get_properties_table",
            lua.create_function(move |_, ()| Ok(proxy.clone()))?,
        )?;
        t.set(
            "getproperty",
            lua.create_function(|lua, v: Value| match to_ref(&v) {
                Some(p) => properties(lua)?.raw_get::<Value>(p.0),
                None => Ok(Value::Nil),
            })?,
        )?;
        t.set(
            "setproperty",
            lua.create_function(|lua, (v, x): (Value, Value)| match to_ref(&v) {
                Some(p) => set_property(lua, p, x),
                None => Ok(()),
            })?,
        )?;
        t.set(
            "flush_properties_table",
            lua.create_function(|lua, ()| {
                let store = lua.create_table()?;
                lua.set_named_registry_value(PROPERTIES_KEY, &store)?;
                with_engine(lua, |e| {
                    e.nodes.props.nodes.clear();
                    e.nodes.props.events.clear();
                })
            })?,
        )?;
        t.set(
            "set_properties_mode",
            lua.create_function(|lua, (flush, copy): (Option<bool>, Option<bool>)| {
                with_engine(lua, |e| {
                    e.nodes.props.flush = flush.unwrap_or(false);
                    e.nodes.props.copy = copy.unwrap_or(false);
                })
            })?,
        )?;
    }
    Ok(())
}

fn install_common(lua: &Lua, t: &Table, direct: bool) -> mlua::Result<()> {
    t.set(
        "types",
        lua.create_function(|lua, ()| {
            let out = lua.create_table()?;
            for (k, v) in &info().names {
                out.set(*k, v.as_str())?;
            }
            Ok(out)
        })?,
    )?;
    t.set(
        "whatsits",
        lua.create_function(|lua, ()| {
            let out = lua.create_table()?;
            for (k, v) in &info().whatsits {
                out.set(*k, v.as_str())?;
            }
            Ok(out)
        })?,
    )?;
    t.set(
        "id",
        lua.create_function(|_, name: String| Ok(info().ids.get(&name).copied()))?,
    )?;
    t.set(
        "subtype",
        lua.create_function(|_, name: String| {
            Ok(info()
                .whatsits
                .iter()
                .find(|(_, n)| *n == name)
                .map(|(k, _)| *k))
        })?,
    )?;
    t.set(
        "type",
        lua.create_function(|lua, v: Value| match &v {
            Value::Integer(n) if !matches!(v, Value::UserData(_)) => {
                Ok(info().names.get(&(*n as u8)).cloned())
            }
            _ => match to_ref(&v) {
                Some(p) => {
                    let t = with_engine(lua, |e| e.nodes.id(p))?;
                    Ok(info().names.get(&t).cloned())
                }
                None => Ok(None),
            },
        })?,
    )?;
    t.set(
        "subtypes",
        lua.create_function(|lua, v: Value| {
            let idn = match &v {
                Value::Integer(n) => *n as u8,
                Value::String(s) => match info().ids.get(&*s.to_str()?) {
                    Some(i) => *i,
                    None => return Ok(Value::Nil),
                },
                _ => return Ok(Value::Nil),
            };
            let out = lua.create_table()?;
            if let Some(st) = info().subtypes.get(&idn) {
                for (k, n) in st {
                    out.set(*k, n.as_str())?;
                }
            }
            Ok(Value::Table(out))
        })?,
    )?;
    t.set(
        "fields",
        lua.create_function(|lua, (v, sub): (Value, Option<i64>)| {
            let idn = match &v {
                Value::Integer(n) => *n as u8,
                Value::String(s) => match info().ids.get(&*s.to_str()?) {
                    Some(i) => *i,
                    None => return Ok(Value::Nil),
                },
                _ => return Ok(Value::Nil),
            };
            let list = if idn == id::WHATSIT {
                sub.and_then(|s| info().whatsit_fields.get(&(s as u16)))
            } else {
                info().fields.get(&idn)
            };
            let out = lua.create_table()?;
            if let Some(fl) = list {
                for (k, n) in fl {
                    out.set(*k, n.as_str())?;
                }
            }
            Ok(Value::Table(out))
        })?,
    )?;
    t.set(
        "is_node",
        lua.create_function(move |_, v: Value| {
            Ok(match &v {
                Value::UserData(u) => u.borrow::<LNode>().is_ok(),
                Value::Integer(n) => direct && *n > 0,
                _ => false,
            })
        })?,
    )?;
    t.set(
        "new",
        lua.create_function(move |lua, (ty, sub): (Value, Option<Value>)| {
            let t = match &ty {
                Value::Integer(n) => *n as u8,
                Value::String(s) => *info()
                    .ids
                    .get(&*s.to_str()?)
                    .ok_or_else(|| mlua::Error::runtime("unknown node type"))?,
                _ => return Err(mlua::Error::runtime("node type expected")),
            };
            let st = match &sub {
                Some(Value::Integer(n)) => *n as u16,
                Some(Value::String(s)) => {
                    let s = s.to_str()?.to_owned();
                    info()
                        .whatsits
                        .iter()
                        .find(|(_, n)| *n == s)
                        .map(|(k, _)| *k)
                        .unwrap_or(0)
                }
                _ => 0,
            };
            let data = if t == id::WHATSIT {
                NodeData::Whatsit(Box::new(new_whatsit(st)))
            } else if t == id::STYLE {
                // Observed: a style node's subtype is its style.
                NodeData::Style {
                    style: st.min(7) as u8,
                }
            } else {
                new_data(t)
            };
            // Observed: new nodes carry the current attributes.
            let p = with_engine(lua, |e| e.new_node(t, st, data))?;
            wrap(lua, p, direct)
        })?,
    )?;
    // Observed: free returns the node's successor.
    t.set(
        "free",
        lua.create_function(move |lua, v: Value| {
            impossible(lua, &v, "free")?;
            let Some(p) = to_ref(&v) else {
                return Ok(Value::Nil);
            };
            let next = with_engine(lua, |e| {
                let n = e.nodes.next(p);
                e.nodes.free(p);
                e.check_double_free();
                n
            })?;
            if next.is_null() {
                Ok(Value::Nil)
            } else {
                wrap(lua, next, direct)
            }
        })?,
    )?;
    t.set(
        "flush_node",
        lua.create_function(|lua, v: Value| {
            impossible(lua, &v, "free")?;
            if let Some(p) = to_ref(&v) {
                with_engine(lua, |e| {
                    e.nodes.free(p);
                    e.check_double_free();
                })?;
            }
            Ok(())
        })?,
    )?;
    t.set(
        "flush_list",
        lua.create_function(|lua, v: Value| {
            impossible(lua, &v, "free")?;
            if let Some(p) = to_ref(&v) {
                with_engine(lua, |e| {
                    e.nodes.flush_list(p);
                    e.check_double_free();
                })?;
            }
            Ok(())
        })?,
    )?;
    t.set(
        "copy",
        lua.create_function(move |lua, v: Value| {
            match impossible(lua, &v, "copy").map(|()| to_ref(&v))? {
                Some(p) => {
                    let q = with_engine(lua, |e| e.nodes.copy_node(p))?;
                    wrap(lua, q, direct)
                }
                None => Ok(Value::Nil),
            }
        })?,
    )?;
    t.set(
        "copy_list",
        lua.create_function(move |lua, v: Value| {
            match impossible(lua, &v, "copy").map(|()| to_ref(&v))? {
                Some(p) => {
                    let q = with_engine(lua, |e| e.nodes.copy_list(p))?;
                    wrap(lua, q, direct)
                }
                None => Ok(Value::Nil),
            }
        })?,
    )?;
    t.set(
        "tail",
        lua.create_function(move |lua, v: Value| match to_ref(&v) {
            Some(p) => {
                let q = with_engine(lua, |e| tail(e, p))?;
                wrap(lua, q, direct)
            }
            None => Ok(Value::Nil),
        })?,
    )?;
    t.set(
        "slide",
        lua.create_function(move |lua, v: Value| match to_ref(&v) {
            Some(p) => {
                let q = with_engine(lua, |e| slide(e, p))?;
                wrap(lua, q, direct)
            }
            None => Ok(Value::Nil),
        })?,
    )?;
    t.set(
        "length",
        lua.create_function(|lua, v: Value| match to_ref(&v) {
            Some(p) => with_engine(lua, |e| count(e, p, None)),
            None => Ok(0),
        })?,
    )?;
    t.set(
        "count",
        lua.create_function(|lua, (ty, v): (i64, Value)| match to_ref(&v) {
            Some(p) => with_engine(lua, |e| count(e, p, Some(ty as u8))),
            None => Ok(0),
        })?,
    )?;
    for (name, by_id) in [("traverse", false), ("traverse_id", true)] {
        t.set(
            name,
            lua.create_function(move |lua, args: MultiValue| {
                let v: Vec<Value> = args.into_iter().collect();
                let (filter, start) = if by_id {
                    (
                        Some(int(v.first().unwrap_or(&Value::Nil)) as u8),
                        v.get(1).cloned(),
                    )
                } else {
                    (None, v.first().cloned())
                };
                if let Some(Value::UserData(u)) = &start
                    && u.is::<LAttr>()
                {
                    let mut entries =
                        attr_entries(lua, u)?.into_iter().filter(move |[_, id, _]| {
                            filter.is_none_or(|f| *id == Value::Integer(i64::from(f)))
                        });
                    let iter = lua.create_function_mut(move |_, (_s, _cur): (Value, Value)| {
                        Ok(match entries.next() {
                            Some([n, _, sub]) if by_id => MultiValue::from_iter([n, sub]),
                            Some([n, id, sub]) => MultiValue::from_iter([n, id, sub]),
                            None => MultiValue::new(),
                        })
                    })?;
                    return Ok((iter, Value::Nil, Value::Nil));
                }
                let start = start.and_then(|s| to_ref(&s)).unwrap_or(NodeRef::NULL);
                let iter = lua.create_function(move |lua, (_s, cur): (Value, Value)| {
                    let next = match to_ref(&cur) {
                        Some(c) => with_engine(lua, |e| e.nodes.next(c))?,
                        None => start,
                    };
                    let mut p = next;
                    let found = with_engine(lua, |e| {
                        while !p.is_null() {
                            if filter.is_none_or(|f| e.nodes.id(p) == f) {
                                return (p, e.nodes.id(p), e.nodes.get(p).subtype);
                            }
                            p = e.nodes.next(p);
                        }
                        (NodeRef::NULL, 0, 0)
                    })?;
                    if found.0.is_null() {
                        return Ok(MultiValue::new());
                    }
                    // `traverse` yields node, id and subtype;
                    // `traverse_id` node and subtype.
                    let n = wrap(lua, found.0, direct)?;
                    let sub = Value::Integer(i64::from(found.2));
                    Ok(if by_id {
                        MultiValue::from_iter([n, sub])
                    } else {
                        MultiValue::from_iter([n, Value::Integer(i64::from(found.1)), sub])
                    })
                })?;
                Ok((iter, Value::Nil, Value::Nil))
            })?,
        )?;
    }
    t.set(
        "insert_after",
        lua.create_function(move |lua, (h, c, n): (Value, Value, Value)| {
            // Observed: without a node to insert, the head comes back.
            let (Some(n), head) = (to_ref(&n), to_ref(&h)) else {
                return Ok(MultiValue::from_iter([h, Value::Nil]));
            };
            let cur = to_ref(&c);
            let head = with_engine(lua, |e| match (head, cur) {
                (None, _) | (_, None) => n,
                (Some(h), Some(c)) => {
                    // The tail of the new list is found before linking:
                    // inserting a node after itself must not make a loop
                    // (found by fuzzing).
                    let nx = e.nodes.next(c);
                    let tail = tail(e, n);
                    e.nodes.link(c, n);
                    e.nodes.link(tail, nx);
                    h
                }
            })?;
            Ok(MultiValue::from_iter([
                wrap(lua, head, direct)?,
                wrap(lua, n, direct)?,
            ]))
        })?,
    )?;
    t.set(
        "insert_before",
        lua.create_function(move |lua, (h, c, n): (Value, Value, Value)| {
            let Some(n) = to_ref(&n) else {
                return Ok(MultiValue::from_iter([h, Value::Nil]));
            };
            let head = to_ref(&h);
            let cur = to_ref(&c);
            let head = with_engine(lua, |e| match (head, cur) {
                (None, _) => n,
                (Some(h), None) => {
                    let t = tail(e, h);
                    e.nodes.link(t, n);
                    h
                }
                (Some(h), Some(c)) => {
                    let pv = e.nodes.get(c).prev;
                    let tail = tail(e, n);
                    e.nodes.link(tail, c);
                    if c == h || pv.is_null() {
                        e.nodes.get_mut(n).prev = NodeRef::NULL;
                        n
                    } else {
                        e.nodes.link(pv, n);
                        h
                    }
                }
            })?;
            Ok(MultiValue::from_iter([
                wrap(lua, head, direct)?,
                wrap(lua, n, direct)?,
            ]))
        })?,
    )?;
    t.set(
        "remove",
        lua.create_function(move |lua, (h, c): (Value, Value)| {
            // Observed: without a node to remove, the head comes back.
            let (Some(h), Some(c)) = (to_ref(&h), to_ref(&c)) else {
                return Ok(MultiValue::from_iter([h, Value::Nil]));
            };
            let (head, next) = with_engine(lua, |e| {
                let pv = e.nodes.get(c).prev;
                let nx = e.nodes.next(c);
                let head = if c == h {
                    nx
                } else {
                    e.nodes.link(pv, nx);
                    h
                };
                if !nx.is_null() && c == h {
                    e.nodes.get_mut(nx).prev = NodeRef::NULL;
                }
                // Observed: the removed node keeps its links.
                (head, nx)
            })?;
            Ok(MultiValue::from_iter([
                wrap(lua, head, direct)?,
                wrap(lua, next, direct)?,
            ]))
        })?,
    )?;
    t.set(
        "has_field",
        lua.create_function(|lua, (v, f): (Value, String)| match to_ref(&v) {
            Some(p) => {
                let t = with_engine(lua, |e| e.nodes.id(p))?;
                Ok(info()
                    .fields
                    .get(&t)
                    .is_some_and(|fl| fl.iter().any(|(_, n)| *n == f)))
            }
            None => Ok(false),
        })?,
    )?;
    t.set(
        "getfield",
        lua.create_function(move |lua, (v, f): (Value, String)| match to_ref(&v) {
            Some(p) => get_field_impl(lua, p, &f, direct),
            None => Ok(Value::Nil),
        })?,
    )?;
    t.set(
        "setfield",
        lua.create_function(|lua, (v, f, x): (Value, String, Value)| match to_ref(&v) {
            Some(p) => set_field(lua, p, &f, x),
            None => Ok(()),
        })?,
    )?;
    // Direct-style accessors (also accepted by node.* in LuaTeX).
    for name in [
        "id", "subtype", "next", "prev", "char", "font", "width", "height", "depth", "list",
        "penalty", "kern", "leader",
    ] {
        let key = if name == "list" { "head" } else { name };
        if name != "id" && name != "subtype" {
            t.set(
                format!("get{name}"),
                lua.create_function(move |lua, v: Value| match to_ref(&v) {
                    Some(p) => get_field_impl(lua, p, key, direct),
                    None => Ok(Value::Nil),
                })?,
            )?;
        } else {
            t.set(
                format!("get{name}"),
                lua.create_function(move |lua, v: Value| match to_ref(&v) {
                    Some(p) => get_field_impl(lua, p, key, direct),
                    None => Ok(Value::Nil),
                })?,
            )?;
        }
        t.set(
            format!("set{name}"),
            lua.create_function(move |lua, (v, x): (Value, Value)| match to_ref(&v) {
                Some(p) => set_field(lua, p, key, x),
                None => Ok(()),
            })?,
        )?;
    }
    install_accessors(lua, t, direct)?;
    // Engine operations that ltluatex installs as callback defaults; the
    // real implementations come with the typesetting code.
    // node.mlist_to_hlist(head, style, penalties): the engine's conversion.
    t.set(
        "mlist_to_hlist",
        lua.create_function(move |lua, args: MultiValue| {
            let v: Vec<Value> = args.into_iter().collect();
            let head = v.first().and_then(to_ref).unwrap_or(NodeRef::NULL);
            // Observed: nodes that cannot be in a math list are LuaTeX's
            // "This can't happen (mlist1)", a boundary "(mlist3)".
            with_engine(lua, |e| {
                let mut p = head;
                let mut steps = e.nodes.capacity();
                while !p.is_null() && steps > 0 {
                    steps -= 1;
                    match e.nodes.id(p) {
                        id::GLYPH
                        | id::MATH
                        | id::MARGIN_KERN
                        | id::LOCAL_PAR
                        | id::DIR
                        | id::SUB_BOX
                        | id::UNSET
                        | id::GLUE_SPEC
                        | id::HLIST
                        | id::VLIST
                        | id::TEMP
                        | id::DELIM
                        | id::MATH_CHAR
                        | id::SUB_MLIST
                        | id::MATH_TEXT_CHAR
                        | 38 => e.confusion("mlist1"),
                        id::BOUNDARY => e.confusion("mlist3"),
                        _ => {}
                    }
                    p = e.nodes.next(p);
                }
            })?;
            let style = match v.get(1) {
                Some(Value::String(s)) => {
                    let s = s.to_str()?.to_string();
                    crate::texlib::MATH_STYLE_NAMES
                        .iter()
                        .position(|n| *n == s)
                        .unwrap_or(2) as i32
                }
                Some(Value::Integer(n)) => (*n as i32).clamp(0, 7),
                _ => 2,
            };
            let pen = matches!(v.get(2), Some(Value::Boolean(true)));
            if head.is_null() {
                return Ok(Value::Nil);
            }
            let r = with_engine(lua, |e| e.mlist_to_hlist(head, style, pen))?;
            if r.is_null() {
                return Ok(Value::Nil);
            }
            wrap(lua, r, direct)
        })?,
    )?;
    // rangedimensions(parent, first [, last]): the natural size of the
    // list from first up to last (exclusive).
    t.set(
        "rangedimensions",
        lua.create_function(|lua, args: MultiValue| {
            let first = args.get(1).and_then(to_ref).unwrap_or(NodeRef::NULL);
            let stop = args.get(2).and_then(to_ref).unwrap_or(NodeRef::NULL);
            if first.is_null() {
                return Ok((0, 0, 0));
            }
            with_engine(lua, |e| e.natural_dimensions(first, stop))
        })?,
    )?;
    // ligaturing(head) and kerning(head): the built-in passes; they give
    // the head, the tail and success.
    for (name, pass) in [
        ("ligaturing", retex_engine::nodeproc::NodePass::Ligaturing),
        ("kerning", retex_engine::nodeproc::NodePass::Kerning),
    ] {
        t.set(
            name,
            lua.create_function(move |lua, args: MultiValue| {
                let Some(h) = args.front().and_then(to_ref) else {
                    return Ok(MultiValue::from_iter([Value::Nil]));
                };
                let (h, tl) = with_engine(lua, |e| e.lua_node_pass(pass, h))?;
                Ok(MultiValue::from_iter([
                    wrap(lua, h, direct)?,
                    wrap(lua, tl, direct)?,
                    Value::Boolean(true),
                ]))
            })?,
        )?;
    }
    for name in ["hyphenating", "flatten_discretionaries"] {
        t.set(
            name,
            lua.create_function(move |_, args: MultiValue| Ok(args))?,
        )?;
    }
    install_list_ops(lua, t, direct)?;
    // The font of a math family in text size.
    t.set(
        "family_font",
        lua.create_function(|lua, fam: i64| {
            if !(0..retex_engine::eqtb::NUM_FAMILIES as i64).contains(&fam) {
                return Ok(0);
            }
            with_engine(lua, |e| i64::from(e.fam_fnt(fam as u32, 0)))
        })?,
    )?;
    t.set(
        "dimensions",
        lua.create_function(|lua, args: MultiValue| {
            // dimensions([glue_set, glue_sign, glue_order,] n [, t]): the
            // natural size of the list from n up to t (exclusive).
            let refs: Vec<NodeRef> = args.iter().filter_map(to_ref).collect();
            let Some(&first) = refs.first() else {
                return Ok((0, 0, 0));
            };
            let stop = refs.get(1).copied().unwrap_or(NodeRef::NULL);
            with_engine(lua, |e| e.natural_dimensions(first, stop))
        })?,
    )?;
    t.set(
        "has_attribute",
        lua.create_function(|lua, (v, n, val): (Value, i64, Option<i64>)| {
            let Some(p) = to_ref(&v) else {
                return Ok(None);
            };
            let a = with_engine(lua, |e| {
                e.nodes
                    .get(p)
                    .attr
                    .as_ref()
                    .and_then(|l| l.iter().find(|(k, _)| i64::from(*k) == n).map(|x| x.1))
            })?;
            Ok(match (a, val) {
                (Some(x), Some(w)) if i64::from(x) != w => None,
                (a, _) => a.map(i64::from),
            })
        })?,
    )?;
    t.set(
        "set_attribute",
        lua.create_function(|lua, (v, n, val): (Value, Value, Value)| {
            // Observed: both numbers are read as `lua_tointeger` does,
            // anything else being 0 (tagpdf passes nil).
            let (n, val) = (to_integer(&n), to_integer(&val));
            if let Some(p) = to_ref(&v) {
                with_engine(lua, |e| set_attr(e, p, n as u32, Some(val as i32)))?;
            }
            Ok(())
        })?,
    )?;
    t.set(
        "unset_attribute",
        lua.create_function(|lua, (v, n): (Value, i64)| {
            if let Some(p) = to_ref(&v) {
                with_engine(lua, |e| set_attr(e, p, n as u32, None))?;
            }
            Ok(())
        })?,
    )?;
    Ok(())
}

/// A value as `lua_tointeger` converts it: integers, floats with an
/// integral value and strings holding one; 0 otherwise.
fn to_integer(v: &Value) -> i64 {
    let float = |f: f64| {
        if f.fract() == 0.0 && f >= i64::MIN as f64 && f < i64::MAX as f64 {
            f as i64
        } else {
            0
        }
    };
    match v {
        Value::Integer(n) => *n,
        Value::Number(f) => float(*f),
        Value::String(s) => match s.to_str() {
            Ok(t) => {
                let t = t.trim();
                t.parse::<i64>()
                    .ok()
                    .or_else(|| t.parse::<f64>().ok().map(float))
                    .unwrap_or(0)
            }
            Err(_) => 0,
        },
        _ => 0,
    }
}

fn set_attr(e: &mut Engine, p: NodeRef, n: u32, v: Option<i32>) {
    let node = e.nodes.get_mut(p);
    let mut list: Vec<(u32, i32)> = node.attr.as_ref().map(|l| l.to_vec()).unwrap_or_default();
    list.retain(|(k, _)| *k != n);
    if let Some(v) = v {
        list.push((n, v));
        list.sort();
    }
    node.attr = if list.is_empty() {
        None
    } else {
        Some(std::rc::Rc::from(list))
    };
}

/// LuaTeX's fatal error for a direct node number that names no node
/// (negative, or beyond the node memory).
fn impossible(lua: &Lua, v: &Value, what: &str) -> mlua::Result<()> {
    // Observed: freeing the temporary head that the node processing
    // callbacks get for a paragraph is "attempt to free an impossible
    // node" too (in a box, it is freed twice later).
    if what == "free"
        && let Some(p) = to_ref(v)
        && with_engine(lua, |e| p == e.nodes.par_temp)?
    {
        let msg = format!("attempt to free an impossible node {}", p.0);
        return match with_engine(lua, |e| e.luatex_fatal("nodes", &msg)) {
            Err(e) => Err(e),
        };
    }
    if let Value::Integer(n) = *v {
        let cap = with_engine(lua, |e| e.nodes.capacity())?;
        if n < 0 || n as u64 >= cap as u64 {
            let msg = format!("attempt to {what} an impossible node {n}");
            return match with_engine(lua, |e| e.luatex_fatal("nodes", &msg)) {
                Err(e) => Err(e),
            };
        }
    }
    Ok(())
}

/// Ends the run for a list that Lua code linked into a loop: walking it
/// would never end (LuaTeX hangs).
fn circular(e: &mut Engine) -> ! {
    e.luatex_fatal("nodes", "circular node list")
}

/// The last node of the list `p` (`node.tail`).
fn tail(e: &mut Engine, p: NodeRef) -> NodeRef {
    match e.nodes.bounded_tail(p) {
        Some(t) => t,
        None => circular(e),
    }
}

fn slide(e: &mut Engine, mut p: NodeRef) -> NodeRef {
    for _ in 0..e.nodes.capacity() {
        let n = e.nodes.next(p);
        if n.is_null() {
            return p;
        }
        e.nodes.get_mut(n).prev = p;
        p = n;
    }
    circular(e)
}

fn count(e: &mut Engine, mut p: NodeRef, ty: Option<u8>) -> i64 {
    let mut n = 0;
    let mut left = e.nodes.capacity();
    while !p.is_null() {
        if left == 0 {
            circular(e);
        }
        left -= 1;
        if ty.is_none_or(|t| e.nodes.id(p) == t) {
            n += 1;
        }
        p = e.nodes.next(p);
    }
    n
}

/// Creates `name` in `t`.
fn set_fn<A, R, F>(lua: &Lua, t: &Table, name: &str, f: F) -> mlua::Result<()>
where
    A: mlua::FromLuaMulti,
    R: mlua::IntoLuaMulti,
    F: Fn(&Lua, A) -> mlua::Result<R> + 'static,
{
    t.set(name, lua.create_function(f)?)
}

/// The glyph's character, font and subtype, if `p` is a glyph.
fn glyph_of(e: &Engine, p: NodeRef) -> Option<(u32, u32, u16)> {
    match &e.nodes.get(p).data {
        NodeData::Glyph(g) => Some((g.chr, g.font, e.nodes.get(p).subtype)),
        _ => None,
    }
}

/// What a list iterator returns besides the node.
type Pick = fn(&Engine, NodeRef) -> Option<Vec<Value>>;

/// An iterator over the list from `start` returning, for each node that
/// `pick` accepts, the node and the values `pick` gives.
fn list_iterator(
    lua: &Lua,
    start: NodeRef,
    direct: bool,
    pick: Pick,
) -> mlua::Result<(mlua::Function, Value, Value)> {
    let iter = lua.create_function(move |lua, (_s, cur): (Value, Value)| {
        let mut p = match to_ref(&cur) {
            Some(c) => with_engine(lua, |e| e.nodes.next(c))?,
            None => start,
        };
        let found = with_engine(lua, |e| {
            while !p.is_null() {
                if let Some(v) = pick(e, p) {
                    return Some((p, v));
                }
                p = e.nodes.next(p);
            }
            None
        })?;
        let Some((p, vals)) = found else {
            return Ok(MultiValue::new());
        };
        let mut out = vec![wrap(lua, p, direct)?];
        out.extend(vals);
        Ok(MultiValue::from_iter(out))
    })?;
    Ok((iter, Value::Nil, Value::Nil))
}

/// The `get…`/`set…` accessors and helpers of LuaTeX's `node.direct`
/// (most are also in `node`), LuaTeX manual §10.6.
fn install_accessors(lua: &Lua, t: &Table, direct: bool) -> mlua::Result<()> {
    // Plain field accessors.
    for (name, key) in [
        ("data", "data"),
        ("lang", "lang"),
        ("fam", "fam"),
        ("sub", "sub"),
        ("sup", "sup"),
        ("nucleus", "nucleus"),
        ("shift", "shift"),
        ("dir", "dir"),
        ("direction", "direction"),
        ("components", "components"),
        ("expansion", "expansion_factor"),
    ] {
        set_fn(
            lua,
            t,
            &format!("get{name}"),
            move |lua, v: Value| match to_ref(&v) {
                Some(p) => get_field_impl(lua, p, key, direct),
                None => Ok(Value::Nil),
            },
        )?;
        set_fn(
            lua,
            t,
            &format!("set{name}"),
            move |lua, (v, x): (Value, Value)| match to_ref(&v) {
                Some(p) => set_field(lua, p, key, x),
                None => Ok(()),
            },
        )?;
    }
    if direct {
        // SyncTeX fields: those of glyphs, kerns, glue, math nodes, boxes
        // and rules (others have none: nil). Zeros are ignored when
        // setting (observed).
        fn has_sync(id: u8) -> bool {
            matches!(
                id,
                id::GLYPH | id::KERN | id::GLUE | id::MATH | id::HLIST | id::VLIST | id::RULE
            )
        }
        set_fn(lua, t, "get_synctex_fields", |lua, v: Value| {
            let Some(p) = to_ref(&v) else {
                return Ok(MultiValue::new());
            };
            let f = with_engine(lua, |e| {
                has_sync(e.nodes.id(p)).then(|| e.nodes.sync_fields(p))
            })?;
            Ok(match f {
                Some((tag, line)) => MultiValue::from_iter([
                    Value::Integer(i64::from(tag)),
                    Value::Integer(i64::from(line)),
                ]),
                None => MultiValue::new(),
            })
        })?;
        set_fn(
            lua,
            t,
            "set_synctex_fields",
            |lua, (v, tag, line): (Value, Option<i64>, Option<i64>)| {
                let Some(p) = to_ref(&v) else {
                    return Ok(());
                };
                with_engine(lua, |e| {
                    if !has_sync(e.nodes.id(p)) {
                        return;
                    }
                    let (mut t0, mut l0) = e.nodes.sync_fields(p);
                    if let Some(t) = tag.filter(|&t| t > 0) {
                        t0 = t as u32;
                    }
                    if let Some(l) = line.filter(|&l| l > 0) {
                        l0 = l as i32;
                    }
                    e.nodes.set_sync_fields(p, (t0, l0));
                })
            },
        )?;
    }
    set_fn(lua, t, "current_attr", |lua, ()| {
        match with_engine(lua, |e| e.cur_attr())? {
            Some(a) => Ok(Value::UserData(lua.create_userdata(LAttr(a))?)),
            None => Ok(Value::Nil),
        }
    })?;
    set_fn(lua, t, "getattributelist", |lua, v: Value| {
        match to_ref(&v) {
            Some(p) => attr_value(lua, p),
            None => Ok(Value::Nil),
        }
    })?;
    set_fn(
        lua,
        t,
        "setattributelist",
        |lua, (v, a): (Value, Value)| match to_ref(&v) {
            Some(p) => set_attr_value(lua, p, &a),
            None => Ok(()),
        },
    )?;
    set_fn(lua, t, "getboth", move |lua, v: Value| {
        let Some(p) = to_ref(&v) else {
            return Ok((Value::Nil, Value::Nil));
        };
        let (pv, nx) = with_engine(lua, |e| (e.nodes.get(p).prev, e.nodes.next(p)))?;
        Ok((wrap(lua, pv, direct)?, wrap(lua, nx, direct)?))
    })?;
    set_fn(
        lua,
        t,
        "setboth",
        |lua, (v, a, b): (Value, Value, Value)| {
            if let Some(p) = to_ref(&v) {
                let a = to_ref(&a).unwrap_or(NodeRef::NULL);
                let b = to_ref(&b).unwrap_or(NodeRef::NULL);
                with_engine(lua, |e| {
                    let n = e.nodes.get_mut(p);
                    n.prev = a;
                    n.next = b;
                })?;
            }
            Ok(())
        },
    )?;
    set_fn(lua, t, "setlink", move |lua, args: MultiValue| {
        let refs: Vec<NodeRef> = args.iter().filter_map(to_ref).collect();
        with_engine(lua, |e| {
            for w in refs.windows(2) {
                e.nodes.link(w[0], w[1]);
            }
        })?;
        match refs.first() {
            Some(p) => wrap(lua, *p, direct),
            None => Ok(Value::Nil),
        }
    })?;
    set_fn(lua, t, "setsplit", |lua, (a, b): (Value, Value)| {
        let (a, b) = (to_ref(&a), to_ref(&b));
        with_engine(lua, |e| {
            if let Some(a) = a {
                e.nodes.get_mut(a).next = NodeRef::NULL;
            }
            if let Some(b) = b {
                e.nodes.get_mut(b).prev = NodeRef::NULL;
            }
        })
    })?;
    set_fn(
        lua,
        t,
        "getwhd",
        move |lua, (v, ex): (Value, Option<bool>)| {
            let Some(p) = to_ref(&v) else {
                return Ok(MultiValue::new());
            };
            let mut out = Vec::new();
            for k in ["width", "height", "depth"] {
                out.push(get_field_impl(lua, p, k, direct)?);
            }
            if ex == Some(true) {
                out.push(get_field_impl(lua, p, "expansion_factor", direct)?);
            }
            Ok(MultiValue::from_iter(out))
        },
    )?;
    set_fn(
        lua,
        t,
        "setwhd",
        |lua, (v, w, h, d): (Value, Value, Value, Value)| {
            if let Some(p) = to_ref(&v) {
                for (k, x) in [("width", w), ("height", h), ("depth", d)] {
                    if !x.is_nil() {
                        set_field(lua, p, k, x)?;
                    }
                }
            }
            Ok(())
        },
    )?;
    set_fn(
        lua,
        t,
        "getdisc",
        move |lua, (v, tails): (Value, Option<bool>)| {
            let Some(p) = to_ref(&v) else {
                return Ok(MultiValue::new());
            };
            let lists = with_engine(lua, |e| match &e.nodes.get(p).data {
                NodeData::Disc {
                    pre, post, replace, ..
                } => {
                    let l = [*pre, *post, *replace];
                    let t = l.map(|h| if h.is_null() { h } else { e.nodes.tail_of(h) });
                    Some((l, t))
                }
                _ => None,
            })?;
            let Some((l, tl)) = lists else {
                return Ok(MultiValue::new());
            };
            let mut out = Vec::new();
            for h in l {
                out.push(wrap(lua, h, direct)?);
            }
            if tails == Some(true) {
                for h in tl {
                    out.push(wrap(lua, h, direct)?);
                }
            }
            Ok(MultiValue::from_iter(out))
        },
    )?;
    set_fn(lua, t, "setdisc", |lua, args: MultiValue| {
        let v: Vec<Value> = args.into_iter().collect();
        let Some(p) = v.first().and_then(to_ref) else {
            return Ok(());
        };
        let get = |i: usize| v.get(i).and_then(to_ref).unwrap_or(NodeRef::NULL);
        let (pre, post, rep) = (get(1), get(2), get(3));
        let sub = v.get(4).filter(|x| !x.is_nil()).map(int);
        let pen = v.get(5).filter(|x| !x.is_nil()).map(int);
        with_engine(lua, |e| {
            if e.nodes.id(p) != id::DISC {
                return;
            }
            e.nodes.set_disc_lists(p, (pre, post, rep));
            if let Some(s) = sub {
                e.nodes.get_mut(p).subtype = s as u16;
            }
            if let (Some(x), NodeData::Disc { penalty, .. }) = (pen, &mut e.nodes.get_mut(p).data) {
                *penalty = x as i32;
            }
        })
    })?;
    set_fn(lua, t, "getglue", |lua, v: Value| {
        let Some(p) = to_ref(&v) else {
            return Ok(MultiValue::new());
        };
        let vals: Vec<Value> = with_engine(lua, |e| match &e.nodes.get(p).data {
            NodeData::Glue { spec: g, .. } | NodeData::Math { glue: g, .. } => vec![
                Value::Integer(g.width.into()),
                Value::Integer(g.stretch.into()),
                Value::Integer(g.shrink.into()),
                Value::Integer(g.stretch_order.into()),
                Value::Integer(g.shrink_order.into()),
            ],
            // Observed order for boxes: set, order, sign.
            NodeData::Box(b) => vec![
                Value::Number(b.glue_set),
                Value::Integer(b.glue_order.into()),
                Value::Integer(b.glue_sign.into()),
            ],
            _ => Vec::new(),
        })?;
        Ok(MultiValue::from_iter(vals))
    })?;
    set_fn(lua, t, "setglue", |lua, args: MultiValue| {
        let v: Vec<Value> = args.into_iter().collect();
        let Some(p) = v.first().and_then(to_ref) else {
            return Ok(());
        };
        let n = |i: usize| v.get(i).map(int).unwrap_or(0);
        with_engine(lua, |e| {
            let g = match &mut e.nodes.get_mut(p).data {
                NodeData::Glue { spec, .. } => spec,
                NodeData::Math { glue, .. } => glue,
                _ => return,
            };
            g.width = n(1) as i32;
            g.stretch = n(2) as i32;
            g.shrink = n(3) as i32;
            g.stretch_order = n(4) as u8;
            g.shrink_order = n(5) as u8;
        })
    })?;
    set_fn(lua, t, "is_zero_glue", |lua, v: Value| {
        let Some(p) = to_ref(&v) else {
            return Ok(false);
        };
        with_engine(lua, |e| match &e.nodes.get(p).data {
            NodeData::Glue { spec: g, .. } | NodeData::Math { glue: g, .. } => {
                g.width == 0 && g.stretch == 0 && g.shrink == 0
            }
            _ => true,
        })
    })?;
    set_fn(lua, t, "getoffsets", |lua, v: Value| {
        let Some(p) = to_ref(&v) else {
            return Ok((Value::Nil, Value::Nil));
        };
        with_engine(lua, |e| match &e.nodes.get(p).data {
            NodeData::Glyph(g) => (
                Value::Integer(g.xoffset.into()),
                Value::Integer(g.yoffset.into()),
            ),
            _ => (Value::Nil, Value::Nil),
        })
    })?;
    set_fn(
        lua,
        t,
        "setoffsets",
        |lua, (v, x, y): (Value, Value, Value)| {
            if let Some(p) = to_ref(&v) {
                if !x.is_nil() {
                    set_field(lua, p, "xoffset", x)?;
                }
                if !y.is_nil() {
                    set_field(lua, p, "yoffset", y)?;
                }
            }
            Ok(())
        },
    )?;
    // is_char: the character of an unprocessed glyph (subtype below 256),
    // false for other glyphs or another font, nil for other nodes.
    set_fn(lua, t, "is_char", |lua, (v, f): (Value, Option<i64>)| {
        let Some(p) = to_ref(&v) else {
            return Ok(Value::Nil);
        };
        Ok(match with_engine(lua, |e| glyph_of(e, p))? {
            Some((c, font, sub)) if sub < 256 && f.is_none_or(|f| f == i64::from(font)) => {
                Value::Integer(c.into())
            }
            Some(_) => Value::Boolean(false),
            None => Value::Nil,
        })
    })?;
    set_fn(lua, t, "is_glyph", |lua, v: Value| {
        let Some(p) = to_ref(&v) else {
            return Ok(MultiValue::from_iter([Value::Boolean(false)]));
        };
        Ok(match with_engine(lua, |e| glyph_of(e, p))? {
            Some((c, font, _)) => {
                MultiValue::from_iter([Value::Integer(c.into()), Value::Integer(font.into())])
            }
            None => MultiValue::from_iter([Value::Boolean(false)]),
        })
    })?;
    set_fn(lua, t, "traverse_char", move |lua, v: Value| {
        let start = to_ref(&v).unwrap_or(NodeRef::NULL);
        list_iterator(lua, start, direct, |e, p| match glyph_of(e, p) {
            Some((c, f, s)) if s < 256 => {
                Some(vec![Value::Integer(c.into()), Value::Integer(f.into())])
            }
            _ => None,
        })
    })?;
    set_fn(lua, t, "traverse_glyph", move |lua, v: Value| {
        let start = to_ref(&v).unwrap_or(NodeRef::NULL);
        list_iterator(lua, start, direct, |e, p| {
            glyph_of(e, p).map(|(c, f, _)| vec![Value::Integer(c.into()), Value::Integer(f.into())])
        })
    })?;
    set_fn(lua, t, "traverse_list", move |lua, v: Value| {
        let start = to_ref(&v).unwrap_or(NodeRef::NULL);
        let (iter, s, c) = list_iterator(lua, start, direct, |e, p| {
            let n = e.nodes.get(p);
            match &n.data {
                NodeData::Box(b) if n.id == id::HLIST || n.id == id::VLIST => Some(vec![
                    Value::Integer(n.id.into()),
                    Value::Integer(n.subtype.into()),
                    // The list as a direct number, wrapped below.
                    Value::Integer(i64::from(b.head.0)),
                ]),
                _ => None,
            }
        })?;
        let wrapper = lua
            .load(
                "local iter, direct = ...
                 return function(s, c)
                   local n, i, st, l = iter(s, c)
                   if n == nil then return nil end
                   if l == 0 then l = nil elseif not direct then l = node.direct.tonode(l) end
                   return n, i, st, l
                 end",
            )
            .set_name("=[retex]")
            .call::<mlua::Function>((iter, direct))?;
        Ok((wrapper, s, c))
    })?;
    set_fn(lua, t, "has_glyph", move |lua, v: Value| {
        let mut p = to_ref(&v).unwrap_or(NodeRef::NULL);
        let found = with_engine(lua, |e| {
            while !p.is_null() {
                let i = e.nodes.id(p);
                if i == id::GLYPH || i == id::DISC {
                    return p;
                }
                p = e.nodes.next(p);
            }
            NodeRef::NULL
        })?;
        wrap(lua, found, direct)
    })?;
    set_fn(
        lua,
        t,
        "first_glyph",
        move |lua, (v, stop): (Value, Value)| {
            let mut p = to_ref(&v).unwrap_or(NodeRef::NULL);
            let stop = to_ref(&stop);
            // Observed: the first glyph whose subtype is 1 or 257 (a plain
            // character); `node.direct` gives 0 when there is none.
            let found = with_engine(lua, |e| {
                while !p.is_null() {
                    if glyph_of(e, p).is_some_and(|(_, _, s)| s & 0xFF == 1) {
                        return p;
                    }
                    if Some(p) == stop {
                        break;
                    }
                    p = e.nodes.next(p);
                }
                NodeRef::NULL
            })?;
            if direct && found.is_null() {
                return Ok(Value::Integer(0));
            }
            wrap(lua, found, direct)
        },
    )?;
    set_fn(lua, t, "get_attribute", |lua, (v, n): (Value, i64)| {
        let Some(p) = to_ref(&v) else {
            return Ok(None);
        };
        with_engine(lua, |e| {
            e.nodes.get(p).attr.as_ref().and_then(|l| {
                l.iter()
                    .find(|(k, _)| i64::from(*k) == n)
                    .map(|x| i64::from(x.1))
            })
        })
    })?;
    set_fn(
        lua,
        t,
        "find_attribute",
        move |lua, (v, n): (Value, i64)| {
            let mut p = to_ref(&v).unwrap_or(NodeRef::NULL);
            let found =
                with_engine(lua, |e| {
                    while !p.is_null() {
                        if let Some(x) =
                            e.nodes.get(p).attr.as_ref().and_then(|l| {
                                l.iter().find(|(k, _)| i64::from(*k) == n).map(|x| x.1)
                            })
                        {
                            return Some((x, p));
                        }
                        p = e.nodes.next(p);
                    }
                    None
                })?;
            match found {
                Some((x, p)) => Ok(MultiValue::from_iter([
                    Value::Integer(x.into()),
                    wrap(lua, p, direct)?,
                ])),
                None => Ok(MultiValue::new()),
            }
        },
    )?;
    set_fn(
        lua,
        t,
        "effective_glue",
        |lua, (g, parent): (Value, Value)| {
            let (Some(g), Some(b)) = (to_ref(&g), to_ref(&parent)) else {
                return Ok(Value::Nil);
            };
            with_engine(lua, |e| {
                let spec = match &e.nodes.get(g).data {
                    NodeData::Glue { spec, .. } => *spec,
                    _ => return Value::Nil,
                };
                let Some(bx) = e.nodes.box_data(b) else {
                    return Value::Number(spec.width.into());
                };
                let mut w = f64::from(spec.width);
                if bx.glue_sign == 1 && spec.stretch_order == bx.glue_order {
                    w += bx.glue_set * f64::from(spec.stretch);
                } else if bx.glue_sign == 2 && spec.shrink_order == bx.glue_order {
                    w -= bx.glue_set * f64::from(spec.shrink);
                }
                Value::Number(w.round())
            })
        },
    )?;
    for (name, protect) in [("protect_glyph", true), ("unprotect_glyph", false)] {
        set_fn(lua, t, name, move |lua, v: Value| {
            if let Some(p) = to_ref(&v) {
                with_engine(lua, |e| {
                    // Observed: protecting turns subtype 1 into 256 and
                    // adds 256 to subtypes up to 256; unprotecting takes
                    // 256 from subtypes above 256.
                    if e.nodes.id(p) == id::GLYPH {
                        let n = e.nodes.get_mut(p);
                        let s = n.subtype;
                        n.subtype = match (protect, s) {
                            (true, 1) => 256,
                            (true, s) if s <= 256 => s + 256,
                            (false, s) if s > 256 => s - 256,
                            (_, s) => s,
                        };
                    }
                })?;
            }
            Ok(())
        })?;
    }
    set_fn(lua, t, "uses_font", |lua, (v, f): (Value, i64)| {
        let Some(p) = to_ref(&v) else {
            return Ok(false);
        };
        with_engine(lua, |e| {
            let uses = |e: &Engine, mut q: NodeRef| {
                while !q.is_null() {
                    if glyph_of(e, q).is_some_and(|(_, font, _)| i64::from(font) == f) {
                        return true;
                    }
                    q = e.nodes.next(q);
                }
                false
            };
            match &e.nodes.get(p).data {
                NodeData::Glyph(g) => i64::from(g.font) == f,
                NodeData::Disc {
                    pre, post, replace, ..
                } => uses(e, *pre) || uses(e, *post) || uses(e, *replace),
                _ => false,
            }
        })
    })?;
    set_fn(lua, t, "getbox", move |lua, n: i64| {
        let p = with_engine(lua, |e| {
            match e.eqtb.get(retex_engine::eqtb::Loc::Box(n as u32)) {
                retex_engine::eqtb::Val::Node(p) => p,
                _ => NodeRef::NULL,
            }
        })?;
        wrap(lua, p, direct)
    })?;
    set_fn(lua, t, "setbox", |lua, args: MultiValue| {
        let mut v: Vec<Value> = args.into_iter().collect();
        let global = matches!(v.first(), Some(Value::String(s)) if &*s.to_str()? == "global");
        if global {
            v.remove(0);
        }
        let n = v.first().map(int).unwrap_or(0) as u32;
        let p = v.get(1).and_then(to_ref).unwrap_or(NodeRef::NULL);
        with_engine(lua, |e| {
            e.define(
                global,
                retex_engine::eqtb::Loc::Box(n),
                retex_engine::eqtb::Val::Node(p),
            )
        })
    })?;
    if direct {
        // Observed: the number itself for a direct node.
        set_fn(lua, t, "is_direct", |_, v: Value| {
            Ok(match v {
                Value::Integer(n) if n > 0 => Value::Integer(n),
                _ => Value::Boolean(false),
            })
        })?;
    } else {
        for (name, next) in [("next", true), ("prev", false)] {
            set_fn(lua, t, name, move |lua, v: Value| {
                let Some(p) = to_ref(&v) else {
                    return Ok(Value::Nil);
                };
                let q = with_engine(lua, |e| {
                    if next {
                        e.nodes.next(p)
                    } else {
                        e.nodes.get(p).prev
                    }
                })?;
                wrap(lua, q, false)
            })?;
        }
    }
    Ok(())
}

/// Registry key of the table of Lua values kept by reference.
const LUA_REFS_KEY: &str = "retex.node.luarefs";

fn lua_refs(lua: &Lua) -> mlua::Result<Table> {
    match lua.named_registry_value::<Value>(LUA_REFS_KEY)? {
        Value::Table(t) => Ok(t),
        _ => {
            let t = lua.create_table()?;
            lua.set_named_registry_value(LUA_REFS_KEY, &t)?;
            Ok(t)
        }
    }
}

/// The table of Lua values kept by reference, with the values of the
/// references node copies made since the last call.
pub(crate) fn lua_refs_synced(lua: &Lua) -> mlua::Result<Table> {
    let refs = lua_refs(lua)?;
    let copies = with_engine(lua, |e| std::mem::take(&mut e.nodes.lua_refs.copies))?;
    for (new, old) in copies {
        let v: Value = refs.raw_get(old)?;
        refs.raw_set(new, v)?;
    }
    Ok(refs)
}

/// Keeps a Lua value by reference; returns its number (see
/// [`retex_engine::nodes::LuaRefs`]; they only show in box displays).
pub(crate) fn lua_ref(lua: &Lua, v: Value) -> mlua::Result<i32> {
    let refs = lua_refs_synced(lua)?;
    let n = with_engine(lua, |e| e.nodes.lua_refs.take())?;
    refs.raw_set(n, v)?;
    Ok(n)
}

/// A whatsit of subtype `sub` as `node.new` makes it.
fn new_whatsit(sub: u16) -> retex_engine::nodes::Whatsit {
    use retex_engine::nodes::{LateData, UserValue, Whatsit, whatsit_sub as ws};
    match sub {
        ws::SPECIAL => Whatsit::Special { data: Vec::new() },
        ws::LATE_LUA => Whatsit::LateLua {
            data: LateData::Bytes(Vec::new()),
            name: Vec::new(),
        },
        ws::PDF_LITERAL | ws::PDF_LATE_LITERAL => Whatsit::PdfLiteral {
            mode: 0,
            data: LateData::Bytes(Vec::new()),
            late: sub == ws::PDF_LATE_LITERAL,
        },
        ws::PDF_COLORSTACK => Whatsit::PdfColorstack {
            stack: 0,
            cmd: 0,
            data: Vec::new(),
        },
        ws::PDF_SETMATRIX => Whatsit::PdfSetmatrix { data: Vec::new() },
        ws::PDF_SAVE => Whatsit::PdfSave,
        ws::PDF_RESTORE => Whatsit::PdfRestore,
        ws::PDF_REFOBJ => Whatsit::PdfRefobj { objnum: 0 },
        ws::PDF_END_LINK => Whatsit::PdfEndLink,
        // Observed: new links and annotations have zero dimensions.
        ws::PDF_START_LINK => Whatsit::PdfStartLink {
            dims: [0; 3],
            objnum: 0,
            attr: Vec::new(),
            action: retex_engine::pdfext::PdfAction::User(Vec::new()),
        },
        ws::PDF_ANNOT => Whatsit::PdfAnnot {
            dims: [0; 3],
            objnum: 0,
            data: Vec::new(),
        },
        ws::SAVE_POS => Whatsit::SavePos,
        ws::PDF_LINK_STATE => Whatsit::PdfLinkState { state: 0 },
        ws::USER_DEFINED => Whatsit::UserDefined {
            user_id: 0,
            value: UserValue::Int(0),
        },
        _ => Whatsit::Other {
            fields: Vec::new(),
            data: Vec::new(),
        },
    }
}

/// The index of `width`, `height` or `depth` in a whatsit's dimensions.
fn dim_index(key: &str) -> usize {
    match key {
        "width" => 0,
        "height" => 1,
        _ => 2,
    }
}

/// Reads a whatsit field.
fn whatsit_field(e: &mut Engine, w: &retex_engine::nodes::Whatsit, key: &str) -> R {
    use retex_engine::nodes::{LateData, UserValue, Whatsit};
    let mut late = |d: &LateData| match d {
        LateData::Bytes(b) | LateData::Lua { data: b, .. } => R::S(b.clone()),
        LateData::Tokens(t) => {
            R::S(e.print_to_string(|e| e.show_token_list(t, 0, t.len(), i64::MAX)))
        }
        LateData::Function { reference } => R::L(*reference),
    };
    match (w, key) {
        (Whatsit::Special { data }, "data") => R::S(data.clone()),
        (Whatsit::LateLua { data, .. }, "data" | "string") => late(data),
        (Whatsit::LateLua { name, .. }, "name") => R::S(name.clone()),
        (Whatsit::PdfLiteral { mode, .. }, "mode") => R::I((*mode).into()),
        (Whatsit::PdfLiteral { data, .. }, "data") => late(data),
        (Whatsit::PdfColorstack { stack, .. }, "stack") => R::I((*stack).into()),
        (Whatsit::PdfColorstack { cmd, .. }, "command") => R::I((*cmd).into()),
        (Whatsit::PdfColorstack { data, .. }, "data") => R::S(data.clone()),
        (Whatsit::PdfSetmatrix { data }, "data") => R::S(data.clone()),
        (Whatsit::PdfRefobj { objnum }, "objnum") => R::I((*objnum).into()),
        // Observed: `link_attr` reads as a string; running dimensions
        // read as -2^30.
        (Whatsit::PdfStartLink { objnum, .. } | Whatsit::PdfAnnot { objnum, .. }, "objnum") => {
            R::I((*objnum).into())
        }
        (Whatsit::PdfStartLink { attr, .. }, "link_attr") => R::S(attr.clone()),
        (Whatsit::PdfAnnot { data, .. }, "data") => R::S(data.clone()),
        (
            Whatsit::PdfStartLink { dims, .. } | Whatsit::PdfAnnot { dims, .. },
            "width" | "height" | "depth",
        ) => R::I(dims[dim_index(key)].into()),
        // lualinksplit reads a link state as `objnum` with the subtype
        // switched to pdf_refobj (the field it shares in LuaTeX).
        (Whatsit::PdfLinkState { state }, "objnum") => R::I((*state).into()),
        (Whatsit::UserDefined { user_id, .. }, "user_id") => R::I((*user_id).into()),
        (Whatsit::UserDefined { value, .. }, "type") => R::I(i64::from(user_type(value))),
        (Whatsit::UserDefined { value, .. }, "value") => match value {
            UserValue::Int(n) => R::I((*n).into()),
            UserValue::Str(s) => R::S(s.clone()),
            UserValue::Tokens(t) => {
                R::S(e.print_to_string(|e| e.show_token_list(t, 0, t.len(), i64::MAX)))
            }
            UserValue::Nodes(p) => R::N(*p),
            UserValue::Lua(n) => R::L(*n),
            UserValue::Attr => R::Nil,
        },
        _ => R::Nil,
    }
}

/// The type letter of a `user_defined` value.
fn user_type(v: &retex_engine::nodes::UserValue) -> u8 {
    use retex_engine::nodes::UserValue;
    match v {
        UserValue::Int(_) => b'd',
        UserValue::Str(_) => b's',
        UserValue::Tokens(_) => b't',
        UserValue::Nodes(_) => b'n',
        UserValue::Lua(_) => b'l',
        UserValue::Attr => b'a',
    }
}

/// Writes a whatsit field.
fn set_whatsit_field(lua: &Lua, p: NodeRef, key: &str, v: Value) -> mlua::Result<()> {
    use retex_engine::nodes::{LateData, Whatsit};
    let s: Option<Vec<u8>> = match &v {
        Value::String(s) => Some(s.as_bytes().to_vec()),
        Value::Integer(n) => Some(n.to_string().into_bytes()),
        Value::Number(n) => Some(crate::texlib::lua_number_string(*n).into_bytes()),
        _ => None,
    };
    let node = to_ref(&v);
    let i = int(&v);
    // The type of a user_defined node decides how `value` is stored.
    let (is_user, utype) = with_engine(lua, |e| match &e.nodes.get(p).data {
        NodeData::Whatsit(w) => match &**w {
            Whatsit::UserDefined { value, .. } => (true, user_type(value)),
            _ => (false, 0),
        },
        _ => (false, 0),
    })?;
    let lref = if is_user && key == "value" && utype == b'l' {
        Some(lua_ref(lua, v.clone())?)
    } else {
        None
    };
    // Observed: outside IniTeX, a string set from Lua is kept as a Lua
    // reference, and box displays show the reference.
    let ini = with_engine(lua, |e| e.ini_version)?;
    let lua_string = |s: Vec<u8>| -> mlua::Result<LateData> {
        if ini {
            Ok(LateData::Bytes(s))
        } else {
            let reference = lua_ref(lua, Value::String(lua.create_string(&s)?))?;
            Ok(LateData::Lua { data: s, reference })
        }
    };
    let late = match (&s, key) {
        (Some(s), "data") => Some(lua_string(s.clone())?),
        // Observed: a function as `\latelua` data is kept by reference,
        // except in IniTeX, which keeps an empty string.
        (None, "data" | "string") if matches!(v, Value::Function(_)) && late_lua(lua, p)? => {
            Some(if ini {
                LateData::Bytes(Vec::new())
            } else {
                LateData::Function {
                    reference: lua_ref(lua, v.clone())?,
                }
            })
        }
        _ => None,
    };
    with_engine(lua, |e| {
        let tokens = |e: &Engine, s: &[u8]| -> retex_engine::token::TokenList {
            let _ = e;
            let toks: Vec<retex_engine::token::Token> = String::from_utf8_lossy(s)
                .chars()
                .map(|c| {
                    if c == ' ' {
                        retex_engine::token::Token::SPACE
                    } else {
                        retex_engine::token::Token::other(c as u32)
                    }
                })
                .collect();
            std::rc::Rc::from(toks)
        };
        let toks = s.as_ref().map(|s| tokens(e, s));
        // Observed: a new value takes its reference before the old one is
        // released.
        let old_ref = e.nodes.lua_ref_of(p);
        set_whatsit_data(e, p, key, &s, &late, &toks, node, i, lref);
        if let Some(r) = old_ref
            && e.nodes.lua_ref_of(p) != Some(r)
        {
            e.nodes.lua_refs.release(r);
        }
    })
}

/// Whether `p` is a `late_lua` whatsit.
fn late_lua(lua: &Lua, p: NodeRef) -> mlua::Result<bool> {
    with_engine(lua, |e| match &e.nodes.get(p).data {
        NodeData::Whatsit(w) => matches!(&**w, retex_engine::nodes::Whatsit::LateLua { .. }),
        _ => false,
    })
}

/// Stores a whatsit field (for [`set_whatsit_field`]).
#[allow(clippy::too_many_arguments)]
fn set_whatsit_data(
    e: &mut Engine,
    p: NodeRef,
    key: &str,
    s: &Option<Vec<u8>>,
    late: &Option<retex_engine::nodes::LateData>,
    toks: &Option<retex_engine::token::TokenList>,
    node: Option<NodeRef>,
    i: i64,
    lref: Option<i32>,
) {
    use retex_engine::nodes::{LateData, UserValue, Whatsit};
    {
        let NodeData::Whatsit(w) = &mut e.nodes.get_mut(p).data else {
            return;
        };
        match (&mut **w, key) {
            (Whatsit::Special { data }, "data") => {
                if let Some(s) = &s {
                    *data = s.clone();
                }
            }
            (Whatsit::LateLua { data, .. }, "data" | "string") => {
                if let Some(l) = late.clone().or_else(|| s.clone().map(LateData::Bytes)) {
                    *data = l;
                }
            }
            (Whatsit::LateLua { name, .. }, "name") => {
                if let Some(s) = &s {
                    *name = s.clone();
                }
            }
            (Whatsit::PdfLiteral { mode, .. }, "mode") => *mode = i as u8,
            (Whatsit::PdfLiteral { data, .. }, "data") => {
                if let Some(l) = late.clone() {
                    *data = l;
                }
            }
            (Whatsit::PdfColorstack { stack, .. }, "stack") => *stack = i as i32,
            (Whatsit::PdfColorstack { cmd, .. }, "command") => *cmd = i as u8,
            (Whatsit::PdfColorstack { data, .. }, "data")
            | (Whatsit::PdfSetmatrix { data }, "data") => {
                if let Some(s) = &s {
                    *data = s.clone();
                }
            }
            (Whatsit::PdfRefobj { objnum }, "objnum")
            | (Whatsit::PdfStartLink { objnum, .. }, "objnum")
            | (Whatsit::PdfAnnot { objnum, .. }, "objnum") => *objnum = i as i32,
            (Whatsit::PdfStartLink { attr: data, .. }, "link_attr")
            | (Whatsit::PdfAnnot { data, .. }, "data") => {
                if let Some(s) = &s {
                    *data = s.clone();
                }
            }
            (
                Whatsit::PdfStartLink { dims, .. } | Whatsit::PdfAnnot { dims, .. },
                "width" | "height" | "depth",
            ) => dims[dim_index(key)] = i as i32,
            (Whatsit::PdfLinkState { state }, "value" | "objnum") => *state = i as i32,
            (Whatsit::UserDefined { user_id, .. }, "user_id") => *user_id = i as i32,
            (Whatsit::UserDefined { value, .. }, "type") => {
                *value = match i as u8 {
                    b's' => UserValue::Str(Vec::new()),
                    b't' => UserValue::Tokens(retex_engine::token::empty_list()),
                    b'n' => UserValue::Nodes(NodeRef::NULL),
                    b'l' => UserValue::Lua(0),
                    b'a' => UserValue::Attr,
                    _ => UserValue::Int(0),
                }
            }
            (Whatsit::UserDefined { value, .. }, "value") => {
                *value = match user_type(value) {
                    b's' => UserValue::Str(s.clone().unwrap_or_default()),
                    b't' => UserValue::Tokens(
                        toks.clone().unwrap_or_else(retex_engine::token::empty_list),
                    ),
                    b'n' => UserValue::Nodes(node.unwrap_or(NodeRef::NULL)),
                    b'l' => UserValue::Lua(lref.unwrap_or(0)),
                    b'a' => UserValue::Attr,
                    _ => UserValue::Int(i as i32),
                }
            }
            _ => {}
        }
    }
}

/// `hpack`, `vpack`, `write`, `last_node`, `end_of_math`,
/// `protect_glyphs` and `unprotect_glyphs` (LuaTeX manual §10.6).
fn install_list_ops(lua: &Lua, t: &Table, direct: bool) -> mlua::Result<()> {
    use retex_engine::build::PackSpec;
    for (name, horizontal) in [("hpack", true), ("vpack", false)] {
        set_fn(lua, t, name, move |lua, args: MultiValue| {
            let v: Vec<Value> = args.into_iter().collect();
            let head = v.first().and_then(to_ref).unwrap_or(NodeRef::NULL);
            let w = v.get(1).map(int).unwrap_or(0) as i32;
            let exactly = matches!(v.get(2), Some(Value::String(s)) if &*s.to_str()? == "exactly");
            let spec = if exactly {
                PackSpec::Exactly(w)
            } else {
                PackSpec::Additional(w)
            };
            let dir = match v.get(3) {
                Some(Value::String(s)) => match &*s.to_str()? {
                    "TLT" => 0,
                    "TRT" => 1,
                    "LTL" => 2,
                    "RTT" => 3,
                    _ => -1,
                },
                Some(Value::Integer(n)) => *n as i8,
                _ => -1,
            };
            let (b, badness) = with_engine(lua, |e| {
                e.pack_dir = dir;
                let b = if horizontal {
                    e.hpack(head, spec)
                } else {
                    e.vpack(head, spec)
                };
                e.pack_dir = -1;
                (b, e.last_badness)
            })?;
            Ok((wrap(lua, b, direct)?, Value::Integer(badness.into())))
        })?;
    }
    // Appends a list to the current list.
    set_fn(lua, t, "write", |lua, v: Value| {
        if let Some(p) = to_ref(&v) {
            with_engine(lua, |e| {
                let tail = tail(e, p);
                e.tail_append(p);
                e.cur_list_mut().tail = tail;
            })?;
        }
        Ok(())
    })?;
    // Removes the last node of the current list and returns it.
    set_fn(lua, t, "last_node", move |lua, ()| {
        let p = with_engine(lua, |e| {
            let l = e.cur_list();
            let (head, tail) = (l.head, l.tail);
            if tail == head {
                return NodeRef::NULL;
            }
            let mut q = head;
            while e.nodes.next(q) != tail {
                q = e.nodes.next(q);
            }
            e.nodes.get_mut(q).next = NodeRef::NULL;
            let n = e.nodes.get_mut(tail);
            n.prev = NodeRef::NULL;
            e.cur_list_mut().tail = q;
            tail
        })?;
        wrap(lua, p, direct)
    })?;
    // The math node that ends the formula starting at a begin math node.
    set_fn(lua, t, "end_of_math", move |lua, v: Value| {
        let Some(mut p) = to_ref(&v) else {
            return Ok(Value::Nil);
        };
        let found = with_engine(lua, |e| {
            if e.nodes.id(p) == id::MATH && e.nodes.subtype(p) == 0 {
                p = e.nodes.next(p);
            }
            while !p.is_null() {
                if e.nodes.id(p) == id::MATH && e.nodes.subtype(p) == 1 {
                    return p;
                }
                p = e.nodes.next(p);
            }
            NodeRef::NULL
        })?;
        wrap(lua, found, direct)
    })?;
    for (name, protect) in [("protect_glyphs", true), ("unprotect_glyphs", false)] {
        set_fn(lua, t, name, move |lua, (h, stop): (Value, Value)| {
            let mut p = to_ref(&h).unwrap_or(NodeRef::NULL);
            let stop = to_ref(&stop);
            with_engine(lua, |e| {
                while !p.is_null() {
                    if e.nodes.id(p) == id::GLYPH {
                        let n = e.nodes.get_mut(p);
                        let s = n.subtype;
                        n.subtype = match (protect, s) {
                            (true, 1) => 256,
                            (true, s) if s <= 256 => s + 256,
                            (false, s) if s > 256 => s - 256,
                            (_, s) => s,
                        };
                    }
                    if Some(p) == stop {
                        break;
                    }
                    p = e.nodes.next(p);
                }
            })
        })?;
    }
    Ok(())
}