quarb 0.33.0

//! The pipeline standard library.
//!
//! Functions come in two families, matching the two pipe operators:
//!
//! - **Scalar** functions (`|`) transform one capsa's topic; some
//!   expand it into several values (e.g. `lines`).
//! - **Aggregate** functions (`@|`) reduce the whole context's topics
//!   to a new list.

use crate::ast::{Arg, FnCall};
use crate::value::Value;
use std::cmp::Ordering;
use unicode_normalization::UnicodeNormalization;
use unicode_segmentation::UnicodeSegmentation;

/// The unit-expression resolver threaded from the executor (the
/// adapter's `unit_scale`), so aggregates read custom units exactly
/// as criteria and ordering do.
type Scale<'a> = &'a dyn Fn(&str) -> Option<(f64, String)>;

/// The internal aggregate standing in for a closing `@| csv` /
/// `@| table` while a tool renders it (see `run_for_rendering`).
pub(crate) const ROWS_FOR_RENDERING: &str = "\u{1}rows";

const SCALAR: &[&str] = &[
    "upper",
    "lower",
    "title",
    "trim",
    "ltrim",
    "rtrim",
    "alpha",
    "digit",
    "alnum",
    // `cc` counts codepoints, `bc` UTF-8 bytes, `wc` words.
    "cc",
    "bc",
    "wc",
    "lc",
    "sc",
    "lines",
    "words",
    "ngrams",
    "levenshtein",
    // Time expressions and the calendar (spec: Time Expressions and
    // the Timeline).
    "timex",
    "time_anchor",
    "period",
    "grain",
    "haversine",
    // Unicode normalization, the stress apparatus, transliteration.
    "nfc",
    "nfd",
    "vowels",
    "stress",
    "stress_at",
    "unstress",
    "accent",
    "translit",
    "number",
    "modernize",
    "gc",
    "sentences",
    "split",
    "substr",
    "pad",
    "lpad",
    "rpad",
    "repeat",
    "indent",
    "round",
    "floor",
    "ceil",
    "abs",
    // The elementary functions and the keyness statistics (the
    // statistics round).
    "log",
    "log2",
    "log10",
    "exp",
    "sqrt",
    "pow",
    "loglik",
    "chi2",
    // The collocation measures (the corpus statistics round).
    "mi",
    "t_score",
    "log_dice",
    "json",
    "jsonl",
    "kaiv",
    "link",
    "xml",
    "markdown",
    "html",
    "atrep",
    "conllu",
    "record",
    "rec",
    "default",
    // The temporal fragment.
    "datetime",
    "epoch",
    "isoformat",
    "year",
    "month",
    "day",
    "hour",
    "minute",
    "second",
    "weekday",
    "date",
    "seconds",
    "minutes",
    "hours",
    "days",
    "duration",
    "td",
    "strptime",
    "tp",
    "bibref",
    "quantity",
    "convert",
    "isodate",
    "isomonth",
    "isoweek",
    "strftime",
    "tfmt",
    "sh",
    "sha256",
    "base64",
    "base64url",
    "base32",
    "crockford32",
    "hex",
    "decode",
    "dec",
];

const AGGREGATE: &[&str] = &[
    "count",
    "sum",
    "product",
    "min",
    "max",
    "mean",
    "avg",
    "median",
    "percentile",
    // The dispersion measures: `std` / `var`, with the long spellings
    // kept as aliases.
    "std",
    "var",
    "stddev",
    "variance",
    // Lexical diversity over a stream of counts (`entropy`,
    // `yule_k`) or of tokens (`mtld`).
    "entropy",
    "yule_k",
    "mtld",
    // Association between two per-capsa expressions, the distance
    // and dispersion measures over paired readings, and the
    // agreement measures over paired labels (the corpus statistics
    // round).
    "corr",
    "spearman",
    "cosine",
    "delta",
    "dp",
    "kappa",
    "precision",
    "recall",
    "f1",
    "json",
    "jsonl",
    "combinations",
    "pairs",
    "triples",
    "csv",
    "table",
    "kaiv",
    "encoding",
    "sort",
    "unique",
    "reverse",
    "first",
    "last",
    "join",
    "ungroup",
    "window",
    "shift",
    "zscore",
    "number",
    "outline",
    "timeline",
];

/// Whether `name` is a whole-context stage that never works per
/// capsa — it rides `@|` only. (Keyed and reducing aggregates also
/// take the plain pipe, working per capsa on a group's members.)
pub fn context_only(name: &str) -> bool {
    matches!(
        name,
        "ungroup"
            | "window"
            | "shift"
            | "zscore"
            | "number"
            | "outline"
            | "timeline"
            | "csv"
            | "table"
            | "encoding"
    )
}

/// Records as columns: the named columns in their order, or the
/// union of the records' fields in first-seen order (a scalar rides
/// a `value` column). A field a record lacks is an empty cell.
/// Aligned text with a rule under the header (widths in grapheme
/// clusters), or RFC 4180 CSV; lines joined, no trailing newline.
pub fn tabulate(values: &[Value], named: Option<&[String]>, csv: bool) -> String {
    tabulate_with(values, named, csv, b',')
}

/// [`tabulate`] with the CSV delimiter chosen (`@| csv(";")`); the
/// table form ignores it.
pub fn tabulate_with(
    values: &[Value],
    named: Option<&[String]>,
    csv: bool,
    delimiter: u8,
) -> String {
    tabulate_in(values, named, csv, delimiter, &|v| match v {
        Value::Null => String::new(),
        Value::Str(s) => s.clone(),
        other => other.display_form(),
    })
}

/// [`tabulate_with`] with the cell renderer chosen — the output
/// locale's, when a tool prints under one.
pub fn tabulate_in(
    values: &[Value],
    named: Option<&[String]>,
    csv: bool,
    delimiter: u8,
    cell: &dyn Fn(&Value) -> String,
) -> String {
    let columns: Vec<String> = match named {
        Some(names) => names.to_vec(),
        None => {
            let mut columns: Vec<String> = Vec::new();
            let mut has_scalar = false;
            for v in values {
                match v {
                    Value::Record(fields) => {
                        for (k, _) in fields {
                            if !columns.contains(k) {
                                columns.push(k.clone());
                            }
                        }
                    }
                    _ => has_scalar = true,
                }
            }
            if has_scalar || columns.is_empty() {
                columns.push("value".to_string());
            }
            columns
        }
    };
    let rows: Vec<Vec<String>> = values
        .iter()
        .map(|v| match v {
            Value::Record(fields) => columns
                .iter()
                .map(|c| {
                    fields
                        .iter()
                        .find(|(k, _)| k == c)
                        .map(|(_, v)| cell(v))
                        .unwrap_or_default()
                })
                .collect(),
            other => columns
                .iter()
                .map(|c| {
                    if c == "value" {
                        cell(other)
                    } else {
                        String::new()
                    }
                })
                .collect(),
        })
        .collect();
    let mut lines: Vec<String> = Vec::with_capacity(rows.len() + 2);
    if csv {
        let sep = (delimiter as char).to_string();
        let quote = |s: &str| -> String {
            if s.contains([delimiter as char, '"', '\n', '\r']) {
                format!("\"{}\"", s.replace('"', "\"\""))
            } else {
                s.to_string()
            }
        };
        let row = |cells: &[String]| {
            cells
                .iter()
                .map(|c| quote(c))
                .collect::<Vec<_>>()
                .join(&sep)
        };
        lines.push(row(&columns));
        lines.extend(rows.iter().map(|r| row(r)));
        return lines.join("\n");
    }
    let width = |s: &str| s.graphemes(true).count();
    let mut widths: Vec<usize> = columns.iter().map(|c| width(c)).collect();
    for row in &rows {
        for (i, c) in row.iter().enumerate() {
            widths[i] = widths[i].max(width(c));
        }
    }
    let line = |cells: &[String]| -> String {
        cells
            .iter()
            .enumerate()
            .map(|(i, c)| format!("{c}{}", " ".repeat(widths[i].saturating_sub(width(c)))))
            .collect::<Vec<_>>()
            .join("  ")
            .trim_end()
            .to_string()
    };
    lines.push(line(&columns));
    lines.push(
        widths
            .iter()
            .map(|w| "-".repeat(*w))
            .collect::<Vec<_>>()
            .join("  "),
    );
    lines.extend(rows.iter().map(|r| line(r)));
    lines.join("\n")
}

/// The outline of a stream of levels: for each row its depth below
/// the shallowest level seen and its dotted number (`1`, `1.1`,
/// `1.2`, `2`). One counter per depth; a row increments its own and
/// forgets the deeper ones. A level that is skipped (1, then 3)
/// counts as present once (`1.1.1`); a row without a level stands
/// at the shallowest.
/// The longest text a repetition may build (`repeat`, `indent`):
/// 64 MiB. Past it the query is refused — a count taken from data
/// (`repeat(::n)`) must not be able to exhaust memory.
pub const MAX_REPEAT_BYTES: usize = 64 << 20;

/// `text` repeated `n` times within [`MAX_REPEAT_BYTES`], else a
/// refusal naming the function and the size it would have built.
fn bounded_repeat(text: &str, n: usize, what: &str) -> Value {
    match text.len().checked_mul(n) {
        Some(bytes) if bytes <= MAX_REPEAT_BYTES => Value::Str(text.repeat(n)),
        _ => {
            crate::exec::record_refusal(format!(
                "{what}({n}): the result would exceed {} bytes",
                MAX_REPEAT_BYTES
            ));
            Value::Null
        }
    }
}

/// How far below the shallowest level an outline may reach: the
/// executor refuses `number` / `outline` past it (levels are data).
pub const MAX_OUTLINE_DEPTH: i64 = 64;

pub fn outline_numbers(levels: &[Option<i64>]) -> Vec<(usize, String)> {
    let base = levels.iter().flatten().copied().min().unwrap_or(0);
    let mut counters: Vec<u64> = Vec::new();
    levels
        .iter()
        .map(|l| {
            let depth = (l.unwrap_or(base) - base).clamp(0, MAX_OUTLINE_DEPTH) as usize;
            counters.truncate(depth + 1);
            if counters.len() == depth + 1 {
                counters[depth] += 1;
            } else {
                counters.resize(depth + 1, 1);
            }
            let number = counters
                .iter()
                .map(u64::to_string)
                .collect::<Vec<_>>()
                .join(".");
            (depth, number)
        })
        .collect()
}

/// Whether `name` is an association aggregate — a reduction of two
/// per-capsa expressions to one number (`corr(:a; :b)`). Evaluated
/// in the executor like the keyed aggregates; this module holds the
/// arithmetic ([`associate`]).
pub fn association(name: &str) -> bool {
    matches!(
        name,
        "corr" | "spearman" | "cosine" | "delta" | "dp" | "kappa" | "precision" | "recall" | "f1"
    )
}

/// Whether `name` is an agreement measure — an association that
/// reads its two expressions as labels, not numbers (`kappa(:g; :p)`
/// over categories, `precision`/`recall`/`f1` over truthiness).
pub fn agreement(name: &str) -> bool {
    matches!(name, "kappa" | "precision" | "recall" | "f1")
}

/// Whether the call carries the bare word `sample` (a string
/// literal, as the parser reads a bare name): the dispersion
/// measures divide by n − 1 instead of n.
pub fn sample_flag(call: &FnCall) -> bool {
    call.args
        .iter()
        .any(|a| matches!(a, Arg::Lit(Value::Str(s)) if s == "sample"))
}

/// Whether the call carries the bare word `atergo`: the a tergo
/// (inverse-lexicographic) order, in which texts compare from their
/// last character toward their first — the reverse dictionary's
/// order.
pub fn atergo_flag(call: &FnCall) -> bool {
    call.args
        .iter()
        .any(|a| matches!(a, Arg::Lit(Value::Str(s)) if s == "atergo"))
}

/// The text ordering a `sort` call asks for, where it asks for one:
/// a locale's collation, the a tergo order, or both — the mirror is
/// then taken over the collation's elements, so a contracting
/// digraph stays one unit. `None` when the call names neither: the
/// standard value comparison applies, and that is the caller's,
/// being unit- and number-aware.
pub(crate) fn text_order(call: &FnCall) -> Option<Box<dyn Fn(&str, &str) -> Ordering>> {
    match (collator_for(call), atergo_flag(call)) {
        (Some(c), true) => Some(Box::new(move |a, b| c.compare_reverse(a, b))),
        (Some(c), false) => Some(Box::new(move |a, b| c.compare(a, b))),
        // Code points from the end; a tie (one text a suffix of the
        // other, or equal) falls to the forward order.
        (None, true) => Some(Box::new(|a, b| {
            a.chars().rev().cmp(b.chars().rev()).then_with(|| a.cmp(b))
        })),
        (None, false) => None,
    }
}

/// The text order `sort` falls to when the query names no locale:
/// the output locale's collation, when the tool set one.
pub(crate) fn default_text_order() -> Option<Box<dyn Fn(&str, &str) -> Ordering>> {
    default_collator()
        .map(|c| -> Box<dyn Fn(&str, &str) -> Ordering> { Box::new(move |a, b| c.compare(a, b)) })
}

/// `sort` without a locale argument: the standard value comparison,
/// with text that has no reading collated under `collate` (the
/// output locale's order) — numbers, dates, quantities and text
/// that reads as one keep their magnitude order whatever the
/// locale.
pub(crate) fn default_cmp(
    a: &Value,
    b: &Value,
    scale: Scale,
    collate: Option<&dyn Fn(&str, &str) -> Ordering>,
) -> Ordering {
    if let (Some(c), Value::Str(x), Value::Str(y)) = (collate, a, b)
        && matches!(a.sort_key_with(scale), crate::value::SortKey::Text(_))
        && matches!(b.sort_key_with(scale), crate::value::SortKey::Text(_))
    {
        return c(x, y);
    }
    a.compare_with(b, scale)
}

/// The collator for the output locale's tag, when the tool set
/// one (`quarb::locale::set_default_collation`).
#[cfg(feature = "colligo")]
fn default_collator() -> Option<colligo::Collator> {
    let tag = crate::locale::default_collation()?;
    Some(
        colligo::Collator::builder(&tag)
            .allow_approximate(true)
            .build()
            .unwrap_or_else(|_| colligo::Collator::root()),
    )
}

#[cfg(not(feature = "colligo"))]
fn default_collator() -> Option<NeverCollator> {
    None
}

/// Keyed aggregates reorder or filter the capsae themselves (nodes
/// and registers preserved), keyed by per-capsa value expressions.
/// They are evaluated in the executor, which has the adapter at
/// hand; this module only names them.
const KEYED: &[&str] = &[
    "sort_by",
    "unique_by",
    "min_by",
    "max_by",
    "top",
    "bottom",
    "group",
];

/// The collator for a `sort(LOCALE)` call, where one was given
/// (the parser validated the tag's shape; root on surprise — a
/// tag colligo's registry doesn't know or support still sorts,
/// under the untailored base table). Approximate-tier locales
/// are accepted: a query sort wants a reasonable total order,
/// not certified fidelity.
#[cfg(feature = "colligo")]
pub(crate) fn collator_for(call: &FnCall) -> Option<colligo::Collator> {
    // The locale is the literal argument that is not the mode word.
    let tag = call.args.iter().find_map(|a| match a {
        Arg::Lit(Value::Str(s)) if s == "atergo" => None,
        Arg::Lit(l) => Some(l.to_string()),
        _ => None,
    })?;
    Some(
        colligo::Collator::builder(&tag)
            .allow_approximate(true)
            .build()
            .unwrap_or_else(|_| colligo::Collator::root()),
    )
}

/// Collation compiled out (`colligo` feature off): never a
/// collator, so both `sort(LOCALE)` call sites fall back to the
/// standard value comparison (codepoint order for text). The
/// uninhabited stub keeps the call sites feature-agnostic.
#[cfg(not(feature = "colligo"))]
pub(crate) struct NeverCollator(std::convert::Infallible);

#[cfg(not(feature = "colligo"))]
impl NeverCollator {
    pub(crate) fn compare(&self, _a: &str, _b: &str) -> Ordering {
        match self.0 {}
    }
    pub(crate) fn compare_reverse(&self, _a: &str, _b: &str) -> Ordering {
        match self.0 {}
    }
}

#[cfg(not(feature = "colligo"))]
pub(crate) fn collator_for(_call: &FnCall) -> Option<NeverCollator> {
    None
}

/// Whether `name` is a keyed aggregate (for `@|`).
pub fn known_keyed(name: &str) -> bool {
    KEYED.contains(&name)
}

/// Whether `name` is a per-capsa scalar function (for `|`).
pub fn known_scalar(name: &str) -> bool {
    SCALAR.contains(&name)
}

/// Whether `name` is an aggregate function (for `@|`).
pub fn known_agg(name: &str) -> bool {
    AGGREGATE.contains(&name) || known_keyed(name)
}

/// The scalar registry, for enumerating consumers (completion,
/// highlighting): every per-capsa `|` function.
pub fn scalar_names() -> &'static [&'static str] {
    SCALAR
}

/// The aggregate registry: every `@|` reducer (keyed aggregates
/// are enumerated separately by [`keyed_names`]).
pub fn aggregate_names() -> &'static [&'static str] {
    AGGREGATE
}

/// The keyed-aggregate registry: `sort_by`, `group`, and friends.
pub fn keyed_names() -> &'static [&'static str] {
    KEYED
}

/// The locale argument of `strptime` / `strftime`: the table for
/// the second argument, English without one; a locale no table
/// covers is refused.
fn date_names(call: &FnCall) -> Option<&'static crate::datenames::Names> {
    let locale = arg_str(call, 1, "");
    match crate::datenames::names(locale) {
        Some(n) => Some(n),
        None => {
            crate::exec::record_refusal(format!(
                "{}: no month and weekday names for locale {locale:?} (shipped: en, zh, es, ar, pt, ru, ja, de, fr, tr, it)",
                call.name
            ));
            None
        }
    }
}

/// The value text of a time expression: a `timex` record's `value`
/// field, text in the value notation as it stands, or anything
/// else with a calendar reading as its period (a complete date).
pub(crate) fn timex_value(v: &Value) -> Option<String> {
    match v {
        Value::Record(fields) => match fields.iter().find(|(k, _)| k == "value") {
            Some((_, Value::Str(s))) => Some(s.clone()),
            Some((_, other)) => other.calendar_reading().map(|p| p.format()),
            None => None,
        },
        Value::Str(s) => Some(s.clone()),
        other => other.calendar_reading().map(|p| p.format()),
    }
}

/// A whole double as an integer where one holds it, else as it is
/// (the cast would saturate at the rim of the integers).
fn whole(n: f64) -> Value {
    if n.abs() < 9.2e18 {
        Value::Int(n as i64)
    } else {
        Value::Float(n)
    }
}

/// The delimiter `csv(";"; …)` names, if it names one, and the
/// arguments after it (the columns). The parser carries the quoted
/// first argument of `csv` as `delimiter=X`; `table` takes none.
pub(crate) fn split_csv_delimiter(call: &FnCall) -> (Option<u8>, &[Arg]) {
    if call.name == "csv"
        && let Some((Arg::Lit(Value::Str(d)), rest)) = call.args.split_first()
        && let Some(d) = d.strip_prefix("delimiter=")
    {
        return (d.as_bytes().first().copied(), rest);
    }
    (None, call.args.as_slice())
}

/// Apply a per-capsa scalar function to a single topic. May return
/// several values (an expanding function like `lines`).
pub fn apply_scalar(
    call: &FnCall,
    topic: Value,
    scale: &dyn Fn(&str) -> Option<(f64, String)>,
) -> Vec<Value> {
    let text = topic.to_string();
    match call.name.as_str() {
        // `number(LOCALE)` — the numeric reading of text under the
        // locale's conventions (`number(ru-RU)` reads `1 234,56`,
        // `number(de-CH)` reads `1'234.56`); a number stays itself;
        // text with no reading, or a locale with no table, is null.
        "number" => {
            let locale = arg_str(call, 0, "");
            let decimal = if locale.is_empty() {
                Some(crate::number::Decimal::Point)
            } else {
                crate::number::locale_convention(locale)
            };
            if decimal.is_none() {
                crate::exec::record_refusal(format!(
                    "number: no number conventions for locale {locale:?}"
                ));
                return vec![Value::Null];
            }
            return vec![match (&topic, decimal) {
                (Value::Int(_) | Value::Float(_), _) => topic.clone(),
                (Value::Str(s), Some(d)) => crate::number::read(s, d).unwrap_or(Value::Null),
                _ => Value::Null,
            }];
        }
        // `timex(LOCALE)` — the time expressions of a text, one
        // record each in the order of the text: `%(text; at; kind;
        // value; grain)`. Found by the locale's finite lists and
        // nothing else; a locale that carries none is refused. A
        // text with no time expression yields nothing.
        "timex" => {
            let locale = arg_str(call, 0, "en");
            if matches!(topic, Value::Null) {
                return Vec::new();
            }
            let Some(found) = crate::timex::find(&text, locale) else {
                crate::exec::record_refusal(format!(
                    "timex: no time-expression lists for locale {locale:?} (carried: {})",
                    crate::timex::CARRIED
                ));
                return Vec::new();
            };
            let opt = |s: Option<String>| s.map_or(Value::Null, Value::Str);
            return found
                .into_iter()
                .map(|f| {
                    Value::Record(vec![
                        ("text".to_string(), Value::Str(f.text)),
                        ("at".to_string(), Value::Int(f.at as i64)),
                        ("kind".to_string(), Value::Str(f.kind.word().to_string())),
                        ("value".to_string(), opt(f.value)),
                        (
                            "grain".to_string(),
                            opt(f.grain.map(|g| g.word().to_string())),
                        ),
                    ])
                })
                .collect();
        }
        // `time_anchor(T)` — a time expression valued against a
        // point: the topic is a `timex` record or its value text,
        // `T` anything with a calendar reading, the result a
        // period. A complete date passes through; a duration, a
        // vague expression, and an offset the anchor's grain cannot
        // carry are null.
        "time_anchor" => {
            let anchor = match call.args.first() {
                Some(Arg::Lit(v)) => v.calendar_reading(),
                _ => {
                    crate::exec::record_refusal(
                        "time_anchor takes the anchor — time_anchor(1899-10-06), \
                         time_anchor($.d)"
                            .into(),
                    );
                    return vec![Value::Null];
                }
            };
            return vec![
                timex_value(&topic)
                    .and_then(|v| crate::period::anchor(&v, anchor.as_ref(), false))
                    .map_or(Value::Null, Value::period),
            ];
        }
        // `period[(GRAIN)]` — the calendar reading as a period; with
        // a grain, the period of that grain holding the value (a
        // finer grain than the value's own is null).
        "period" => {
            let reading = topic.calendar_reading();
            return vec![match (reading, call.args.first()) {
                (None, _) => Value::Null,
                (Some(p), None) => Value::period(p),
                (Some(p), Some(Arg::Lit(Value::Str(g)))) => {
                    match crate::period::Grain::from_word(g) {
                        Some(g) => p.at(g).map_or(Value::Null, Value::period),
                        None => {
                            crate::exec::record_refusal(format!(
                                "period: {g:?} is not a grain (year, month, day, hour, minute, second)"
                            ));
                            Value::Null
                        }
                    }
                }
                _ => Value::Null,
            }];
        }
        // `grain` — a period's grain as its word.
        "grain" => {
            return vec![match &topic {
                Value::Period { grain, .. } => Value::Str(grain.word().to_string()),
                _ => Value::Null,
            }];
        }
        "upper" => vec![Value::Str(text.to_uppercase())],
        "lower" => vec![Value::Str(text.to_lowercase())],
        // Title case, Python-shaped: each word's first alphabetic
        // character uppercases, the rest of the word lowercases.
        "title" => {
            let mut out = String::with_capacity(text.len());
            let mut boundary = true;
            for c in text.chars() {
                if c.is_alphabetic() {
                    if boundary {
                        out.extend(c.to_uppercase());
                        boundary = false;
                    } else {
                        out.extend(c.to_lowercase());
                    }
                } else {
                    out.push(c);
                    boundary = true;
                }
            }
            vec![Value::Str(out)]
        }
        "trim" => vec![Value::Str(text.trim().to_string())],
        "ltrim" => vec![Value::Str(text.trim_start().to_string())],
        "rtrim" => vec![Value::Str(text.trim_end().to_string())],
        // `cc` counts codepoints (né `chars`, the pre-0.25 alias);
        // `bc` counts UTF-8 bytes; `wc` counts words.
        "cc" => vec![Value::Int(text.chars().count() as i64)],
        // `gc` counts grapheme clusters (UAX #29): what the eye
        // counts — a stressed vowel with its acute is one.
        "gc" => vec![Value::Int(text.graphemes(true).count() as i64)],
        "bc" => vec![Value::Int(text.len() as i64)],
        "wc" => vec![Value::Int(text.split_whitespace().count() as i64)],
        "lc" => vec![Value::Int(text.lines().count() as i64)],
        // UAX #29 sentence segmentation (unicode-segmentation):
        // `sentences` splits (each segment trimmed, empties
        // dropped), `sc` counts the same segments.
        "sentences" => sentences_of(&text)
            .into_iter()
            .map(|t| Value::Str(t.to_string()))
            .collect(),
        "sc" => {
            vec![Value::Int(sentences_of(&text).len() as i64)]
        }
        // `substr(a..b)` — the range predicate's spellings, on
        // characters: `substr(1..3)`, `substr(..3)`, `substr(2..)`,
        // `substr(..-3)`, `substr(4..-4)`; a bare position
        // (`substr(3)`) is the `[n]` reading, one character.
        // 1-based like its ancestors (SQL SUBSTR, XPath
        // substring, awk/Perl substr).
        // 1-based, inclusive, negative counts from the end;
        // out-of-range clamps, a crossed range is the empty
        // string, and 0 refuses — it is no position.
        "substr" => {
            let (a, b) = match call.args.first() {
                Some(Arg::Range(a, b)) => (*a, *b),
                Some(Arg::Lit(Value::Int(i))) => (Some(*i), Some(*i)),
                _ => {
                    crate::exec::record_refusal(
                        "substr takes a range — substr(1..3), substr(..3), \
                         substr(2..), substr(-2..) — or one position"
                            .into(),
                    );
                    return vec![Value::Null];
                }
            };
            if a == Some(0) || b == Some(0) {
                crate::exec::record_refusal(
                    "substr(0): positions are 1-based — 1 is the first \
                     character, -1 the last"
                        .into(),
                );
                return vec![Value::Null];
            }
            let n = text.chars().count() as i64;
            let pos = |i: i64| -> i64 { if i < 0 { n + i + 1 } else { i } };
            let from = pos(a.unwrap_or(1)).max(1);
            let to = pos(b.unwrap_or(-1)).min(n);
            if from > to {
                vec![Value::Str(String::new())]
            } else {
                vec![Value::Str(
                    text.chars()
                        .skip(from as usize - 1)
                        .take((to - from + 1) as usize)
                        .collect(),
                )]
            }
        }
        // `pad(n)` centers to n characters (the extra character
        // of an odd split falls right, as Python's center);
        // `lpad(n)` / `rpad(n)` pad one side. Spaces by default
        // (`lpad(n, "0")` with the given text, repeated and cut
        // to fit, SQL-shaped); text already n or longer passes
        // through untouched.
        // Widths count grapheme clusters, so a column of stressed
        // words aligns: замо́к is five cells, not six.
        "pad" => {
            let n = arg_int(call, 0).unwrap_or(0).max(0) as usize;
            let fill = arg_str(call, 1, " ");
            let have = text.graphemes(true).count();
            if have >= n || fill.is_empty() {
                vec![Value::Str(text.clone())]
            } else {
                let left = (n - have) / 2;
                let right = n - have - left;
                let l: String = fill.chars().cycle().take(left).collect();
                let r: String = fill.chars().cycle().take(right).collect();
                vec![Value::Str(format!("{l}{text}{r}"))]
            }
        }
        "lpad" | "rpad" => {
            let n = arg_int(call, 0).unwrap_or(0).max(0) as usize;
            let fill = arg_str(call, 1, " ");
            let have = text.graphemes(true).count();
            if have >= n || fill.is_empty() {
                vec![Value::Str(text.clone())]
            } else {
                let pad: String = fill.chars().cycle().take(n - have).collect();
                vec![Value::Str(if call.name == "lpad" {
                    format!("{pad}{text}")
                } else {
                    format!("{text}{pad}")
                })]
            }
        }
        // `repeat(n)` — the text n times (0 is the empty string).
        // Repetition lives here alone: `"a" * 3` stays
        // null-propagating arithmetic.
        "repeat" => {
            let n = arg_int(call, 0).unwrap_or(0).max(0) as usize;
            vec![bounded_repeat(&text, n, "repeat")]
        }
        // `indent(n)` / `indent(n; unit)` — the text behind n copies
        // of the unit (two spaces by default): the level of a tree
        // listing made visible. A null or negative n indents by
        // nothing.
        "indent" => {
            let n = arg_num(call, 0).map_or(0, |f| f as i64).max(0) as usize;
            let unit = arg_str(call, 1, "  ");
            vec![match bounded_repeat(&unit, n, "indent") {
                Value::Str(pad) => Value::Str(format!("{pad}{text}")),
                v => v,
            }]
        }
        "lines" => text.lines().map(|s| Value::Str(s.to_string())).collect(),
        // The character classes — POSIX's alpha / digit / alnum,
        // Rust's `is_alphabetic` / `is_numeric` / `is_alphanumeric`
        // (Unicode: \p{L}, \p{N}, both): keep the class, turn every
        // other character into a space, so `| words` then spreads
        // the kept runs. One optional argument names extra
        // characters to keep — `alpha("’")` for apostrophes,
        // `digit(".,-")` for decimals and signs. Classes, not
        // parsers: `digit` never reads the string it keeps.
        "alpha" | "digit" | "alnum" => {
            let keep = arg_str(call, 0, "");
            let class: fn(char) -> bool = match call.name.as_str() {
                "alpha" => char::is_alphabetic,
                "digit" => char::is_numeric,
                _ => char::is_alphanumeric,
            };
            vec![Value::Str(
                text.chars()
                    .map(|c| if class(c) || keep.contains(c) { c } else { ' ' })
                    .collect(),
            )]
        }
        "words" => text
            .split_whitespace()
            .map(|s| Value::Str(s.to_string()))
            .collect(),
        // `ngrams(n)` — the n-word windows of the text (whitespace
        // words, as `words` splits them), each joined by one space,
        // one value per window; `ngrams(2)` the bigrams. A text
        // shorter than n yields nothing. Windows stay inside the
        // value they came from, so over a paragraph spread no
        // window straddles two paragraphs.
        "ngrams" => {
            let n = arg_int(call, 0).unwrap_or(2).max(1) as usize;
            let ws: Vec<&str> = text.split_whitespace().collect();
            ws.windows(n).map(|w| Value::Str(w.join(" "))).collect()
        }
        // `haversine(lat1; lon1; lat2; lon2)` — the great-circle
        // distance between two points in kilometres (a sphere of
        // 6371 km), for a gazetteer's coordinates. A missing
        // coordinate gives null.
        "haversine" => {
            // the call form puts the first latitude in topic position
            let (lat1, from) = if call.args.len() >= 4 {
                (arg_num(call, 0), 1)
            } else {
                (topic.numeric(), 0)
            };
            let (Some(lat1), Some(lon1), Some(lat2), Some(lon2)) = (
                lat1,
                arg_num(call, from),
                arg_num(call, from + 1),
                arg_num(call, from + 2),
            ) else {
                return vec![Value::Null];
            };
            let (p1, p2) = (lat1.to_radians(), lat2.to_radians());
            let (dp, dl) = ((lat2 - lat1).to_radians(), (lon2 - lon1).to_radians());
            let a = (dp / 2.0).sin().powi(2) + p1.cos() * p2.cos() * (dl / 2.0).sin().powi(2);
            vec![Value::Float(2.0 * 6371.0 * a.sqrt().asin())]
        }
        // `levenshtein(other)` — the edit distance between the
        // topic's text and the argument's, in codepoints (insert,
        // delete, substitute, each 1). A null argument gives null.
        "levenshtein" => {
            let other = match call.args.first() {
                Some(Arg::Lit(Value::Null)) => return vec![Value::Null],
                Some(Arg::Lit(v)) => v.to_string(),
                _ => {
                    crate::exec::record_refusal(
                        "levenshtein takes the other text — levenshtein(\"word\"), \
                         levenshtein(::name)"
                            .into(),
                    );
                    return vec![Value::Null];
                }
            };
            vec![Value::Int(levenshtein(&text, &other) as i64)]
        }
        // Unicode normalization (UAX #15): `nfc` composes, `nfd`
        // decomposes. A stress mark is a combining acute (U+0301)
        // after its vowel and no Cyrillic vowel has a precomposed
        // acute form, so a stressed Russian word keeps its two code
        // points under either form.
        "nfc" | "nfd" => {
            if matches!(topic, Value::Null) {
                return vec![Value::Null];
            }
            let out: String = if call.name == "nfc" {
                text.nfc().collect()
            } else {
                text.nfd().collect()
            };
            vec![Value::Str(out)]
        }
        // `vowels` counts the vowel letters of the composed text —
        // Cyrillic and Latin, case-folded; an optional argument
        // names the alphabet (`vowels("аеиоу")`).
        "vowels" => {
            if matches!(topic, Value::Null) {
                return vec![Value::Null];
            }
            let alphabet = arg_str(call, 0, DEFAULT_VOWELS);
            let n = text.nfc().filter(|c| is_vowel(*c, alphabet)).count();
            vec![Value::Int(n as i64)]
        }
        // `stress(n)` places the combining acute (U+0301) after the
        // n-th vowel of the composed text — 1-based, negative from
        // the end (`substr`'s convention). A word with fewer vowels
        // has no such position and gives null; 0 refuses. A vowel
        // already marked stays as it is, and ё, which carries its
        // stress in the letter, counts as a vowel but is never
        // marked. `stress(n; "аеиоу")` names the vowel alphabet.
        "stress" => {
            let n = match call.args.first() {
                Some(Arg::Lit(v)) => v.numeric().map(|f| f as i64),
                _ => None,
            };
            let Some(n) = n.filter(|n| *n != 0) else {
                crate::exec::record_refusal(
                    "stress takes a vowel position — stress(3), stress(-1); \
                     positions are 1-based, negative from the end"
                        .into(),
                );
                return vec![Value::Null];
            };
            if matches!(topic, Value::Null) {
                return vec![Value::Null];
            }
            let alphabet = arg_str(call, 1, DEFAULT_VOWELS);
            let chars: Vec<char> = text.nfc().collect();
            let vowels: Vec<usize> = chars
                .iter()
                .enumerate()
                .filter(|(_, c)| is_vowel(**c, alphabet))
                .map(|(i, _)| i)
                .collect();
            let k = if n < 0 {
                vowels.len() as i64 + n
            } else {
                n - 1
            };
            if k < 0 || k as usize >= vowels.len() {
                return vec![Value::Null];
            }
            let at = vowels[k as usize];
            let mut out = String::with_capacity(text.len() + 2);
            for (i, c) in chars.iter().enumerate() {
                out.push(*c);
                if i == at && !matches!(c, 'ё' | 'Ё') && chars.get(i + 1) != Some(&'\u{301}') {
                    out.push('\u{301}');
                }
            }
            vec![Value::Str(out)]
        }
        // `stress_at` — the ordinal of the stressed vowel in a marked
        // form: the vowel before the acute, else a ё, else the one
        // vowel of a monosyllable; null when nothing decides.
        "stress_at" => {
            if matches!(topic, Value::Null) {
                return vec![Value::Null];
            }
            let alphabet = arg_str(call, 0, DEFAULT_VOWELS);
            match stress_at(&text, alphabet) {
                Some(n) => vec![Value::Int(n as i64)],
                None => vec![Value::Null],
            }
        }
        // `unstress` — the form with its stress marks removed (the
        // acute and the grave); ё stays, being a letter.
        "unstress" => {
            if matches!(topic, Value::Null) {
                return vec![Value::Null];
            }
            vec![Value::Str(
                text.nfc()
                    .filter(|c| !matches!(c, '\u{301}' | '\u{300}'))
                    .collect(),
            )]
        }
        // `accent(style)` — a marked form in a display convention:
        // "acute" (the mark, as is), "upper" (the stressed vowel in
        // capitals: замОк), "apostrophe" (an apostrophe after it:
        // замо'к), "none" (unmarked). ё is left as the letter it is.
        "accent" => {
            if matches!(topic, Value::Null) {
                return vec![Value::Null];
            }
            let style = arg_str(call, 0, "acute");
            let alphabet = arg_str(call, 1, DEFAULT_VOWELS);
            let chars: Vec<char> = text.nfc().collect();
            let bare: String = chars
                .iter()
                .filter(|c| !matches!(c, '\u{301}' | '\u{300}'))
                .collect();
            let Some(n) = stress_at(&text, alphabet) else {
                return vec![Value::Str(bare)];
            };
            let bare_chars: Vec<char> = bare.chars().collect();
            let at = bare_chars
                .iter()
                .enumerate()
                .filter(|(_, c)| is_vowel(**c, alphabet))
                .nth(n - 1)
                .map(|(i, _)| i);
            let Some(at) = at else {
                return vec![Value::Str(bare)];
            };
            let is_yo = matches!(bare_chars[at], 'ё' | 'Ё');
            let mut out = String::with_capacity(bare.len() + 2);
            for (i, c) in bare_chars.iter().enumerate() {
                match style {
                    "upper" if i == at => out.extend(c.to_uppercase()),
                    "apostrophe" if i == at => {
                        out.push(*c);
                        if !is_yo {
                            out.push('\'');
                        }
                    }
                    "acute" if i == at => {
                        out.push(*c);
                        if !is_yo {
                            out.push('\u{301}');
                        }
                    }
                    "none" | "upper" | "apostrophe" | "acute" => out.push(*c),
                    other => {
                        crate::exec::record_refusal(format!(
                            "accent takes a style — accent(\"acute\"), accent(\"upper\"), \
                             accent(\"apostrophe\"), accent(\"none\") — not '{other}'"
                        ));
                        return vec![Value::Null];
                    }
                }
            }
            vec![Value::Str(out)]
        }
        // `translit(scheme)` — the text in Latin letters under an ISO
        // transliteration scheme; no argument picks each script's own
        // ISO scheme; for Russian the systems in use beside ISO 9
        // answer to their own names: gost/гост, scientific/научная,
        // bgn/бгн, passport/паспорт.
        "translit" => {
            if matches!(topic, Value::Null) {
                return vec![Value::Null];
            }
            let scheme = arg_str(call, 0, "");
            match crate::translit::translit(&text, scheme) {
                Ok(s) => vec![Value::Str(s)],
                Err(e) => {
                    crate::exec::record_refusal(e);
                    vec![Value::Null]
                }
            }
        }
        // `modernize(table)` — a historical spelling folded to the
        // modern one, letter by letter, case kept: `ru-1918` (the
        // pre-reform Russian alphabet, the final ъ dropped) and
        // `long-s` (the long s and the typographic ligatures).
        "modernize" => {
            if matches!(topic, Value::Null) {
                return vec![Value::Null];
            }
            let table = arg_str(call, 0, "");
            match crate::translit::modernize(&text, table) {
                Ok(s) => vec![Value::Str(s)],
                Err(e) => {
                    crate::exec::record_refusal(e);
                    vec![Value::Null]
                }
            }
        }
        "split" => {
            let sep = arg_str(call, 0, ",");
            text.split(sep).map(|s| Value::Str(s.to_string())).collect()
        }

        // Hashing and encodings (RFC 4648; SHA-256 per FIPS
        // 180-4), over the topic's text bytes.
        "sha256" => vec![Value::Str(crate::encoding::sha256_hex(text.as_bytes()))],
        "base64" => vec![Value::Str(crate::encoding::base64(text.as_bytes()))],
        "base64url" => vec![Value::Str(crate::encoding::base64url(text.as_bytes()))],
        "base32" => vec![Value::Str(crate::encoding::base32(text.as_bytes()))],
        "crockford32" => vec![Value::Str(crate::encoding::crockford32(text.as_bytes()))],
        // `decode(SCHEME)` (alias `dec`) inverts the reversible
        // encodings: the parser validated the scheme, so a bad one
        // is unreachable here. Malformed input or bytes that are
        // not UTF-8 become null (propagating — strings are text).
        "decode" | "dec" => {
            let scheme = arg_str(call, 0, "");
            // Structured formats parse to a value (record/list/
            // scalar); the byte encodings decode to text. Malformed
            // input, or non-UTF-8 bytes, become null.
            vec![match scheme {
                "json" => crate::encoding::json_to_value(&text).unwrap_or(Value::Null),
                "yaml" => crate::encoding::yaml_to_value(&text).unwrap_or(Value::Null),
                "toml" => crate::encoding::toml_to_value(&text).unwrap_or(Value::Null),
                "xml" => crate::encoding::xml_to_value(&text).unwrap_or(Value::Null),
                _ => crate::encoding::decode(scheme, &text)
                    .and_then(|b| String::from_utf8(b).ok())
                    .map(Value::Str)
                    .unwrap_or(Value::Null),
            }]
        }
        "hex" => vec![Value::Str(crate::encoding::hex(text.as_bytes()))],

        // Temporal scalars (spec: The Temporal Fragment). All are
        // defined via the temporal reading, so they serve typed
        // instants, epoch integers, and ISO text alike; no reading
        // means null.
        "datetime" => vec![match &topic {
            Value::Instant { .. } => topic.clone(),
            Value::Str(s) => crate::temporal::parse_iso(s)
                .map(|(secs, nanos, offset_min)| Value::Instant {
                    secs,
                    nanos,
                    offset_min,
                })
                .unwrap_or(Value::Null),
            other => other
                .temporal_reading()
                .map(|(secs, nanos)| Value::Instant {
                    secs,
                    nanos,
                    offset_min: None,
                })
                .unwrap_or(Value::Null),
        }],
        "epoch" => vec![
            topic
                .temporal_reading()
                .map(|(secs, _)| Value::Int(secs))
                .unwrap_or(Value::Null),
        ],
        // `isoformat` is the reading, formatted UTC (spec: The
        // Temporal Fragment) — a typed instant renders in UTC, not
        // its written display offset, so it agrees with the text and
        // epoch paths rather than short-circuiting to Display.
        "isoformat" => vec![
            topic
                .temporal_reading()
                .map(|(s, n)| Value::Str(crate::temporal::format_instant(s, n, None)))
                .unwrap_or(Value::Null),
        ],
        "year" | "month" | "day" | "hour" | "minute" | "second" => {
            vec![
                topic
                    .temporal_reading()
                    .map(|(secs, _)| {
                        let (y, mo, d, h, mi, se) = crate::temporal::components(secs);
                        Value::Int(match call.name.as_str() {
                            "year" => y,
                            "month" => mo as i64,
                            "day" => d as i64,
                            "hour" => h as i64,
                            "minute" => mi as i64,
                            _ => se as i64,
                        })
                    })
                    .unwrap_or(Value::Null),
            ]
        }
        "isodate" | "isomonth" | "isoweek" => vec![
            topic
                .temporal_reading()
                .map(|(secs, _)| {
                    let (y, mo, d, ..) = crate::temporal::components(secs);
                    Value::Str(match call.name.as_str() {
                        "isodate" => format!("{y:04}-{mo:02}-{d:02}"),
                        "isomonth" => format!("{y:04}-{mo:02}"),
                        _ => {
                            let (gy, gw) = crate::temporal::iso_week(secs);
                            format!("{gy:04}-W{gw:02}")
                        }
                    })
                })
                .unwrap_or(Value::Null),
        ],
        // `strftime("%Y-%m-%d %H:%M")` (alias `tfmt`) — the
        // C/POSIX formatting standard Perl, Python, and Ruby
        // share, in the instant's own offset.
        // `strftime(fmt[; LOCALE])` — a second argument names the
        // locale whose month and weekday names `%B %b %A %a` write;
        // without it the English names. A locale with no table
        // refuses.
        "strftime" | "tfmt" => {
            let fmt = arg_str(call, 0, "%Y-%m-%dT%H:%M:%S").to_string();
            let Some(names) = date_names(call) else {
                return vec![Value::Null];
            };
            vec![match &topic {
                Value::Instant {
                    secs,
                    nanos,
                    offset_min,
                } => Value::Str(crate::temporal::strftime_in(
                    &fmt,
                    *secs,
                    *nanos,
                    *offset_min,
                    names,
                )),
                other => other
                    .temporal_reading()
                    .map(|(s, n)| Value::Str(crate::temporal::strftime_in(&fmt, s, n, None, names)))
                    .unwrap_or(Value::Null),
            }]
        }
        "weekday" => vec![
            topic
                .temporal_reading()
                .map(|(secs, _)| Value::Int(crate::temporal::weekday(secs) as i64))
                .unwrap_or(Value::Null),
        ],
        "date" => vec![
            topic
                .temporal_reading()
                .map(|(secs, _)| Value::Instant {
                    secs: secs.div_euclid(86400) * 86400,
                    nanos: 0,
                    offset_min: None,
                })
                .unwrap_or(Value::Null),
        ],
        // The unit words: a numeric topic scales the unit into a
        // duration (`30 | days` = P30D); a duration topic reads in
        // the unit (`P342D | days` = 342, `P1DT12H | days` = 1.5) —
        // the constructor's inverse, decided by the topic's type.
        "seconds" | "minutes" | "hours" | "days" => {
            let unit: f64 = match call.name.as_str() {
                "seconds" => 1.0,
                "minutes" => 60.0,
                "hours" => 3600.0,
                _ => 86400.0,
            };
            if let Value::Duration { secs, nanos } = topic {
                let n = (secs as f64 + nanos as f64 / 1e9) / unit;
                return vec![if n.fract() == 0.0 && n.abs() < 1e15 {
                    Value::Int(n as i64)
                } else {
                    Value::Float(n)
                }];
            }
            vec![
                topic
                    .numeric()
                    .map(|n| {
                        let total = n * unit;
                        Value::Duration {
                            secs: total.floor() as i64,
                            nanos: ((total - total.floor()) * 1e9) as u32,
                        }
                    })
                    .unwrap_or(Value::Null),
            ]
        }

        // `duration` (alias `td`) — the span parser, defined via the
        // durational reading: span text (`5d3h5min`, `P5DT3H5M`) or
        // a number (seconds) to a duration, a duration passing
        // through. The untyped substrate's explicit opt-in, exactly
        // as `| datetime` is for instants.
        "duration" | "td" => vec![
            topic
                .durational_reading()
                .or_else(|| match &topic {
                    // The mounted unit table's time units read too
                    // (`5rep`), builtin span text having had first
                    // claim — same order as comparisons.
                    Value::Str(s) => crate::temporal::span_from_units(s, scale),
                    _ => None,
                })
                .map(|(secs, nanos)| Value::Duration { secs, nanos })
                .unwrap_or(Value::Null),
        ],
        // `strptime(fmt)` (alias `tp`) — strftime's inverse: a TEXT
        // topic parsed per the same C/POSIX specifiers with the same
        // fixed English names. A parsed %z is kept for display;
        // fields the format omits default to the Unix epoch's;
        // non-text topics and non-matching text are null.
        // `strptime(fmt[; LOCALE])` — the names read under the
        // locale's table, in every form it lists; the format's
        // literal text matches as written (`'%d %B %Y г.'`).
        "strptime" | "tp" => {
            let fmt = arg_str(call, 0, "%Y-%m-%dT%H:%M:%S").to_string();
            let Some(names) = date_names(call) else {
                return vec![Value::Null];
            };
            vec![match &topic {
                Value::Str(s) => crate::temporal::strptime_in(s, &fmt, names)
                    .map(|(secs, nanos, offset_min)| Value::Instant {
                        secs,
                        nanos,
                        offset_min,
                    })
                    .unwrap_or(Value::Null),
                _ => Value::Null,
            }]
        }

        // `bibref(STANDARD)` — one reference text read under a
        // citation standard (gost, gb7714, cmos, ams) into a record
        // of its fields, `:genus` and the list `:label`; a text
        // that is no reference answers null, as `strptime` does for
        // a text that is no date; an unknown standard is refused
        // naming the ones this build reads.
        "bibref" => {
            let standard = arg_str(call, 0, "").to_string();
            if !crate::bibref::STANDARDS.contains(&standard.as_str()) {
                crate::exec::record_refusal(format!(
                    "bibref: unknown standard {standard:?} — this build reads {}",
                    crate::bibref::STANDARDS.join(", ")
                ));
                return vec![Value::Null];
            }
            vec![match &topic {
                Value::Str(s) => match crate::bibref::parse(&standard, s) {
                    Ok(Some(r)) => {
                        let mut rec: Vec<(String, Value)> = r
                            .fields
                            .iter()
                            .map(|(k, v)| (k.to_string(), Value::Str(v.clone())))
                            .collect();
                        if let Some(g) = r.genus {
                            rec.push(("genus".into(), Value::Str(g.into())));
                        }
                        if let Some(l) = r.label {
                            rec.push(("label".into(), Value::Str(l)));
                        }
                        Value::Record(rec)
                    }
                    _ => Value::Null,
                },
                _ => Value::Null,
            }]
        }

        // `quantity` — the unit-text parser, defined via the unital
        // reading: `5km` / `0.2 kW` to a quantity, a quantity
        // passing through, no reading null. The untyped substrate's
        // explicit opt-in, as `| datetime` and `| duration` are for
        // their fragments.
        "quantity" => vec![match &topic {
            Value::Quantity { .. } => topic.clone(),
            Value::Str(s) => crate::quantity::parse_unit_text_with(s, scale)
                .map(|(value, base, wv, wu)| Value::Quantity {
                    value,
                    base,
                    written: Some((wv, wu)),
                })
                .unwrap_or(Value::Null),
            _ => Value::Null,
        }],
        // `convert(unit)` — explicit unit conversion: a quantity
        // re-expressed in a compatible unit (the base magnitude is
        // untouched; only the written display form changes). A
        // dimension mismatch or a non-quantity topic is null —
        // this is also the sanctioned road where arithmetic
        // refuses to guess (numbers never lift into ±). Unit-shaped
        // TEXT lifts through the unital reading first: invoking
        // convert by name is explicit intent, so `2KiB |
        // convert(B)` needs no separate `| quantity` (the expression head's
        // author-spelling scope).
        "convert" => {
            let target = arg_str(call, 0, "").to_string();
            let lifted;
            let topic = match &topic {
                Value::Str(s) => match crate::quantity::parse_unit_text_with(s, scale) {
                    Some((value, base, wv, wu)) => {
                        lifted = Value::Quantity {
                            value,
                            base,
                            written: Some((wv, wu)),
                        };
                        &lifted
                    }
                    None => &topic,
                },
                t => t,
            };
            vec![match &topic {
                Value::Quantity { value, base, .. } => match scale(&target) {
                    Some((factor, tbase)) if &tbase == base => Value::Quantity {
                        value: *value,
                        base: base.clone(),
                        written: Some((*value / factor, target)),
                    },
                    _ => Value::Null,
                },
                _ => Value::Null,
            }]
        }

        // Numeric scalars: a non-numeric topic becomes Null. A
        // QUANTITY rounds in its display unit and stays a quantity
        // — `(::speed | convert('km/h')) | round` is a whole
        // number of km/h, not of base meters-per-second.
        "round" | "floor" | "ceil" if matches!(topic, Value::Quantity { .. }) => {
            let Value::Quantity {
                value,
                base,
                written,
            } = &topic
            else {
                unreachable!()
            };
            let (wv, wu) = written.clone().unwrap_or_else(|| (*value, base.clone()));
            let rounded = match call.name.as_str() {
                "round" => match round_digits(call) {
                    Some(d) => round_to(wv, d),
                    None => wv.round(),
                },
                "floor" => wv.floor(),
                _ => wv.ceil(),
            };
            let factor = scale(&wu).map(|(f, _)| f).unwrap_or(1.0);
            vec![Value::Quantity {
                value: rounded * factor,
                base: base.clone(),
                written: Some((rounded, wu)),
            }]
        }
        // Bare `round` reads to an integer; `round(d)` keeps `d`
        // decimal places and stays a float (`round(0)` included —
        // the argument form always answers in the topic's float
        // world, the bare form in the integer one). Serialization
        // stays shortest-round-trip — `round(d)` is the in-query
        // remedy for presenting arithmetic like 68.99000000000001.
        // (a whole number past the integers stays a float: the
        // cast would saturate at i64::MAX)
        "round" => vec![numeric_scalar(&topic, |n| match round_digits(call) {
            Some(d) => Value::Float(round_to(n, d)),
            None => whole(n.round()),
        })],
        "floor" => vec![numeric_scalar(&topic, |n| whole(n.floor()))],
        "ceil" => vec![numeric_scalar(&topic, |n| whole(n.ceil()))],
        "abs" => vec![match topic {
            // (`i64::MIN` has no integer absolute value)
            Value::Int(n) => n
                .checked_abs()
                .map_or(Value::Float(-(n as f64)), Value::Int),
            // A quantity has no numeric reading and only the rounders
            // are quantity-aware (spec: The Quantital Fragment), so
            // `abs` over a quantity is null rather than silently
            // dropping its unit to a bare base-magnitude float.
            Value::Quantity { .. } => Value::Null,
            other => numeric_scalar(&other, |n| Value::Float(n.abs())),
        }],
        // The elementary functions over the numeric reading: an
        // undefined value (a logarithm of a non-positive, a root of
        // a negative, an overflow) is null. `log(base)` takes a base;
        // a quantity has no numeric reading here, as for `abs`.
        "log" | "log2" | "log10" | "exp" | "sqrt" => vec![match topic {
            Value::Quantity { .. } => Value::Null,
            other => numeric_scalar(&other, |n| match call.name.as_str() {
                "log" => match arg_num(call, 0) {
                    None if call.args.is_empty() => finite(n.ln()),
                    Some(b) if b > 0.0 && b != 1.0 => finite(n.ln() / b.ln()),
                    _ => Value::Null,
                },
                "log2" => finite(n.log2()),
                "log10" => finite(n.log10()),
                "exp" => finite(n.exp()),
                _ => finite(n.sqrt()),
            }),
        }],
        // `pow(y)` — the topic to the power `y`; an integer topic
        // with a non-negative integer exponent stays an integer
        // while it fits.
        "pow" => vec![match (topic, call.args.first()) {
            (Value::Quantity { .. }, _) => Value::Null,
            (Value::Int(x), Some(Arg::Lit(Value::Int(y)))) if *y >= 0 => {
                match u32::try_from(*y).ok().and_then(|y| x.checked_pow(y)) {
                    Some(v) => Value::Int(v),
                    None => finite((x as f64).powf(*y as f64)),
                }
            }
            (other, _) => match arg_num(call, 0) {
                Some(y) => numeric_scalar(&other, |x| finite(x.powf(y))),
                None => {
                    crate::exec::record_refusal(
                        "pow takes the exponent — pow(2), pow(::a; ::b)".into(),
                    );
                    Value::Null
                }
            },
        }],
        // The keyness statistics: the topic is the word's count in
        // the first corpus, the arguments its corpus size, then the
        // count and size in the second corpus.
        "loglik" | "chi2" => vec![match (
            topic.numeric(),
            arg_num(call, 0),
            arg_num(call, 1),
            arg_num(call, 2),
        ) {
            (Some(a), Some(na), Some(b), Some(nb)) => {
                if call.name == "loglik" {
                    loglik(a, na, b, nb)
                } else {
                    chi2(a, na, b, nb)
                }
            }
            _ if call.args.len() < 3 => {
                crate::exec::record_refusal(format!(
                    "{0} takes the corpus size, then the other count and size — \
                     {0}(na; b; nb), {0}(::a; ::na; ::b; ::nb)",
                    call.name
                ));
                Value::Null
            }
            _ => Value::Null,
        }],
        // The collocation measures: the topic is the pair's count,
        // the arguments the two words' counts and the corpus size
        // (`log_dice` needs no size).
        "mi" | "t_score" | "log_dice" => vec![{
            let need = if call.name == "log_dice" { 2 } else { 3 };
            match (
                topic.numeric(),
                arg_num(call, 0),
                arg_num(call, 1),
                arg_num(call, 2),
            ) {
                (Some(fxy), Some(fx), Some(fy), n) if call.args.len() >= need => {
                    match call.name.as_str() {
                        "mi" => n.map_or(Value::Null, |n| mi(fxy, fx, fy, n)),
                        "t_score" => n.map_or(Value::Null, |n| t_score(fxy, fx, fy, n)),
                        _ => log_dice(fxy, fx, fy),
                    }
                }
                _ if call.args.len() < need => {
                    crate::exec::record_refusal(if call.name == "log_dice" {
                        "log_dice takes the two words' counts — log_dice(fx; fy), \
                         log_dice(::fxy; ::fx; ::fy)"
                            .to_string()
                    } else {
                        format!(
                            "{0} takes the two words' counts and the corpus size — \
                             {0}(fx; fy; n), {0}(::fxy; ::fx; ::fy; ::n)",
                            call.name
                        )
                    });
                    Value::Null
                }
                _ => Value::Null,
            }
        }],
        // `s/pat/repl/mods` — regex substitution on the topic's
        // text. Sed semantics: first occurrence by default, `g`
        // global, `i` case-insensitive; `$1`-style capture
        // references in the replacement. The pattern was validated
        // at parse time; a failed recompile passes the topic through.
        "s" => {
            let pattern = arg_str(call, 0, "");
            let replacement = arg_str(call, 1, "");
            let mods = arg_str(call, 2, "");
            let case = if mods.contains('i') { "(?i)" } else { "" };
            let Some(re) = crate::exec::compiled_regex(&format!("{case}{pattern}")) else {
                return vec![topic];
            };
            let out = if mods.contains('g') {
                re.replace_all(&text, replacement)
            } else {
                re.replace(&text, replacement)
            };
            vec![Value::Str(out.into_owned())]
        }
        // `default(v)` — replace a null topic with `v` (pandas'
        // fillna, jq's `//`); non-null topics pass through.
        "default" => vec![match topic {
            Value::Null => call
                .args
                .first()
                .and_then(|a| match a {
                    Arg::Lit(v) => Some(v.clone()),
                    Arg::Expr(_) | Arg::Range(_, _) => None,
                })
                .unwrap_or(Value::Null),
            other => other,
        }],
        // Serialize the topic as strict JSON text. (`record` is also
        // named here but constructed in the executor, which has the
        // adapter at hand for its expression arguments.)
        "json" | "jsonl" => vec![Value::Str(topic.to_json())],
        // The one-value kaiv document; `@| kaiv` renders the whole
        // stream as one (the serialization family, the kaiv member).
        "kaiv" => vec![Value::Str(
            crate::kaiv_out::document(std::slice::from_ref(&topic)).unwrap_or_else(|e| e),
        )],
        // `| link` reads the capsa's node (the executor, which has
        // the adapter, handles it); a bare value has nothing to
        // link and passes through.
        "link" => vec![topic],
        _ => vec![topic],
    }
}

/// Apply `f` to the topic's numeric value, or `Null` when it has
/// none.
fn numeric_scalar(topic: &Value, f: impl Fn(f64) -> Value) -> Value {
    topic.numeric().map(f).unwrap_or(Value::Null)
}

/// The digits argument of `round(d)`, when one was given. A
/// non-integer argument reads as absent, like `arg_str`'s fallback.
fn round_digits(call: &FnCall) -> Option<i64> {
    match call.args.first() {
        Some(Arg::Lit(Value::Int(d))) => Some(*d),
        _ => None,
    }
}

/// Round to `d` decimal places (negative `d` reaches left of the
/// point, SQL-style). Scale-round-descale over f64: the answer is
/// the nearest representable double, so `68.99000000000001 |
/// round(2)` prints `68.99`. A scaling overflow (astronomically
/// large topic with large `d`) leaves the value untouched — beyond
/// f64's 17 significant digits the rounding is an identity anyway.
fn round_to(n: f64, d: i64) -> f64 {
    let factor = 10f64.powi(d.clamp(-30, 30) as i32);
    let scaled = n * factor;
    if scaled.is_finite() {
        scaled.round() / factor
    } else {
        n
    }
}

/// Apply a reducing aggregate to the whole value list. The
/// order/selection family (`sort`, `unique`, `reverse`, `first`,
/// `last`) and the keyed aggregates are capsa-preserving and live in
/// the executor instead.
pub fn apply(call: &FnCall, input: Vec<Value>, scale: Scale) -> Vec<Value> {
    match call.name.as_str() {
        // What `run_for_rendering` leaves where a closing `@| csv` /
        // `@| table` stood: the rows themselves, for the tool to
        // tabulate. Not a name a query can write.
        ROWS_FOR_RENDERING => input,
        "count" => vec![Value::Int(input.len() as i64)],
        "sum" => vec![sum(&input, scale)],
        "product" => vec![product(&input)],
        "min" => extreme(input, std::cmp::Ordering::Less, scale),
        "max" => extreme(input, std::cmp::Ordering::Greater, scale),
        "mean" | "avg" => vec![mean(&input, scale)],
        "median" => vec![median(&input, scale)],
        // `percentile(p)` — the p-th percentile, 0 ≤ p ≤ 100, by
        // linear interpolation between the order statistics (R's
        // type 7, NumPy's default): `percentile(50)` is the median,
        // `percentile(0)` the minimum, `percentile(100)` the maximum.
        "percentile" => {
            let p = match call.args.first() {
                Some(Arg::Lit(Value::Int(i))) => Some(*i as f64),
                Some(Arg::Lit(Value::Float(f))) => Some(*f),
                _ => None,
            };
            match p {
                Some(p) if (0.0..=100.0).contains(&p) => vec![quantile(&input, p / 100.0, scale)],
                _ => {
                    crate::exec::record_refusal(
                        "percentile takes a number from 0 to 100 — percentile(90)".into(),
                    );
                    vec![Value::Null]
                }
            }
        }
        // `std(sample)` / `var(sample)` divide by n − 1; `stddev` and
        // `variance` are the long aliases.
        "std" | "stddev" => vec![spread(
            &input,
            f64::sqrt,
            scale,
            usize::from(sample_flag(call)),
        )],
        "var" | "variance" => vec![spread(&input, |v| v, scale, usize::from(sample_flag(call)))],
        // Lexical diversity. `entropy` and `yule_k` read the stream
        // as counts (the output of `group | count`): Shannon entropy
        // in bits, Yule's characteristic K. `mtld(t)` reads it as
        // tokens: McCarthy–Jarvis's measure of textual lexical
        // diversity, the type-token-ratio factor `t` (default 0.72),
        // forward and backward averaged.
        "entropy" => vec![entropy(&counts(&input))],
        "yule_k" => vec![yule_k(&counts(&input))],
        "mtld" => {
            let t = match call.args.first() {
                None => Some(0.72),
                Some(Arg::Lit(Value::Float(f))) if *f > 0.0 && *f < 1.0 => Some(*f),
                _ => None,
            };
            match t {
                Some(t) => vec![mtld(&input, t)],
                None => {
                    crate::exec::record_refusal(
                        "mtld takes a type-token ratio between 0 and 1 — mtld(0.72)".into(),
                    );
                    vec![Value::Null]
                }
            }
        }
        "join" => vec![Value::Str(join(&input, arg_str(call, 0, "")))],
        // The stream as one JSON document — an array — or as JSON
        // Lines, one document per line.
        "json" => {
            let items: Vec<String> = input.iter().map(Value::to_json).collect();
            vec![Value::Str(format!("[{}]", items.join(", ")))]
        }
        "jsonl" => {
            let items: Vec<String> = input.iter().map(Value::to_json).collect();
            vec![Value::Str(items.join("\n"))]
        }
        // The stream as one CSV document, or as one aligned text
        // table: a header and a row per value, the header never
        // apart from its rows. Named columns select and order the
        // fields; without them, every field.
        "csv" | "table" => {
            // `csv(";"; year; title)`: a quoted first argument is the
            // delimiter (a bare word is a column, so no collision).
            // The stage is a value like any other and never
            // depends on a locale: a tool that prints under one
            // takes a closing `@| csv` / `@| table` off the query
            // and renders it itself (`run_for_rendering`).
            let (delimiter, args) = split_csv_delimiter(call);
            let columns: Vec<String> = args
                .iter()
                .filter_map(|a| match a {
                    Arg::Lit(Value::Str(s)) => Some(s.clone()),
                    _ => None,
                })
                .collect();
            let columns = (!columns.is_empty()).then_some(columns.as_slice());
            vec![Value::Str(tabulate_with(
                &input,
                columns,
                call.name == "csv",
                delimiter.unwrap_or(b','),
            ))]
        }
        // The stream as one kaiv document: results under
        // `/@results`, records as namespaces, lists as arrays,
        // units kept. Provenance rides qua's `--kaiv`, not the
        // stage (the stage sees values, not nodes).
        "kaiv" => vec![Value::Str(
            crate::kaiv_out::document(&input).unwrap_or_else(|e| e),
        )],
        // The order/selection family over an explicit value list —
        // reached from the per-capsa list reductions (`| last` on a
        // group's list topic); the `@|` forms are capsa-preserving
        // and intercepted in the executor before this point.
        // `sort` orders by the standard value comparison; with a
        // locale argument (`sort(ru-RU)` — any Unicode locale
        // identifier), values sort by their text under that
        // locale's collation (colligo; CLDR-derived), and with the
        // word `atergo` in the a tergo order. Reverse by piping
        // into `| reverse`.
        "sort" => {
            let mut v = input;
            match text_order(call) {
                Some(cmp) => v.sort_by(|a, b| cmp(&a.to_string(), &b.to_string())),
                None => {
                    let collate = default_text_order();
                    v.sort_by(|a, b| default_cmp(a, b, scale, collate.as_deref()))
                }
            }
            v
        }
        "reverse" => {
            let mut v = input;
            v.reverse();
            v
        }
        // `combinations(n)` — every unordered n-member subset of
        // the stream's distinct values, each once, as a list whose
        // members stand in the values' own order: (a, b) and (b, a)
        // are one combination and one value, so a group counts
        // them together. `pairs` and `triples` are n = 2 and 3.
        "combinations" | "pairs" | "triples" => {
            let n = match call.name.as_str() {
                "pairs" => 2,
                "triples" => 3,
                _ => arg_int(call, 0).unwrap_or(2).max(0) as usize,
            };
            let mut seen = std::collections::HashSet::new();
            let mut items: Vec<Value> = input
                .into_iter()
                .filter(|v| !matches!(v, Value::Null) && seen.insert(v.to_string()))
                .collect();
            items.sort_by(|a, b| a.compare_with(b, scale));
            let mut out = Vec::new();
            if n >= 1 && n <= items.len() {
                let mut idx: Vec<usize> = (0..n).collect();
                loop {
                    out.push(Value::list(idx.iter().map(|&i| items[i].clone()).collect()));
                    // the next index set in lexicographic order
                    let Some(k) = (0..n).rev().find(|&k| idx[k] != k + items.len() - n) else {
                        break;
                    };
                    idx[k] += 1;
                    for j in k + 1..n {
                        idx[j] = idx[j - 1] + 1;
                    }
                }
            }
            out
        }
        "unique" => {
            let mut seen: Vec<String> = Vec::new();
            input
                .into_iter()
                .filter(|v| {
                    let k = v.to_string();
                    if seen.contains(&k) {
                        false
                    } else {
                        seen.push(k);
                        true
                    }
                })
                .collect()
        }
        "first" => input.into_iter().next().into_iter().collect(),
        "last" => input.into_iter().next_back().into_iter().collect(),
        _ => input,
    }
}

/// The sum of the numeric readings: values with no reading are
/// skipped as missing and an empty (or wholly non-numeric) input
/// reduces to null (spec: numeric reductions). Exact while every
/// operand is an integer, promoting to float on overflow — as
/// arithmetic does — rather than wrapping.
/// The durational fold's verdict: engaged when a typed duration is
/// present, refusing entirely if any element lacks a durational
/// reading — a silent partial total would lie.
enum DurFold {
    /// No typed duration present — the numeric path proceeds.
    Absent,
    /// Every element read as a span: fold these.
    Spans(Vec<(i64, u32)>),
    /// A typed duration mixed with span-less elements: refuse.
    Unsound,
}

fn durational_fold(input: &[Value]) -> DurFold {
    if !input.iter().any(|v| matches!(v, Value::Duration { .. })) {
        return DurFold::Absent;
    }
    match input.iter().map(Value::durational_reading).collect() {
        Some(spans) => DurFold::Spans(spans),
        None => DurFold::Unsound,
    }
}

/// The quantital fold's verdict: engaged when a typed quantity is
/// present. Unit text then lifts through the unital reading — the
/// fold is iterated `+`, and `Q + '500 m'` lifts — but every
/// element must land on one shared base, and a bare number refuses
/// exactly as `Q + 5` does: a cross-dimension fold (watts plus
/// meters) or a dimensionless stowaway would total nonsense
/// silently.
enum QuantFold {
    /// No quantities present — the numeric path proceeds.
    Absent,
    /// Every element read on this base: fold `mags` (the base
    /// magnitudes, in order) and mint the result on it. When every
    /// element was also *written* in one unit, `unit` carries it
    /// as (base-per-unit factor, name), so the total can display
    /// as `570.5 W` instead of the raw base expression.
    Same {
        base: String,
        unit: Option<(f64, String)>,
        mags: Vec<f64>,
    },
    /// Mixed dimensions, a bare number, or unreadable text: refuse.
    Unsound,
}

fn quantital_fold(input: &[Value], scale: Scale) -> QuantFold {
    if !input.iter().any(|v| matches!(v, Value::Quantity { .. })) {
        return QuantFold::Absent;
    }
    let mut base: Option<String> = None;
    let mut unit: Option<(f64, String)> = None;
    let mut unit_ok = true;
    let mut mags = Vec::with_capacity(input.len());
    for v in input {
        let (value, b, written): (f64, String, Option<(f64, String)>) = match v {
            Value::Quantity {
                value,
                base,
                written,
            } => (*value, base.clone(), written.clone()),
            Value::Str(s) => match crate::quantity::parse_unit_text_with(s, scale) {
                Some((bv, b, wmag, wunit)) => (bv, b, Some((wmag, wunit))),
                None => return QuantFold::Unsound,
            },
            _ => return QuantFold::Unsound,
        };
        match &base {
            None => base = Some(b),
            Some(prev) if *prev == b => {}
            Some(_) => return QuantFold::Unsound,
        }
        match (unit_ok, &written) {
            (true, Some((mag, u))) if *mag != 0.0 => match &unit {
                None => unit = Some((value / mag, u.clone())),
                Some((_, prev)) if prev == u => {}
                Some(_) => unit_ok = false,
            },
            _ => unit_ok = false,
        }
        mags.push(value);
    }
    match base {
        Some(base) => QuantFold::Same {
            base,
            unit: unit.filter(|_| unit_ok),
            mags,
        },
        None => QuantFold::Absent,
    }
}

/// Mint a fold's result on its base, re-expressed in the shared
/// written unit where one survived.
fn quantital_result(value: f64, base: String, unit: Option<(f64, String)>) -> Value {
    Value::Quantity {
        value,
        base,
        written: unit.map(|(f, u)| (value / f, u)),
    }
}

fn sum(input: &[Value], scale: Scale) -> Value {
    // Quantities total to a typed quantity in the base unit —
    // mixed units of one dimension welcome (kW + W + BTU/h), unit
    // text lifted alongside; mixed dimensions refused.
    match quantital_fold(input, scale) {
        QuantFold::Unsound => return Value::Null,
        QuantFold::Same { base, unit, mags } => {
            let value = mags.iter().sum();
            return quantital_result(value, base, unit);
        }
        QuantFold::Absent => {}
    }
    // Durations total to a typed duration (`PT15H45M`), the
    // durational counterpart.
    let spans = match durational_fold(input) {
        DurFold::Unsound => return Value::Null,
        DurFold::Spans(spans) => Some(spans),
        DurFold::Absent => None,
    };
    if let Some(spans) = spans {
        let mut secs: i64 = 0;
        let mut nanos: i64 = 0;
        for (s, n) in spans {
            match secs.checked_add(s) {
                Some(t) => secs = t,
                None => return Value::Null,
            }
            nanos += n as i64;
        }
        match secs.checked_add(nanos.div_euclid(1_000_000_000)) {
            Some(t) => secs = t,
            None => return Value::Null,
        }
        return Value::Duration {
            secs,
            nanos: nanos.rem_euclid(1_000_000_000) as u32,
        };
    }
    if !input.iter().any(|v| v.numeric().is_some()) {
        return Value::Null;
    }
    if input.iter().all(|v| matches!(v, Value::Int(_))) {
        let mut acc: i64 = 0;
        let mut overflowed = false;
        for v in input {
            if let Value::Int(n) = v {
                match acc.checked_add(*n) {
                    Some(s) => acc = s,
                    None => {
                        overflowed = true;
                        break;
                    }
                }
            }
        }
        if !overflowed {
            return Value::Int(acc);
        }
    }
    Value::Float(input.iter().filter_map(Value::numeric).sum())
}

/// The product of the numeric readings: exact while every operand
/// is an integer, promoting to float on overflow (as arithmetic
/// does) rather than wrapping; float otherwise. An empty input
/// multiplies to 1 (the fold identity).
/// The product of the numeric readings. Empty input is the fold's
/// identity, 1; input with no reading at all is null, as `sum`'s
/// is. One quantity among numbers scales (`2 km` by 3 is `6 km`);
/// two quantities would multiply their dimensions, which the
/// unital fragment does not combine, so that is refused rather
/// than answered on a dropped unit.
fn product(input: &[Value]) -> Value {
    if !input.is_empty() && !input.iter().any(|v| v.numeric().is_some()) {
        return Value::Null;
    }
    let quantities: Vec<&Value> = input
        .iter()
        .filter(|v| matches!(v, Value::Quantity { .. }))
        .collect();
    match quantities.as_slice() {
        [] => {}
        [
            Value::Quantity {
                value,
                base,
                written,
            },
        ] => {
            let factor: f64 = input
                .iter()
                .filter(|v| !matches!(v, Value::Quantity { .. }))
                .filter_map(Value::numeric)
                .product();
            return Value::Quantity {
                value: value * factor,
                base: base.clone(),
                written: written.as_ref().map(|(m, u)| (m * factor, u.clone())),
            };
        }
        _ => {
            crate::exec::record_refusal(
                "product: two quantities would multiply their units, which the unital \
                 fragment does not combine; take the magnitudes first"
                    .into(),
            );
            return Value::Null;
        }
    }
    if input.iter().all(|v| matches!(v, Value::Int(_))) {
        let mut acc: i64 = 1;
        let mut overflowed = false;
        for v in input {
            if let Value::Int(n) = v {
                match acc.checked_mul(*n) {
                    Some(p) => acc = p,
                    None => {
                        overflowed = true;
                        break;
                    }
                }
            }
        }
        if !overflowed {
            return Value::Int(acc);
        }
    }
    Value::Float(input.iter().filter_map(Value::numeric).product())
}

fn mean(input: &[Value], scale: Scale) -> Value {
    // The mean of same-base quantities is a quantity on that base.
    match quantital_fold(input, scale) {
        QuantFold::Unsound => return Value::Null,
        QuantFold::Same { base, unit, mags } => {
            let value = mags.iter().sum::<f64>() / mags.len() as f64;
            return quantital_result(value, base, unit);
        }
        QuantFold::Absent => {}
    }
    // The mean of durations is a duration.
    let spans = match durational_fold(input) {
        DurFold::Unsound => return Value::Null,
        DurFold::Spans(spans) => Some(spans),
        DurFold::Absent => None,
    };
    if let Some(spans) = spans {
        let total: i128 = spans
            .iter()
            .map(|(s, n)| *s as i128 * 1_000_000_000 + *n as i128)
            .sum();
        let avg = total / spans.len() as i128;
        return Value::Duration {
            secs: (avg.div_euclid(1_000_000_000)) as i64,
            nanos: avg.rem_euclid(1_000_000_000) as u32,
        };
    }
    let nums: Vec<f64> = input.iter().filter_map(Value::numeric).collect();
    if nums.is_empty() {
        Value::Null
    } else {
        Value::Float(nums.iter().sum::<f64>() / nums.len() as f64)
    }
}

/// The middle numeric value; an even count averages the two middle
/// values. All-integer input with an odd count stays an integer.
fn median(input: &[Value], scale: Scale) -> Value {
    // The median of same-base quantities is a quantity on that
    // base; mixed dimensions refuse.
    match quantital_fold(input, scale) {
        QuantFold::Unsound => return Value::Null,
        QuantFold::Same {
            base,
            unit,
            mut mags,
        } => {
            // total_cmp: query arithmetic can mint NaN (float
            // overflow subtraction), which must not panic the sort.
            mags.sort_by(f64::total_cmp);
            let mid = mags.len() / 2;
            let value = if mags.len() % 2 == 1 {
                mags[mid]
            } else {
                (mags[mid - 1] + mags[mid]) / 2.0
            };
            return quantital_result(value, base, unit);
        }
        QuantFold::Absent => {}
    }
    // A typed duration mixed with span-less numerics would skip the
    // durations and report the median of the leftovers — refuse,
    // like the folds.
    if matches!(durational_fold(input), DurFold::Unsound) {
        return Value::Null;
    }
    let mut nums: Vec<f64> = input.iter().filter_map(Value::numeric).collect();
    if nums.is_empty() {
        return Value::Null;
    }
    nums.sort_by(f64::total_cmp);
    let mid = nums.len() / 2;
    if nums.len() % 2 == 1 {
        let m = nums[mid];
        if input.iter().all(|v| matches!(v, Value::Int(_))) {
            Value::Int(m as i64)
        } else {
            Value::Float(m)
        }
    } else {
        Value::Float((nums[mid - 1] + nums[mid]) / 2.0)
    }
}

/// The q-th quantile (0 ≤ q ≤ 1) by linear interpolation between
/// the sorted values (R type 7): at rank h = (n − 1)·q the value
/// is v[⌊h⌋] + (h − ⌊h⌋)·(v[⌊h⌋+1] − v[⌊h⌋]). Same-base quantities
/// yield a quantity; mixed dimensions refuse; integers stay
/// integers when the rank lands on an element.
fn quantile(input: &[Value], q: f64, scale: Scale) -> Value {
    fn at(mut sorted: Vec<f64>, q: f64) -> Option<(f64, bool)> {
        if sorted.is_empty() {
            return None;
        }
        sorted.sort_by(f64::total_cmp);
        let h = (sorted.len() - 1) as f64 * q;
        let lo = h.floor() as usize;
        let frac = h - lo as f64;
        let v = if frac == 0.0 || lo + 1 >= sorted.len() {
            sorted[lo]
        } else {
            sorted[lo] + frac * (sorted[lo + 1] - sorted[lo])
        };
        Some((v, frac == 0.0))
    }
    match quantital_fold(input, scale) {
        QuantFold::Unsound => return Value::Null,
        QuantFold::Same { base, unit, mags } => {
            return match at(mags, q) {
                Some((v, _)) => quantital_result(v, base, unit),
                None => Value::Null,
            };
        }
        QuantFold::Absent => {}
    }
    if matches!(durational_fold(input), DurFold::Unsound) {
        return Value::Null;
    }
    let nums: Vec<f64> = input.iter().filter_map(Value::numeric).collect();
    match at(nums, q) {
        Some((v, exact)) if exact && input.iter().all(|v| matches!(v, Value::Int(_))) => {
            Value::Int(v as i64)
        }
        Some((v, _)) => Value::Float(v),
        None => Value::Null,
    }
}

/// The Levenshtein distance between two texts, in codepoints.
fn levenshtein(a: &str, b: &str) -> usize {
    let a: Vec<char> = a.chars().collect();
    let b: Vec<char> = b.chars().collect();
    if a.is_empty() {
        return b.len();
    }
    if b.is_empty() {
        return a.len();
    }
    let mut prev: Vec<usize> = (0..=b.len()).collect();
    let mut cur = vec![0usize; b.len() + 1];
    for (i, ca) in a.iter().enumerate() {
        cur[0] = i + 1;
        for (j, cb) in b.iter().enumerate() {
            let cost = usize::from(ca != cb);
            cur[j + 1] = (prev[j + 1] + 1).min(cur[j] + 1).min(prev[j] + cost);
        }
        std::mem::swap(&mut prev, &mut cur);
    }
    prev[b.len()]
}

/// Variance, post-processed by `finish` (identity for `variance`,
/// square root for `stddev`); `ddof` 0 is the population measure,
/// 1 the sample measure (null below two values).
fn spread(input: &[Value], finish: impl Fn(f64) -> f64, scale: Scale, ddof: usize) -> Value {
    // Statistical moments over mixed dimensions are nonsense too.
    // Same-base spreads stay bare magnitudes for now (a stddev
    // carries the base's unit, a variance its square — typing them
    // is a ruling for the quantital round's next pass).
    let nums: Vec<f64> = match quantital_fold(input, scale) {
        QuantFold::Unsound => return Value::Null,
        // The engaged fold's magnitudes include lifted unit text,
        // which the numeric path below would silently drop.
        QuantFold::Same { mags, .. } => mags,
        QuantFold::Absent => {
            if matches!(durational_fold(input), DurFold::Unsound) {
                return Value::Null;
            }
            input.iter().filter_map(Value::numeric).collect()
        }
    };
    if nums.len() <= ddof {
        return Value::Null;
    }
    let n = nums.len() as f64;
    let m = nums.iter().sum::<f64>() / n;
    let var = nums.iter().map(|x| (x - m) * (x - m)).sum::<f64>() / (n - ddof as f64);
    finite(finish(var))
}

/// A float as a value, null when it is not finite (an overflow, a
/// logarithm of nothing, a zero denominator).
fn finite(x: f64) -> Value {
    if x.is_finite() {
        Value::Float(x)
    } else {
        Value::Null
    }
}

/// The numeric readings of a stream, non-readings dropped.
fn readings(input: &[Value]) -> Vec<f64> {
    input.iter().filter_map(Value::numeric).collect()
}

/// A stream read as counts: the positive numeric readings.
fn counts(input: &[Value]) -> Vec<f64> {
    readings(input).into_iter().filter(|c| *c > 0.0).collect()
}

/// Shannon entropy in bits of a distribution given as counts.
fn entropy(counts: &[f64]) -> Value {
    let total: f64 = counts.iter().sum();
    if total <= 0.0 {
        return Value::Null;
    }
    let h = -counts
        .iter()
        .map(|c| {
            let p = c / total;
            p * p.log2()
        })
        .sum::<f64>();
    finite(h)
}

/// Yule's characteristic K over counts: 10⁴ (Σc² − N) / N², N = Σc.
fn yule_k(counts: &[f64]) -> Value {
    let total: f64 = counts.iter().sum();
    if total <= 0.0 {
        return Value::Null;
    }
    let squares: f64 = counts.iter().map(|c| c * c).sum();
    finite(10_000.0 * (squares - total) / (total * total))
}

/// MTLD (McCarthy & Jarvis 2010) over a token stream: the mean
/// length of the runs whose type-token ratio stays above `t`,
/// forward and backward averaged; the trailing partial run counts
/// as (1 − TTR) / (1 − t) of a factor.
fn mtld(input: &[Value], t: f64) -> Value {
    let tokens: Vec<String> = input.iter().map(Value::to_string).collect();
    if tokens.is_empty() {
        return Value::Null;
    }
    let one_way = |toks: &mut dyn Iterator<Item = &String>| -> f64 {
        let mut factors = 0.0;
        let mut types = std::collections::HashSet::new();
        let mut n = 0usize;
        let mut ttr = 1.0;
        for tok in toks {
            n += 1;
            types.insert(tok.as_str());
            ttr = types.len() as f64 / n as f64;
            if ttr <= t {
                factors += 1.0;
                types.clear();
                n = 0;
                ttr = 1.0;
            }
        }
        if n > 0 {
            factors += (1.0 - ttr) / (1.0 - t);
        }
        factors
    };
    let forward = one_way(&mut tokens.iter());
    let backward = one_way(&mut tokens.iter().rev());
    let n = tokens.len() as f64;
    let mean_of = |f: f64| if f > 0.0 { n / f } else { f64::INFINITY };
    let (a, b) = (mean_of(forward), mean_of(backward));
    if !a.is_finite() || !b.is_finite() {
        // No run ever fell below `t`: the text is too short or too
        // varied to measure.
        return Value::Null;
    }
    finite((a + b) / 2.0)
}

/// The association measures over paired readings: Pearson's `corr`,
/// Spearman's rank correlation, the cosine of the two vectors.
/// Fewer than two pairs, or a zero spread on either side, is null.
pub fn associate(name: &str, pairs: &[(f64, f64)]) -> Value {
    if pairs.len() < 2 {
        return Value::Null;
    }
    match name {
        "corr" => pearson(pairs),
        "spearman" => {
            let xs = average_ranks(pairs.iter().map(|p| p.0));
            let ys = average_ranks(pairs.iter().map(|p| p.1));
            pearson(&xs.into_iter().zip(ys).collect::<Vec<_>>())
        }
        "cosine" => {
            let dot: f64 = pairs.iter().map(|(x, y)| x * y).sum();
            let nx: f64 = pairs.iter().map(|(x, _)| x * x).sum::<f64>().sqrt();
            let ny: f64 = pairs.iter().map(|(_, y)| y * y).sum::<f64>().sqrt();
            if nx == 0.0 || ny == 0.0 {
                Value::Null
            } else {
                finite(dot / (nx * ny))
            }
        }
        "delta" => delta(pairs),
        "dp" => dp(pairs),
        _ => Value::Null,
    }
}

/// Burrows's Delta between two profiles given as paired standard
/// scores: the mean absolute difference over the pairs.
fn delta(pairs: &[(f64, f64)]) -> Value {
    let n = pairs.len() as f64;
    finite(pairs.iter().map(|(x, y)| (x - y).abs()).sum::<f64>() / n)
}

/// Gries's deviation of proportions: each pair is a part's count of
/// the word and the part's size; DP is half the sum over the parts
/// of |observed share − expected share|, where the expected share is
/// the part's share of the corpus. 0 is an even spread, 1 a word
/// confined to one vanishing part; a corpus without the word, or
/// without tokens, is null.
fn dp(pairs: &[(f64, f64)]) -> Value {
    let total: f64 = pairs.iter().map(|p| p.0).sum();
    let size: f64 = pairs.iter().map(|p| p.1).sum();
    if !(total > 0.0) || !(size > 0.0) || pairs.iter().any(|p| p.0 < 0.0 || p.1 < 0.0) {
        return Value::Null;
    }
    let sum: f64 = pairs
        .iter()
        .map(|(n, s)| (n / total - s / size).abs())
        .sum();
    finite(sum / 2.0)
}

/// The agreement measures over paired labels: Cohen's κ over the
/// categories the two sides name, and precision, recall and F₁ of
/// the second side against the first, a label read as positive by
/// its truthiness. No pairs is null; κ with one category on both
/// sides is null (no chance agreement to correct for).
pub fn agree(name: &str, pairs: &[(Value, Value)]) -> Value {
    if pairs.is_empty() {
        return Value::Null;
    }
    match name {
        "kappa" => {
            let n = pairs.len() as f64;
            let mut labels: Vec<String> = Vec::new();
            let mut key = |v: &Value| {
                let k = v.to_string();
                if !labels.contains(&k) {
                    labels.push(k.clone());
                }
                k
            };
            let keyed: Vec<(String, String)> =
                pairs.iter().map(|(a, b)| (key(a), key(b))).collect();
            let observed = keyed.iter().filter(|(a, b)| a == b).count() as f64 / n;
            let expected: f64 = labels
                .iter()
                .map(|l| {
                    let pa = keyed.iter().filter(|(a, _)| a == l).count() as f64 / n;
                    let pb = keyed.iter().filter(|(_, b)| b == l).count() as f64 / n;
                    pa * pb
                })
                .sum();
            if (1.0 - expected).abs() < f64::EPSILON {
                Value::Null
            } else {
                finite((observed - expected) / (1.0 - expected))
            }
        }
        _ => {
            let tp = pairs
                .iter()
                .filter(|(g, p)| g.is_truthy() && p.is_truthy())
                .count() as f64;
            let fp = pairs
                .iter()
                .filter(|(g, p)| !g.is_truthy() && p.is_truthy())
                .count() as f64;
            let fn_ = pairs
                .iter()
                .filter(|(g, p)| g.is_truthy() && !p.is_truthy())
                .count() as f64;
            let precision = if tp + fp > 0.0 {
                Some(tp / (tp + fp))
            } else {
                None
            };
            let recall = if tp + fn_ > 0.0 {
                Some(tp / (tp + fn_))
            } else {
                None
            };
            match name {
                "precision" => precision.map_or(Value::Null, finite),
                "recall" => recall.map_or(Value::Null, finite),
                _ => match (precision, recall) {
                    (Some(p), Some(r)) if p + r > 0.0 => finite(2.0 * p * r / (p + r)),
                    (Some(_), Some(_)) => Value::Float(0.0),
                    _ => Value::Null,
                },
            }
        }
    }
}

fn pearson(pairs: &[(f64, f64)]) -> Value {
    let n = pairs.len() as f64;
    let mx = pairs.iter().map(|p| p.0).sum::<f64>() / n;
    let my = pairs.iter().map(|p| p.1).sum::<f64>() / n;
    let sxy: f64 = pairs.iter().map(|(x, y)| (x - mx) * (y - my)).sum();
    let sxx: f64 = pairs.iter().map(|(x, _)| (x - mx) * (x - mx)).sum();
    let syy: f64 = pairs.iter().map(|(_, y)| (y - my) * (y - my)).sum();
    if sxx == 0.0 || syy == 0.0 {
        Value::Null
    } else {
        finite(sxy / (sxx * syy).sqrt())
    }
}

/// Ranks 1..n with ties given the average of their positions.
fn average_ranks(values: impl Iterator<Item = f64>) -> Vec<f64> {
    let values: Vec<f64> = values.collect();
    let mut order: Vec<usize> = (0..values.len()).collect();
    order.sort_by(|&a, &b| values[a].total_cmp(&values[b]));
    let mut ranks = vec![0.0; values.len()];
    let mut i = 0;
    while i < order.len() {
        let mut j = i;
        while j + 1 < order.len() && values[order[j + 1]] == values[order[i]] {
            j += 1;
        }
        // Positions i..=j (0-based) share the rank (i + j) / 2 + 1.
        let rank = (i + j) as f64 / 2.0 + 1.0;
        for &k in &order[i..=j] {
            ranks[k] = rank;
        }
        i = j + 1;
    }
    ranks
}

/// Standard scores: each reading becomes (x − mean) / sd over the
/// readings present (population sd, or sample with `sample`); a
/// missing reading, or a stream with no spread, is null.
pub fn zscores(xs: &[Option<f64>], sample: bool) -> Vec<Value> {
    let present: Vec<f64> = xs.iter().flatten().copied().collect();
    let ddof = usize::from(sample);
    if present.len() <= ddof.max(1) {
        return vec![Value::Null; xs.len()];
    }
    let n = present.len() as f64;
    let m = present.iter().sum::<f64>() / n;
    let var = present.iter().map(|x| (x - m) * (x - m)).sum::<f64>() / (n - ddof as f64);
    let sd = var.sqrt();
    if sd == 0.0 || !sd.is_finite() {
        return vec![Value::Null; xs.len()];
    }
    xs.iter()
        .map(|x| match x {
            Some(x) => finite((x - m) / sd),
            None => Value::Null,
        })
        .collect()
}

/// Dunning's log-likelihood G² of a word seen `a` times in `na`
/// tokens against `b` times in `nb`, signed positive where the first
/// corpus over-represents it (0 · log 0 = 0).
fn loglik(a: f64, na: f64, b: f64, nb: f64) -> Value {
    if !(na > 0.0 && nb > 0.0) || a < 0.0 || b < 0.0 || a > na || b > nb || a + b == 0.0 {
        return Value::Null;
    }
    let e1 = na * (a + b) / (na + nb);
    let e2 = nb * (a + b) / (na + nb);
    let term = |o: f64, e: f64| if o > 0.0 { o * (o / e).ln() } else { 0.0 };
    let g2 = 2.0 * (term(a, e1) + term(b, e2));
    finite(if a / na >= b / nb { g2 } else { -g2 })
}

/// Pearson's χ² on the 2×2 table [[a, na − a], [b, nb − b]], no
/// continuity correction, signed like [`loglik`]; a zero marginal
/// is null.
fn chi2(a: f64, na: f64, b: f64, nb: f64) -> Value {
    if !(na > 0.0 && nb > 0.0) || a < 0.0 || b < 0.0 || a > na || b > nb {
        return Value::Null;
    }
    let (c, d) = (na - a, nb - b);
    let n = na + nb;
    let (col1, col2) = (a + b, c + d);
    if col1 == 0.0 || col2 == 0.0 {
        return Value::Null;
    }
    let diff = a * d - b * c;
    let x2 = n * diff * diff / (col1 * col2 * na * nb);
    finite(if a / na >= b / nb { x2 } else { -x2 })
}

/// Pointwise mutual information of a pair seen `fxy` times whose
/// words are seen `fx` and `fy` times in `n` tokens: log₂ of the
/// observed count over the expected `fx · fy / n`. A zero count or
/// size, or a pair count above either word's, is null.
fn mi(fxy: f64, fx: f64, fy: f64, n: f64) -> Value {
    if !(fxy > 0.0 && fx > 0.0 && fy > 0.0 && n > 0.0) || fxy > fx || fxy > fy {
        return Value::Null;
    }
    finite((fxy * n / (fx * fy)).log2())
}

/// The t-score of the same pair: (observed − expected) / √observed.
fn t_score(fxy: f64, fx: f64, fy: f64, n: f64) -> Value {
    if !(fxy > 0.0 && fx > 0.0 && fy > 0.0 && n > 0.0) || fxy > fx || fxy > fy {
        return Value::Null;
    }
    finite((fxy - fx * fy / n) / fxy.sqrt())
}

/// Rychlý's logDice: 14 + log₂ of the Dice coefficient
/// `2 · fxy / (fx + fy)`, needing no corpus size; at most 14.
fn log_dice(fxy: f64, fx: f64, fy: f64) -> Value {
    if !(fxy > 0.0 && fx > 0.0 && fy > 0.0) || fxy > fx || fxy > fy {
        return Value::Null;
    }
    finite(14.0 + (2.0 * fxy / (fx + fy)).log2())
}

/// Whether a value carries a reading in some fragment (numeric,
/// temporal, durational, or unital) — the readings [`Value::compare`]
/// orders by beyond its bare string fallback. A value with none (a
/// non-numeric string, a bool, null) is missing to the numeric
/// reductions.
fn has_reading(v: &Value, scale: Scale) -> bool {
    v.numeric().is_some()
        || v.temporal_reading().is_some()
        || v.durational_reading().is_some()
        || match v {
            // The unital probe pays the threaded resolver, so
            // custom-unit text is admitted exactly as it compares.
            Value::Str(s) => crate::quantity::parse_unit_text_with(s, scale).is_some(),
            Value::Quantity { .. } => true,
            _ => false,
        }
}

/// `min` / `max`: numeric reductions that coerce through the reading,
/// skip a value with no reading as missing (so a junk string can no
/// longer win via the comparison's string fallback), and reduce an
/// empty (or wholly readingless) input to null (spec).
fn extreme(input: Vec<Value>, want: std::cmp::Ordering, scale: Scale) -> Vec<Value> {
    // Ordering across dimensions is meaningless: a min over watts
    // and meters would pick by raw magnitude. Refuse, like the
    // numeric folds.
    if matches!(quantital_fold(&input, scale), QuantFold::Unsound) {
        return vec![Value::Null];
    }
    match input
        .into_iter()
        .filter(|v| has_reading(v, scale))
        .reduce(|a, b| {
            if a.compare_with(&b, scale) == want {
                a
            } else {
                b
            }
        }) {
        Some(v) => vec![v],
        None => vec![Value::Null],
    }
}

fn join(input: &[Value], sep: &str) -> String {
    input
        .iter()
        .map(|v| v.to_string())
        .collect::<Vec<_>>()
        .join(sep)
}

/// The `n`-th call argument as a literal string, or `default` if
/// absent (or not a string literal).
/// The UAX #29 sentences of a text, trimmed, empties dropped —
/// with the session's sentence bonds applied when any are loaded.
fn sentences_of(text: &str) -> Vec<&str> {
    let raw: Vec<&str> = match crate::sentence_bonds() {
        Some(b) => b.unicode_sentences(text),
        None => {
            use unicode_segmentation::UnicodeSegmentation;
            text.unicode_sentences().collect()
        }
    };
    raw.into_iter()
        .map(str::trim)
        .filter(|t| !t.is_empty())
        .collect()
}

/// The vowel letters `vowels` and `stress` count by default: the
/// Cyrillic and the Latin ones, case-folded at the comparison.
const DEFAULT_VOWELS: &str = "аеёиоуыэюяaeiouy";

fn is_vowel(c: char, alphabet: &str) -> bool {
    c.to_lowercase().any(|l| alphabet.contains(l))
}

/// The 1-based ordinal of the stressed vowel of a marked form, by
/// the same rules `stress(n)` writes it: the vowel carrying the
/// acute; else a ё; else the one vowel of a monosyllable.
fn stress_at(text: &str, alphabet: &str) -> Option<usize> {
    let chars: Vec<char> = text.nfc().collect();
    let mut n = 0;
    for (i, c) in chars.iter().enumerate() {
        if is_vowel(*c, alphabet) {
            n += 1;
            if chars.get(i + 1) == Some(&'\u{301}') {
                return Some(n);
            }
        }
    }
    let mut n = 0;
    for c in &chars {
        if is_vowel(*c, alphabet) {
            n += 1;
            if matches!(c, 'ё' | 'Ё') {
                return Some(n);
            }
        }
    }
    (chars.iter().filter(|c| is_vowel(**c, alphabet)).count() == 1).then_some(1)
}

fn arg_int(call: &FnCall, n: usize) -> Option<i64> {
    match call.args.get(n) {
        Some(Arg::Lit(Value::Int(i))) => Some(*i),
        _ => None,
    }
}

fn arg_str<'a>(call: &'a FnCall, n: usize, default: &'a str) -> &'a str {
    match call.args.get(n) {
        Some(Arg::Lit(Value::Str(s))) => s,
        _ => default,
    }
}

/// The numeric reading of the n-th literal argument (an expression
/// argument has been evaluated to a literal by the time the call
/// runs).
fn arg_num(call: &FnCall, n: usize) -> Option<f64> {
    match call.args.get(n) {
        Some(Arg::Lit(v)) => v.numeric(),
        _ => None,
    }
}

#[cfg(test)]
mod tests {
    use super::*;

    #[test]
    fn outline_numbers_count_per_level() {
        let n = |ls: &[i64]| -> Vec<(usize, String)> {
            outline_numbers(&ls.iter().map(|&l| Some(l)).collect::<Vec<_>>())
        };
        let nums = |ls: &[i64]| n(ls).into_iter().map(|(_, s)| s).collect::<Vec<_>>();
        assert_eq!(
            nums(&[1, 2, 2, 3, 2, 1, 2]),
            ["1", "1.1", "1.2", "1.2.1", "1.3", "2", "2.1"]
        );
        // the shallowest level seen is the top, whatever its number
        assert_eq!(
            n(&[3, 4, 3]),
            [
                (0, "1".to_string()),
                (1, "1.1".to_string()),
                (0, "2".to_string())
            ]
        );
        // a skipped level counts as present once
        assert_eq!(nums(&[1, 3, 3, 2]), ["1", "1.1.1", "1.1.2", "1.2"]);
        // a row without a level stands at the top
        assert_eq!(
            outline_numbers(&[Some(1), None, Some(2)]),
            [
                (0, "1".to_string()),
                (0, "2".to_string()),
                (1, "2.1".to_string())
            ]
        );
    }

    fn agg(name: &str, input: Vec<Value>) -> Vec<Value> {
        let call = FnCall {
            name: name.into(),
            args: Vec::new(),
        };
        apply(&call, input, &crate::quantity::scale_expr)
    }

    fn sc(name: &str, topic: Value) -> Vec<Value> {
        let call = FnCall {
            name: name.into(),
            args: Vec::new(),
        };
        apply_scalar(&call, topic, &crate::quantity::scale_expr)
    }

    /// `haversine` is the great-circle distance in kilometres, the
    /// first latitude in topic position as the call form puts it.
    #[test]
    fn haversine_in_kilometres() {
        let args = |v: &[f64]| {
            v.iter()
                .map(|x| Arg::Lit(Value::Float(*x)))
                .collect::<Vec<_>>()
        };
        let km = scalar_with(
            "haversine",
            Value::Float(40.71),
            args(&[-74.01, 48.86, 2.35]),
        );
        let Value::Float(d) = km[0] else {
            panic!("{km:?}")
        };
        assert!((d - 5837.4).abs() < 1.0, "{d}");
        let same = scalar_with(
            "haversine",
            Value::Float(31.78),
            args(&[35.23, 31.78, 35.23]),
        );
        assert_eq!(same, vec![Value::Float(0.0)]);
        assert_eq!(
            scalar_with("haversine", Value::Null, args(&[1.0, 2.0, 3.0])),
            vec![Value::Null]
        );
    }

    /// The unit words read a duration as a number of that unit —
    /// the constructor's inverse — whole as an integer, else a
    /// float; a numeric topic still makes a duration.
    #[test]
    fn unit_words_read_a_duration() {
        let d = |secs: i64| Value::Duration { secs, nanos: 0 };
        assert_eq!(
            scalar_with("days", d(30 * 86400), vec![]),
            vec![Value::Int(30)]
        );
        assert_eq!(
            scalar_with("hours", d(90 * 60), vec![]),
            vec![Value::Float(1.5)]
        );
        assert_eq!(
            scalar_with("minutes", d(90), vec![]),
            vec![Value::Float(1.5)]
        );
        assert_eq!(scalar_with("seconds", d(90), vec![]), vec![Value::Int(90)]);
        assert_eq!(
            scalar_with("days", Value::Int(30), vec![]),
            vec![d(30 * 86400)]
        );
    }

    /// `ngrams(n)`: the n-word windows of a text as space-joined
    /// strings, one per window; a text shorter than n yields none;
    /// the default n is 2.
    #[test]
    fn ngrams_windows_the_words() {
        let call = |n: Option<i64>| FnCall {
            name: "ngrams".into(),
            args: n.map(|n| vec![Arg::Lit(Value::Int(n))]).unwrap_or_default(),
        };
        let text = Value::Str("a  b c\nd".into());
        let strs = |vs: Vec<Value>| vs.into_iter().map(|v| v.to_string()).collect::<Vec<_>>();
        assert_eq!(
            strs(apply_scalar(
                &call(Some(2)),
                text.clone(),
                &crate::quantity::scale_expr
            )),
            vec!["a b", "b c", "c d"]
        );
        assert_eq!(
            strs(apply_scalar(
                &call(Some(3)),
                text.clone(),
                &crate::quantity::scale_expr
            )),
            vec!["a b c", "b c d"]
        );
        assert_eq!(
            strs(apply_scalar(
                &call(None),
                text.clone(),
                &crate::quantity::scale_expr
            )),
            vec!["a b", "b c", "c d"]
        );
        assert!(apply_scalar(&call(Some(5)), text, &crate::quantity::scale_expr).is_empty());
    }

    /// The character classes keep their class (plus the named
    /// extras) and space out the rest, so `words` then spreads
    /// the kept runs; `digit` keeps characters, never a value.
    #[test]
    fn character_classes_space_out_the_rest() {
        let call = |name: &str, keep: Option<&str>| FnCall {
            name: name.into(),
            args: keep
                .map(|k| vec![Arg::Lit(Value::Str(k.into()))])
                .unwrap_or_default(),
        };
        let one = |name: &str, keep: Option<&str>, text: &str| {
            apply_scalar(
                &call(name, keep),
                Value::Str(text.into()),
                &crate::quantity::scale_expr,
            )
            .pop()
            .unwrap()
            .to_string()
        };
        assert_eq!(
            one("alpha", None, "Tom’s 2 dogs—a fence!"),
            "Tom s   dogs a fence "
        );
        assert_eq!(one("alpha", Some("’"), "Tom’s 2 dogs"), "Tom’s   dogs");
        assert_eq!(
            one("digit", None, "Hartford, 1876: $1.50"),
            "          1876   1 50"
        );
        assert_eq!(one("digit", Some("."), "$1.50 x 3,000"), " 1.50   3 000");
        assert_eq!(one("alnum", None, "No. 2—Huck’s"), "No  2 Huck s");
        assert_eq!(
            one("alnum", Some("’-"), "well-to-do Huck’s"),
            "well-to-do Huck’s"
        );
        // Unicode classes, not ASCII: letters and digits of any script.
        assert_eq!(one("alpha", None, "Пушкин 1799"), "Пушкин     ");
        assert_eq!(one("digit", None, "٣ apples"), "٣       ");
    }

    fn ints(ns: &[i64]) -> Vec<Value> {
        ns.iter().map(|&n| Value::Int(n)).collect()
    }

    fn scalar_with(name: &str, topic: Value, args: Vec<crate::ast::Arg>) -> Vec<Value> {
        let call = FnCall {
            name: name.into(),
            args,
        };
        apply_scalar(&call, topic, &crate::quantity::scale_expr)
    }

    /// The 0.25 text round: slice/pads/repeat/title, the one-sided
    /// trims, and the count family (cc codepoints, bc bytes, wc
    /// words, lc lines; `chars` the pre-0.25 alias of cc).
    #[test]
    fn text_round_functions() {
        use crate::ast::Arg;
        let s = |t: &str| Value::Str(t.to_string());
        let int = |n: i64| Arg::Lit(Value::Int(n));
        let lit = |t: &str| Arg::Lit(Value::Str(t.to_string()));
        assert_eq!(
            sc("title", s("emu WAR of 1932")),
            vec![s("Emu War Of 1932")]
        );
        assert_eq!(sc("ltrim", s("  x  ")), vec![s("x  ")]);
        assert_eq!(sc("rtrim", s("  x  ")), vec![s("  x")]);
        // counts: codepoints vs bytes vs words vs lines
        assert_eq!(sc("cc", s("льюис")), vec![Value::Int(5)]);
        assert_eq!(sc("cc", s("льюис")), vec![Value::Int(5)]);
        assert_eq!(sc("bc", s("льюис")), vec![Value::Int(10)]);
        assert_eq!(sc("wc", s("a b c")), vec![Value::Int(3)]);
        assert_eq!(sc("lc", s("a\nb\nc")), vec![Value::Int(3)]);
        // Plain UAX #29: terminators followed by space+uppercase
        // break; a mid-sentence number's dot does not. (The base
        // algorithm carries no abbreviation list — "Dr. Smith"
        // splits; that tailoring is locale data, documented as
        // out of scope.)
        let prose = s("He paid 3.50 today. Then he slept! Did he?");
        assert_eq!(
            sc("sentences", prose.clone()),
            vec![s("He paid 3.50 today."), s("Then he slept!"), s("Did he?"),]
        );
        assert_eq!(sc("sc", prose), vec![Value::Int(3)]);
        assert_eq!(
            sc("sc", s("Dr. Smith went home.")),
            vec![Value::Int(2)],
            "the untailored algorithm splits after the abbreviation"
        );
        // substr: the range predicate's spellings, on characters
        let range = |a: Option<i64>, b: Option<i64>| vec![Arg::Range(a, b)];
        assert_eq!(
            scalar_with("substr", s("abcdef"), range(Some(2), Some(4))),
            vec![s("bcd")]
        );
        assert_eq!(
            scalar_with("substr", s("abcdef"), range(None, Some(3))),
            vec![s("abc")]
        );
        assert_eq!(
            scalar_with("substr", s("abcdef"), range(Some(-2), None)),
            vec![s("ef")]
        );
        assert_eq!(
            scalar_with("substr", s("abcdef"), range(Some(4), Some(-4))),
            vec![s("")]
        );
        assert_eq!(
            scalar_with("substr", s("льюис"), range(None, Some(2))),
            vec![s("ль")]
        );
        // a bare position is the [n] reading: one character
        assert_eq!(
            scalar_with("substr", s("abcdef"), vec![int(3)]),
            vec![s("c")]
        );
        assert_eq!(
            scalar_with("substr", s("abcdef"), range(Some(5), Some(3))),
            vec![s("")]
        );
        // pads: to width, spaces by default, custom fill cut to fit
        assert_eq!(scalar_with("lpad", s("7"), vec![int(3)]), vec![s("  7")]);
        assert_eq!(
            scalar_with("lpad", s("7"), vec![int(3), lit("0")]),
            vec![s("007")]
        );
        assert_eq!(
            scalar_with("rpad", s("ab"), vec![int(5), lit("xy")]),
            vec![s("abxyx")]
        );
        assert_eq!(
            scalar_with("lpad", s("abcd"), vec![int(3)]),
            vec![s("abcd")]
        );
        // centered: the odd extra falls right (Python's center)
        assert_eq!(scalar_with("pad", s("ab"), vec![int(5)]), vec![s(" ab  ")]);
        assert_eq!(
            scalar_with("indent", s("ab"), vec![int(2)]),
            vec![s("    ab")]
        );
        assert_eq!(
            scalar_with("indent", s("ab"), vec![int(2), lit("\t")]),
            vec![s("\t\tab")]
        );
        assert_eq!(scalar_with("indent", s("ab"), vec![int(0)]), vec![s("ab")]);
        assert_eq!(scalar_with("indent", s("ab"), vec![int(-3)]), vec![s("ab")]);
        assert_eq!(
            scalar_with("pad", s("ab"), vec![int(6), lit("-")]),
            vec![s("--ab--")]
        );
        // repeat: the one home for repetition
        assert_eq!(
            scalar_with("repeat", s("ab"), vec![int(3)]),
            vec![s("ababab")]
        );
        assert_eq!(scalar_with("repeat", s("ab"), vec![int(0)]), vec![s("")]);
    }

    #[test]
    fn mean_and_alias() {
        assert_eq!(agg("mean", ints(&[1, 2, 3, 4])), vec![Value::Float(2.5)]);
        assert_eq!(agg("avg", ints(&[1, 2, 3, 4])), vec![Value::Float(2.5)]);
        assert_eq!(agg("mean", vec![]), vec![Value::Null]);
    }

    #[test]
    fn quantital_folds_type_and_refuse() {
        let q = |value: f64, written: Option<(f64, &str)>| Value::Quantity {
            value,
            base: "kg*m^2/s^3".into(),
            written: written.map(|(m, u)| (m, u.to_string())),
        };
        // Same written unit: the total keeps it.
        let watts = vec![q(142.5, Some((142.5, "W"))), q(290.0, Some((290.0, "W")))];
        assert_eq!(
            agg("sum", watts.clone()),
            vec![q(432.5, Some((432.5, "W")))]
        );
        assert_eq!(agg("mean", watts), vec![q(216.25, Some((216.25, "W")))]);
        // Mixed units of one dimension: base magnitudes, no unit.
        let mixed = vec![q(1200.0, Some((1.2, "kW"))), q(350.0, Some((350.0, "W")))];
        assert_eq!(agg("sum", mixed.clone()), vec![q(1550.0, None)]);
        assert_eq!(agg("median", mixed), vec![q(775.0, None)]);
        // Mixed DIMENSIONS refuse — watts plus meters is nonsense.
        let bad = vec![
            q(100.0, Some((100.0, "W"))),
            Value::Quantity {
                value: 2000.0,
                base: "m".into(),
                written: Some((2.0, "km".into())),
            },
        ];
        for f in ["sum", "mean", "median", "min", "max", "stddev"] {
            assert_eq!(agg(f, bad.clone()), vec![Value::Null], "{f}");
        }
        // A dimensionless stowaway refuses too.
        assert_eq!(
            agg("sum", vec![q(1.0, None), Value::Int(5)]),
            vec![Value::Null]
        );
    }

    #[test]
    fn durational_sum_and_mean() {
        let d = |secs: i64| Value::Duration { secs, nanos: 0 };
        // Durations total and average to typed durations.
        assert_eq!(
            agg("sum", vec![d(2700), d(43200), d(10800)]),
            vec![d(56700)] // PT15H45M
        );
        assert_eq!(
            agg("mean", vec![d(2700), d(43200), d(10800)]),
            vec![d(18900)] // PT5H15M
        );
        // Mixed with span text and numbers-as-seconds: still spans.
        assert_eq!(
            agg(
                "sum",
                vec![d(60), Value::Str("2min".into()), Value::Int(60)]
            ),
            vec![d(240)]
        );
        // Any unreadable element refuses the whole fold — a silent
        // partial total would lie.
        assert_eq!(
            agg("sum", vec![d(60), Value::Str("soon".into())]),
            vec![Value::Null]
        );
        // Including a *numeric* span-less element: the refusal must
        // not fall through to a numeric total that skips the
        // durations (sum over [PT1M, "5"] is not 5).
        assert_eq!(
            agg("sum", vec![d(60), Value::Str("5".into())]),
            vec![Value::Null]
        );
        assert_eq!(
            agg("mean", vec![d(60), Value::Str("5".into())]),
            vec![Value::Null]
        );
        assert_eq!(
            agg("median", vec![d(60), Value::Str("5".into())]),
            vec![Value::Null]
        );
        assert_eq!(
            agg("stddev", vec![d(60), Value::Str("5".into())]),
            vec![Value::Null]
        );
    }

    #[test]
    fn compare_is_a_total_order() {
        // The old pairwise fallbacks cycled (10 < "1z" < "9" < 10);
        // the canonical key sorts the same triple deterministically:
        // the magnitude line first, readingless text after.
        assert_eq!(
            agg(
                "sort",
                vec![
                    Value::Int(10),
                    Value::Str("1z".into()),
                    Value::Str("9".into())
                ]
            ),
            vec![
                Value::Str("9".into()),
                Value::Int(10),
                Value::Str("1z".into())
            ]
        );
        // Rank order: null, booleans, the line (readings included),
        // then text.
        assert_eq!(
            agg(
                "sort",
                vec![
                    Value::Str("b".into()),
                    Value::Str("2h".into()),
                    Value::Int(5),
                    Value::Null,
                    Value::Bool(true),
                ]
            ),
            vec![
                Value::Null,
                Value::Bool(true),
                Value::Int(5),
                Value::Str("2h".into()), // 7200 s on the line
                Value::Str("b".into()),
            ]
        );
    }

    #[test]
    fn compare_with_pays_the_custom_resolver() {
        use std::cmp::Ordering;
        // "zorkmid" exists only in the custom table: unital order
        // (10 > 5) with it, string order ("10…" < "5…") without.
        let custom = |e: &str| (e == "zorkmid").then(|| (3.0, "m".to_string()));
        let (a, b) = (
            Value::Str("10 zorkmid".into()),
            Value::Str("5 zorkmid".into()),
        );
        assert_eq!(a.compare_with(&b, &custom), Ordering::Greater);
        assert_eq!(
            a.compare_with(&b, &crate::quantity::scale_expr),
            Ordering::Less
        );
    }

    #[test]
    fn quantital_fold_lifts_text_refuses_numbers() {
        let q = |value: f64, written: Option<(f64, &str)>| Value::Quantity {
            value,
            base: "B".into(),
            written: written.map(|(v, u)| (v, u.to_string())),
        };
        // A typed quantity engages the fold; unit text lifts, as in
        // ± arithmetic — and the shared written unit survives.
        let mixed = vec![
            q(10_000_000.0, Some((10.0, "MB"))),
            Value::Str("5MB".into()),
        ];
        assert_eq!(agg("sum", mixed.clone())[0].to_string(), "15 MB");
        assert_eq!(agg("mean", mixed.clone())[0].to_string(), "7.5 MB");
        assert_eq!(agg("min", mixed)[0].to_string(), "5MB");
        // A bare number refuses, exactly as `Q + 5` does…
        assert_eq!(
            agg("sum", vec![q(10_000_000.0, None), Value::Int(5)]),
            vec![Value::Null]
        );
        // …and so do cross-dimension text and readingless text.
        assert_eq!(
            agg("sum", vec![q(10_000_000.0, None), Value::Str("5km".into())]),
            vec![Value::Null]
        );
        assert_eq!(
            agg(
                "sum",
                vec![q(10_000_000.0, None), Value::Str("soon".into())]
            ),
            vec![Value::Null]
        );
    }

    #[test]
    fn extremes_pair_unit_text_unitally() {
        // Two unit texts order by magnitude, not lexicographically
        // ("5MB" must lose to "10MB"), and a bare number reads in
        // the partner's base.
        assert_eq!(
            agg(
                "max",
                vec![Value::Str("5MB".into()), Value::Str("10MB".into())]
            ),
            vec![Value::Str("10MB".into())]
        );
        assert_eq!(
            agg(
                "min",
                vec![Value::Str("5MB".into()), Value::Str("10MB".into())]
            ),
            vec![Value::Str("5MB".into())]
        );
        assert_eq!(
            agg("max", vec![Value::Str("5MB".into()), Value::Int(10)]),
            vec![Value::Str("5MB".into())]
        );
    }

    #[test]
    fn median_survives_nan() {
        // Query arithmetic can mint NaN (float-overflow subtraction);
        // the sort must not panic on it.
        let vs = vec![Value::Float(f64::NAN), Value::Int(1), Value::Int(3)];
        assert_eq!(agg("median", vs).len(), 1);
    }

    #[test]
    fn median_odd_even_empty() {
        assert_eq!(agg("median", ints(&[5, 1, 3])), vec![Value::Int(3)]);
        assert_eq!(agg("median", ints(&[4, 1, 3, 2])), vec![Value::Float(2.5)]);
        assert_eq!(
            agg(
                "median",
                vec![Value::Float(1.5), Value::Float(2.5), Value::Float(9.0)]
            ),
            vec![Value::Float(2.5)]
        );
        assert_eq!(agg("median", vec![]), vec![Value::Null]);
    }

    #[test]
    fn spread_measures() {
        // population variance of 2,4,4,4,5,5,7,9 is 4, stddev 2
        let data = ints(&[2, 4, 4, 4, 5, 5, 7, 9]);
        assert_eq!(agg("variance", data.clone()), vec![Value::Float(4.0)]);
        assert_eq!(agg("stddev", data.clone()), vec![Value::Float(2.0)]);
        assert_eq!(agg("stddev", vec![]), vec![Value::Null]);
        // The compact spellings are the same measures.
        assert_eq!(agg("var", data.clone()), agg("variance", data.clone()));
        assert_eq!(agg("std", data.clone()), agg("stddev", data));
        assert!(known_agg("std") && known_agg("var"));
    }

    fn sample(name: &str) -> FnCall {
        FnCall {
            name: name.into(),
            args: vec![Arg::Lit(Value::Str("sample".into()))],
        }
    }

    #[test]
    fn sample_spread_uses_n_minus_one() {
        // 1,3,5,7: population variance 5, sample variance 20/3.
        let data = ints(&[1, 3, 5, 7]);
        assert_eq!(agg("variance", data.clone()), vec![Value::Float(5.0)]);
        let v = apply(&sample("variance"), data.clone(), &|_| None);
        assert_eq!(v, vec![Value::Float(20.0 / 3.0)]);
        let s = apply(&sample("stddev"), data, &|_| None);
        assert_eq!(s, vec![Value::Float((20.0f64 / 3.0).sqrt())]);
        // One value has a population spread of 0 and no sample spread.
        assert_eq!(agg("variance", ints(&[4])), vec![Value::Float(0.0)]);
        assert_eq!(
            apply(&sample("variance"), ints(&[4]), &|_| None),
            vec![Value::Null]
        );
        assert!(sample_flag(&sample("stddev")));
        assert!(!sample_flag(&FnCall {
            name: "stddev".into(),
            args: Vec::new(),
        }));
    }

    #[test]
    fn diversity_aggregates() {
        // Two equal counts: one bit; a single count: no entropy.
        assert_eq!(agg("entropy", ints(&[1, 1])), vec![Value::Float(1.0)]);
        assert_eq!(agg("entropy", ints(&[4])), vec![Value::Float(-0.0)]);
        assert_eq!(agg("entropy", ints(&[1, 1, 1, 1])), vec![Value::Float(2.0)]);
        assert_eq!(agg("entropy", vec![]), vec![Value::Null]);
        // Yule's K over counts 2,1,1: N = 4, Σc² = 6.
        assert_eq!(
            agg("yule_k", ints(&[2, 1, 1])),
            vec![Value::Float(10_000.0 * 2.0 / 16.0)]
        );
        assert_eq!(agg("yule_k", vec![]), vec![Value::Null]);
        // MTLD: with t = 0.5, `a a b b c c` — forward: a(1) a(.5 → factor,
        // reset) b(1) b(.5 → factor) c(1) c(.5 → factor): 3 factors, no
        // remainder; backward the same; 6 / 3 = 2.
        let toks: Vec<Value> = ["a", "a", "b", "b", "c", "c"]
            .iter()
            .map(|s| Value::Str(s.to_string()))
            .collect();
        let half = FnCall {
            name: "mtld".into(),
            args: vec![Arg::Lit(Value::Float(0.5))],
        };
        assert_eq!(
            apply(&half, toks.clone(), &|_| None),
            vec![Value::Float(2.0)]
        );
        // All distinct: the ratio never falls to t, so the partial
        // remainder is the only factor — (1 − 1) / (1 − t) = 0 → null.
        let distinct: Vec<Value> = ["a", "b", "c"]
            .iter()
            .map(|s| Value::Str(s.to_string()))
            .collect();
        assert_eq!(apply(&half, distinct, &|_| None), vec![Value::Null]);
        assert_eq!(agg("mtld", vec![]), vec![Value::Null]);
        // A threshold outside (0, 1) is refused.
        let bad = FnCall {
            name: "mtld".into(),
            args: vec![Arg::Lit(Value::Int(2))],
        };
        assert_eq!(apply(&bad, toks, &|_| None), vec![Value::Null]);
    }

    #[test]
    fn collocation_measures() {
        // Twenty pairs of a 100-word x and a 200-word y in a million
        // tokens: expected 0.02, so MI = log2(1000) and the t-score
        // is (20 − 0.02) / √20.
        assert_eq!(mi(20.0, 100.0, 200.0, 1e6), Value::Float(1000f64.log2()));
        assert_eq!(
            t_score(20.0, 100.0, 200.0, 1e6),
            Value::Float((20.0 - 0.02) / 20f64.sqrt())
        );
        // logDice caps at 14 when the pair is both words entirely.
        assert_eq!(log_dice(5.0, 5.0, 5.0), Value::Float(14.0));
        assert_eq!(
            log_dice(1.0, 5.0, 3.0),
            Value::Float(14.0 + (2.0 / 8.0f64).log2())
        );
        assert_eq!(mi(0.0, 1.0, 1.0, 10.0), Value::Null);
        assert_eq!(mi(3.0, 2.0, 5.0, 10.0), Value::Null);
        assert_eq!(log_dice(1.0, 0.0, 3.0), Value::Null);
    }

    #[test]
    fn distance_and_dispersion() {
        assert_eq!(
            associate("delta", &[(1.0, 0.0), (0.0, 2.0)]),
            Value::Float(1.5)
        );
        // Two equal parts: a word all in one part has DP 0.5, an
        // even split 0.
        assert_eq!(
            associate("dp", &[(4.0, 10.0), (0.0, 10.0)]),
            Value::Float(0.5)
        );
        assert_eq!(
            associate("dp", &[(2.0, 10.0), (2.0, 10.0)]),
            Value::Float(0.0)
        );
        assert_eq!(associate("dp", &[(0.0, 10.0), (0.0, 10.0)]), Value::Null);
    }

    #[test]
    fn agreement_measures() {
        let s = |x: &str| Value::Str(x.to_string());
        let pairs = vec![
            (s("a"), s("a")),
            (s("a"), s("b")),
            (s("b"), s("b")),
            (s("b"), s("b")),
        ];
        // observed 0.75; expected 0.5·0.25 + 0.5·0.75 = 0.5 → κ = 0.5
        assert_eq!(agree("kappa", &pairs), Value::Float(0.5));
        assert_eq!(agree("kappa", &[(s("a"), s("a"))]), Value::Null);
        let b = |x: bool| Value::Bool(x);
        let pairs = vec![
            (b(true), b(true)),
            (b(true), b(false)),
            (b(false), b(true)),
            (b(false), b(false)),
        ];
        assert_eq!(agree("precision", &pairs), Value::Float(0.5));
        assert_eq!(agree("recall", &pairs), Value::Float(0.5));
        assert_eq!(agree("f1", &pairs), Value::Float(0.5));
        assert_eq!(agree("precision", &[(b(false), b(false))]), Value::Null);
        assert_eq!(agree("f1", &[]), Value::Null);
    }

    #[test]
    fn association_pairs() {
        let line = [(1.0, 2.0), (2.0, 4.0), (3.0, 6.0)];
        assert_eq!(associate("corr", &line), Value::Float(1.0));
        let anti = [(1.0, 3.0), (2.0, 2.0), (3.0, 1.0)];
        assert_eq!(associate("corr", &anti), Value::Float(-1.0));
        // Spearman on a monotone but non-linear relation is 1; ties
        // take the average rank.
        let curve = [(1.0, 1.0), (2.0, 10.0), (3.0, 100.0)];
        assert_eq!(associate("spearman", &curve), Value::Float(1.0));
        assert_eq!(
            average_ranks([5.0, 1.0, 5.0].into_iter()),
            vec![2.5, 1.0, 2.5]
        );
        // Orthogonal vectors have cosine 0; parallel ones 1.
        let orth = [(1.0, 0.0), (0.0, 1.0)];
        assert_eq!(associate("cosine", &orth), Value::Float(0.0));
        assert_eq!(associate("cosine", &line), Value::Float(1.0));
        // Degenerate: one pair, or no spread.
        assert_eq!(associate("corr", &[(1.0, 2.0)]), Value::Null);
        assert_eq!(associate("corr", &[(1.0, 2.0), (1.0, 3.0)]), Value::Null);
    }

    #[test]
    fn standard_scores() {
        // 2, 4, 6: mean 4, population sd √(8/3).
        let z = zscores(&[Some(2.0), Some(4.0), Some(6.0), None], false);
        let sd = (8.0f64 / 3.0).sqrt();
        assert_eq!(
            z,
            vec![
                Value::Float(-2.0 / sd),
                Value::Float(0.0),
                Value::Float(2.0 / sd),
                Value::Null
            ]
        );
        // Sample sd is 2.
        let z = zscores(&[Some(2.0), Some(4.0), Some(6.0)], true);
        assert_eq!(
            z,
            vec![Value::Float(-1.0), Value::Float(0.0), Value::Float(1.0)]
        );
        // No spread, or a single reading: every score null.
        assert_eq!(
            zscores(&[Some(3.0), Some(3.0)], false),
            vec![Value::Null; 2]
        );
        assert_eq!(zscores(&[Some(3.0)], false), vec![Value::Null]);
        assert!(context_only("zscore") && association("spearman"));
    }

    #[test]
    fn math_scalars() {
        let c = |name: &str, args: Vec<Arg>| FnCall {
            name: name.into(),
            args,
        };
        let run = |call: &FnCall, topic: Value| apply_scalar(call, topic, &|_| None);
        assert_eq!(
            run(&c("sqrt", vec![]), Value::Int(16)),
            vec![Value::Float(4.0)]
        );
        assert_eq!(run(&c("sqrt", vec![]), Value::Int(-1)), vec![Value::Null]);
        assert_eq!(
            run(&c("log2", vec![]), Value::Int(8)),
            vec![Value::Float(3.0)]
        );
        assert_eq!(
            run(&c("log10", vec![]), Value::Int(1000)),
            vec![Value::Float(3.0)]
        );
        assert_eq!(run(&c("log", vec![]), Value::Int(0)), vec![Value::Null]);
        assert_eq!(
            run(&c("log", vec![Arg::Lit(Value::Int(2))]), Value::Int(8)),
            vec![Value::Float(3.0)]
        );
        assert_eq!(
            run(&c("log", vec![Arg::Lit(Value::Int(1))]), Value::Int(8)),
            vec![Value::Null]
        );
        assert_eq!(
            run(&c("exp", vec![]), Value::Int(0)),
            vec![Value::Float(1.0)]
        );
        assert_eq!(run(&c("exp", vec![]), Value::Int(1000)), vec![Value::Null]);
        // pow: integers stay integers while they fit.
        assert_eq!(
            run(&c("pow", vec![Arg::Lit(Value::Int(10))]), Value::Int(2)),
            vec![Value::Int(1024)]
        );
        assert_eq!(
            run(&c("pow", vec![Arg::Lit(Value::Int(100))]), Value::Int(10)),
            vec![Value::Float(1e100)]
        );
        assert_eq!(
            run(&c("pow", vec![Arg::Lit(Value::Float(0.5))]), Value::Int(9)),
            vec![Value::Float(3.0)]
        );
        assert_eq!(run(&c("pow", vec![]), Value::Int(9)), vec![Value::Null]);
        assert_eq!(
            run(
                &c("sqrt", vec![]),
                Value::Quantity {
                    value: 4.0,
                    base: "m".into(),
                    written: None,
                }
            ),
            vec![Value::Null]
        );
    }

    #[test]
    fn keyness_scalars() {
        let c = |name: &str, args: &[i64]| FnCall {
            name: name.into(),
            args: args.iter().map(|&n| Arg::Lit(Value::Int(n))).collect(),
        };
        let run = |call: &FnCall, a: i64| apply_scalar(call, Value::Int(a), &|_| None);
        // 10 of 1000 against 2 of 1000: over-represented in the first.
        let g = run(&c("loglik", &[1000, 2, 1000]), 10);
        let Value::Float(g) = g[0] else {
            panic!("{g:?}")
        };
        assert!(g > 0.0);
        // 2·[10·ln(10/6) + 2·ln(2/6)] = 5.822.
        assert!((g - 5.822).abs() < 0.001, "{g}");
        // Swapping the corpora negates the sign, same magnitude.
        let h = run(&c("loglik", &[1000, 10, 1000]), 2);
        assert_eq!(h, vec![Value::Float(-g)]);
        // A word absent from both, or a count above its total: null.
        assert_eq!(run(&c("loglik", &[1000, 0, 1000]), 0), vec![Value::Null]);
        assert_eq!(run(&c("loglik", &[5, 2, 1000]), 10), vec![Value::Null]);
        // χ² on [[10, 990], [2, 998]] is 5.37 (no correction).
        let x = run(&c("chi2", &[1000, 2, 1000]), 10);
        let Value::Float(x) = x[0] else {
            panic!("{x:?}")
        };
        assert!((x - 5.37).abs() < 0.01, "{x}");
        assert_eq!(run(&c("chi2", &[1000, 0, 1000]), 0), vec![Value::Null]);
        // Too few arguments: refused (null).
        assert_eq!(run(&c("loglik", &[1000]), 10), vec![Value::Null]);
        assert!(known_scalar("loglik") && known_agg("entropy") && known_agg("corr"));
    }

    #[test]
    #[cfg(feature = "colligo")]
    fn locale_collation() {
        let call = |loc: Option<&str>| FnCall {
            name: "sort".into(),
            args: loc
                .map(|l| vec![crate::ast::Arg::Lit(Value::Str(l.into()))])
                .unwrap_or_default(),
        };
        let words = || {
            vec![
                Value::Str("ёж".into()),
                Value::Str("Öl".into()),
                Value::Str("еда".into()),
                Value::Str("Zebra".into()),
            ]
        };
        let texts =
            |vs: Vec<Value>| -> Vec<String> { vs.into_iter().map(|v| v.to_string()).collect() };
        // Russian: ё collates adjacent to е (colligo's deliberate
        // dictionary treatment orders it as a distinct letter
        // after е; еда < ёж either way); Cyrillic reordered first.
        assert_eq!(
            texts(apply(
                &call(Some("ru-RU")),
                words(),
                &crate::quantity::scale_expr
            )),
            ["еда", "ёж", "Öl", "Zebra"]
        );
        // Swedish: Ö is its own letter, after Z.
        assert_eq!(
            texts(apply(
                &call(Some("sv-SE")),
                words(),
                &crate::quantity::scale_expr
            )),
            ["Zebra", "Öl", "еда", "ёж"]
        );
        // German: Ö sorts with O, before Z.
        assert_eq!(
            texts(apply(
                &call(Some("de-DE")),
                words(),
                &crate::quantity::scale_expr
            )),
            ["Öl", "Zebra", "еда", "ёж"]
        );
        // No locale: the standard comparison (codepoint for text).
        assert_eq!(
            texts(apply(&call(None), words(), &crate::quantity::scale_expr)),
            ["Zebra", "Öl", "еда", "ёж"]
        );
    }

    #[test]
    fn encodings() {
        let apply1 = |name: &str, v: &str| {
            apply_scalar(
                &FnCall {
                    name: name.into(),
                    args: Vec::new(),
                },
                Value::Str(v.into()),
                &crate::quantity::scale_expr,
            )
            .pop()
            .unwrap()
            .to_string()
        };
        assert_eq!(apply1("base64", "Odyssey"), "T2R5c3NleQ==");
        assert_eq!(apply1("base64url", "Odyssey"), "T2R5c3NleQ");
        assert_eq!(apply1("base32", "foobar"), "MZXW6YTBOI======");
        assert_eq!(apply1("hex", "quarb"), "7175617262");
        assert_eq!(
            apply1("sha256", "abc"),
            "ba7816bf8f01cfea414140de5dae2223b00361a396177a9cb410ff61f20015ad"
        );
    }

    #[test]
    fn numeric_scalars() {
        assert_eq!(sc("round", Value::Float(2.5)), vec![Value::Int(3)]);
        assert_eq!(sc("round", Value::Str("2.4".into())), vec![Value::Int(2)]);
        assert_eq!(sc("floor", Value::Float(2.9)), vec![Value::Int(2)]);
        assert_eq!(sc("ceil", Value::Float(2.1)), vec![Value::Int(3)]);
        assert_eq!(sc("abs", Value::Int(-4)), vec![Value::Int(4)]);
        assert_eq!(sc("abs", Value::Float(-1.5)), vec![Value::Float(1.5)]);
        assert_eq!(sc("round", Value::Str("n/a".into())), vec![Value::Null]);
    }

    fn sc_args(name: &str, args: Vec<Arg>, topic: Value) -> Vec<Value> {
        let call = FnCall {
            name: name.into(),
            args,
        };
        apply_scalar(&call, topic, &crate::quantity::scale_expr)
    }

    #[test]
    fn round_with_digits() {
        let d = |n: i64| vec![Arg::Lit(Value::Int(n))];
        // The motivating case: arithmetic noise prints clean.
        assert_eq!(
            sc_args("round", d(2), Value::Float(68.99000000000001)),
            vec![Value::Float(68.99)]
        );
        assert_eq!(
            sc_args("round", d(2), Value::Float(3.5700000000000003)),
            vec![Value::Float(3.57)]
        );
        // The argument form always answers float, `round(0)` included.
        assert_eq!(
            sc_args("round", d(0), Value::Float(2.5)),
            vec![Value::Float(3.0)]
        );
        // Negative digits reach left of the point, SQL-style.
        assert_eq!(
            sc_args("round", d(-1), Value::Float(2568.5)),
            vec![Value::Float(2570.0)]
        );
        // Numeric reading still applies; no reading is still null.
        assert_eq!(
            sc_args("round", d(1), Value::Str("2.44".into())),
            vec![Value::Float(2.4)]
        );
        assert_eq!(
            sc_args("round", d(2), Value::Str("n/a".into())),
            vec![Value::Null]
        );
        // A quantity rounds in its display unit and stays one.
        let q = Value::Quantity {
            value: 3.14159,
            base: "m".into(),
            written: Some((3.14159, "m".into())),
        };
        assert_eq!(
            sc_args("round", d(2), q),
            vec![Value::Quantity {
                value: 3.14,
                base: "m".into(),
                written: Some((3.14, "m".into())),
            }]
        );
    }

    #[test]
    fn length_alias_is_gone() {
        assert!(!known_agg("length"));
        assert!(known_agg("mean") && known_agg("avg") && known_agg("median"));
        assert!(known_scalar("round") && known_scalar("abs"));
    }

    #[test]
    fn isoformat_renders_utc() {
        // isoformat is "the reading, formatted UTC": a typed instant
        // with a written +01:00 offset renders in UTC, not its
        // display offset — the same as the text path right beside it.
        let (secs, nanos, offset_min) =
            crate::temporal::parse_iso("2024-02-15T14:26:40+01:00").unwrap();
        assert_eq!(offset_min, Some(60));
        let inst = Value::Instant {
            secs,
            nanos,
            offset_min,
        };
        assert_eq!(
            sc("isoformat", inst),
            vec![Value::Str("2024-02-15T13:26:40".into())]
        );
        assert_eq!(
            sc("isoformat", Value::Str("2024-02-15T14:26:40+01:00".into())),
            vec![Value::Str("2024-02-15T13:26:40".into())]
        );
    }

    #[test]
    fn quantity_rounders_use_written_unit() {
        // A quantity rounds in its written display unit and stays a
        // quantity, recomputing the base magnitude as rounded*factor.
        let q = Value::Quantity {
            value: 5700.0,
            base: "m".into(),
            written: Some((5.7, "km".into())),
        };
        assert_eq!(
            sc("round", q.clone()),
            vec![Value::Quantity {
                value: 6000.0,
                base: "m".into(),
                written: Some((6.0, "km".into())),
            }]
        );
        assert_eq!(
            sc("floor", q.clone()),
            vec![Value::Quantity {
                value: 5000.0,
                base: "m".into(),
                written: Some((5.0, "km".into())),
            }]
        );
        assert_eq!(
            sc("ceil", q),
            vec![Value::Quantity {
                value: 6000.0,
                base: "m".into(),
                written: Some((6.0, "km".into())),
            }]
        );
    }

    #[test]
    fn abs_over_quantity_is_null() {
        // A quantity has no numeric reading and `abs` is not a
        // rounder, so it is null rather than a bare base float.
        let q = Value::Quantity {
            value: -5000.0,
            base: "m".into(),
            written: Some((-5.0, "km".into())),
        };
        assert_eq!(sc("abs", q), vec![Value::Null]);
    }

    #[test]
    fn numeric_reductions_over_empty_are_null() {
        assert_eq!(agg("sum", vec![]), vec![Value::Null]);
        assert_eq!(agg("min", vec![]), vec![Value::Null]);
        assert_eq!(agg("max", vec![]), vec![Value::Null]);
        // Wholly non-numeric input skips every value as missing.
        assert_eq!(agg("sum", vec![Value::Str("x".into())]), vec![Value::Null]);
        // `product` keeps the spec's fold-from-1 identity.
        assert_eq!(agg("product", vec![]), vec![Value::Int(1)]);
        assert_eq!(
            agg("product", vec![Value::Str("x".into())]),
            vec![Value::Null]
        );
        // one quantity scales; two are refused, never answered bare
        let km = |v: f64| Value::Quantity {
            value: v * 1000.0,
            base: "m".into(),
            written: Some((v, "km".into())),
        };
        assert_eq!(agg("product", vec![km(2.0), Value::Int(3)]), vec![km(6.0)]);
        assert_eq!(agg("product", vec![km(2.0), km(3.0)]), vec![Value::Null]);
        assert!(crate::exec::take_refusal().unwrap().contains("units"));
    }

    #[test]
    fn rounding_past_the_integers_stays_a_float() {
        let f = |name: &str, v: Value| {
            let call = FnCall {
                name: name.into(),
                args: vec![],
            };
            apply_scalar(&call, v, &|_| None).remove(0)
        };
        assert_eq!(f("round", Value::Float(2.5)), Value::Int(3));
        assert_eq!(f("round", Value::Float(1e30)), Value::Float(1e30));
        assert_eq!(f("floor", Value::Float(-1e30)), Value::Float(-1e30));
        assert_eq!(f("ceil", Value::Float(1e19)), Value::Float(1e19));
        assert_eq!(f("abs", Value::Int(-7)), Value::Int(7));
        assert_eq!(
            f("abs", Value::Int(i64::MIN)),
            Value::Float(9_223_372_036_854_775_808.0)
        );
    }

    #[test]
    fn sum_and_product_promote_on_overflow() {
        // The all-integer fast path promotes to float on overflow,
        // matching the +/* operators rather than wrapping/panicking.
        let big = 9_000_000_000_000_000_000i64;
        assert_eq!(
            agg("sum", vec![Value::Int(big), Value::Int(big)]),
            vec![Value::Float(big as f64 + big as f64)]
        );
        let m = 4_000_000_000i64;
        assert_eq!(
            agg("product", vec![Value::Int(m), Value::Int(m)]),
            vec![Value::Float(m as f64 * m as f64)]
        );
    }

    #[test]
    fn extreme_skips_missing_and_keeps_typed() {
        // A value with no reading (a junk string) is skipped rather
        // than winning via the comparison's string fallback.
        assert_eq!(
            agg("max", vec![Value::Str("banana".into()), Value::Int(42)]),
            vec![Value::Int(42)]
        );
        assert_eq!(
            agg("min", vec![Value::Str("apple".into()), Value::Int(5)]),
            vec![Value::Int(5)]
        );
        // Numeric strings carry a reading: they compare numerically
        // and the original value is preserved (CSV-cell semantics).
        assert_eq!(
            agg(
                "max",
                vec![Value::Str("512.3292".into()), Value::Str("80".into())]
            ),
            vec![Value::Str("512.3292".into())]
        );
        // Instants keep working (the newest date), via the temporal
        // reading rather than being skipped.
        let a = Value::Instant {
            secs: 100,
            nanos: 0,
            offset_min: None,
        };
        let b = Value::Instant {
            secs: 200,
            nanos: 0,
            offset_min: None,
        };
        assert_eq!(agg("max", vec![a.clone(), b.clone()]), vec![b.clone()]);
        assert_eq!(agg("min", vec![a.clone(), b]), vec![a]);
    }
}

#[cfg(test)]
mod distance_and_quantile_tests {
    use super::*;

    fn call(name: &str, args: Vec<Arg>) -> FnCall {
        FnCall {
            name: name.into(),
            args,
        }
    }

    fn ints(ns: &[i64]) -> Vec<Value> {
        ns.iter().map(|&n| Value::Int(n)).collect()
    }

    #[test]
    fn levenshtein_counts_codepoint_edits() {
        assert_eq!(levenshtein("kitten", "sitting"), 3);
        assert_eq!(levenshtein("flaw", "lawn"), 2);
        assert_eq!(levenshtein("", "abc"), 3);
        assert_eq!(levenshtein("abc", ""), 3);
        assert_eq!(levenshtein("same", "same"), 0);
        // Codepoints, not bytes.
        assert_eq!(levenshtein("льюис", "льюиc"), 1);
        let c = call("levenshtein", vec![Arg::Lit(Value::Str("colour".into()))]);
        assert_eq!(
            apply_scalar(&c, Value::Str("color".into()), &|_| None),
            vec![Value::Int(1)]
        );
        let null = call("levenshtein", vec![Arg::Lit(Value::Null)]);
        assert_eq!(
            apply_scalar(&null, Value::Str("color".into()), &|_| None),
            vec![Value::Null]
        );
    }

    #[test]
    fn percentile_interpolates_between_the_order_statistics() {
        let p = |n: i64, input: Vec<Value>| {
            apply(
                &call("percentile", vec![Arg::Lit(Value::Int(n))]),
                input,
                &|_| None,
            )
        };
        let ten: Vec<Value> = ints(&[1, 2, 3, 4, 5, 6, 7, 8, 9, 10]);
        assert_eq!(p(90, ten.clone()), vec![Value::Float(9.1)]);
        assert_eq!(p(50, ten.clone()), vec![Value::Float(5.5)]);
        assert_eq!(p(0, ten.clone()), vec![Value::Int(1)]);
        assert_eq!(p(100, ten.clone()), vec![Value::Int(10)]);
        // The median's own results, where the rank lands on a value.
        assert_eq!(p(50, ints(&[5, 1, 3])), vec![Value::Int(3)]);
        assert_eq!(p(50, ints(&[4, 1, 3, 2])), vec![Value::Float(2.5)]);
        assert_eq!(p(50, ints(&[7])), vec![Value::Int(7)]);
        assert_eq!(p(50, vec![]), vec![Value::Null]);
        // A fractional p.
        let q = apply(
            &call("percentile", vec![Arg::Lit(Value::Float(25.5))]),
            ten.clone(),
            &|_| None,
        );
        assert_eq!(q, vec![Value::Float(3.295)]);
        // Out of range or missing: refused (null).
        assert_eq!(p(101, ten.clone()), vec![Value::Null]);
        assert_eq!(
            apply(&call("percentile", vec![]), ten, &|_| None),
            vec![Value::Null]
        );
        assert!(known_agg("percentile") && known_scalar("levenshtein"));
    }
}

#[cfg(test)]
mod atergo_and_stress_tests {
    use super::*;

    fn call(name: &str, args: Vec<Arg>) -> FnCall {
        FnCall {
            name: name.into(),
            args,
        }
    }
    fn word(s: &str) -> Arg {
        Arg::Lit(Value::Str(s.into()))
    }
    fn strs(ws: &[&str]) -> Vec<Value> {
        ws.iter().map(|w| Value::Str((*w).into())).collect()
    }
    fn texts(vs: Vec<Value>) -> Vec<String> {
        vs.into_iter().map(|v| v.to_string()).collect()
    }
    fn scalar(name: &str, args: Vec<Arg>, topic: &str) -> Vec<Value> {
        apply_scalar(&call(name, args), Value::Str(topic.into()), &|_| None)
    }
    fn parses(q: &str) -> bool {
        crate::lexer::lex(q)
            .and_then(|t| crate::parser::parse(&t))
            .is_ok()
    }

    #[test]
    fn atergo_compares_from_the_end() {
        let words = ["дом", "стол", "ёж", "еда", "нож"];
        let got = texts(apply(
            &call("sort", vec![word("atergo")]),
            strs(&words),
            &crate::quantity::scale_expr,
        ));
        // the reversed-code-point rule, spelled out
        let mut want: Vec<&str> = words.to_vec();
        want.sort_by(|a, b| a.chars().rev().cmp(b.chars().rev()));
        assert_eq!(got, want);
        // concretely: …а, then …ож before …ёж (о < ё in code points),
        // then …л, then …м
        assert_eq!(got, ["еда", "нож", "ёж", "стол", "дом"]);
        // a suffix sorts before what it ends: ties fall forward
        let got = texts(apply(
            &call("sort", vec![word("atergo")]),
            strs(&["стол", "ол", "л"]),
            &crate::quantity::scale_expr,
        ));
        assert_eq!(got, ["л", "ол", "стол"]);
    }

    #[test]
    #[cfg(feature = "colligo")]
    fn atergo_under_a_locale() {
        let words = ["ёж", "еж", "нож", "стол", "дом", "Öl"];
        let got = texts(apply(
            &call("sort", vec![word("ru-RU"), word("atergo")]),
            strs(&words),
            &crate::quantity::scale_expr,
        ));
        // Russian: ё follows е, so …же < …жё < …жо; Cyrillic before
        // Latin under the locale's reorder, from the end as well.
        assert_eq!(got, ["еж", "ёж", "нож", "стол", "дом", "Öl"]);
        // A tailoring with no contractions mirrors exactly: the
        // locale a tergo order is the locale order of the reversed
        // texts.
        let coll = colligo::Collator::builder("ru-RU")
            .allow_approximate(true)
            .build()
            .unwrap();
        let rev = |s: &str| s.chars().rev().collect::<String>();
        for a in words {
            for b in words {
                assert_eq!(
                    coll.compare_reverse(a, b),
                    coll.compare(&rev(a), &rev(b)),
                    "{a} {b}"
                );
            }
        }
    }

    #[test]
    fn sort_argument_shapes() {
        assert!(parses("/w @| sort"));
        assert!(parses("/w @| sort(ru-RU)"));
        assert!(parses("/w @| sort(atergo)"));
        assert!(parses("/w @| sort(ru-RU; atergo)"));
        assert!(parses("/w | sort(ru-RU, atergo)"));
        // the mode follows the locale, and there is one locale
        assert!(!parses("/w @| sort(atergo; ru-RU)"));
        assert!(!parses("/w @| sort(ru-RU; sv-SE)"));
        assert!(!parses("/w @| sort(atergo; atergo)"));
        assert!(!parses("/w @| sort(nonsense!)"));
    }

    #[test]
    fn stress_places_the_acute_after_the_nth_vowel() {
        let s = |n: i64, w: &str| scalar("stress", vec![Arg::Lit(Value::Int(n))], w);
        let ok = |w: &str| vec![Value::Str(w.into())];
        assert_eq!(s(3, "молоко"), ok("молоко\u{301}"));
        assert_eq!(s(-1, "молоко"), ok("молоко\u{301}"));
        assert_eq!(s(1, "молоко"), ok("мо\u{301}локо"));
        assert_eq!(s(-3, "молоко"), ok("мо\u{301}локо"));
        assert_eq!(s(4, "молоко"), vec![Value::Null]);
        assert_eq!(s(-4, "молоко"), vec![Value::Null]);
        assert_eq!(s(0, "молоко"), vec![Value::Null]);
        // ё carries its stress and is never marked; it still counts
        assert_eq!(s(1, "Ёлка"), ok("Ёлка"));
        assert_eq!(s(2, "Ёлка"), ok("Ёлка\u{301}"));
        // idempotent on a vowel already marked
        assert_eq!(s(3, "молоко\u{301}"), ok("молоко\u{301}"));
        // the Latin vowels are in the default alphabet
        assert_eq!(s(-1, "kefir"), ok("kefi\u{301}r"));
        // a named alphabet
        assert_eq!(
            scalar("stress", vec![Arg::Lit(Value::Int(1)), word("ы")], "сыр"),
            ok("сы\u{301}р")
        );
        // a position that arrives as text (the expression path)
        assert_eq!(scalar("stress", vec![word("2")], "вода"), ok("вода\u{301}"));
        // no position refuses
        assert_eq!(scalar("stress", vec![], "вода"), vec![Value::Null]);
        // a decomposed input is composed first: й is one letter
        assert_eq!(s(-1, "и\u{306}од"), ok("йо\u{301}д"));
        assert!(known_scalar("stress") && known_scalar("vowels"));
    }

    #[test]
    fn stress_family_reads_and_displays() {
        let one = |name: &str, args: Vec<Arg>, w: &str| scalar(name, args, w);
        assert_eq!(
            one("stress_at", vec![], "молоко\u{301}"),
            vec![Value::Int(3)]
        );
        assert_eq!(
            one("stress_at", vec![], "за\u{301}мок"),
            vec![Value::Int(1)]
        );
        assert_eq!(one("stress_at", vec![], "ёлка"), vec![Value::Int(1)]);
        assert_eq!(one("stress_at", vec![], "дом"), vec![Value::Int(1)]);
        assert_eq!(one("stress_at", vec![], "молоко"), vec![Value::Null]);
        assert_eq!(
            one("unstress", vec![], "молоко\u{301}"),
            vec![Value::Str("молоко".into())]
        );
        assert_eq!(
            one("unstress", vec![], "обою\u{300}доо\u{301}стрый"),
            vec![Value::Str("обоюдоострый".into())]
        );
        assert_eq!(
            one("accent", vec![word("upper")], "замо\u{301}к"),
            vec![Value::Str("замОк".into())]
        );
        assert_eq!(
            one("accent", vec![word("apostrophe")], "замо\u{301}к"),
            vec![Value::Str("замо'к".into())]
        );
        assert_eq!(
            one("accent", vec![word("acute")], "замОк"),
            vec![Value::Str("замОк".into())]
        );
        assert_eq!(
            one("accent", vec![word("none")], "замо\u{301}к"),
            vec![Value::Str("замок".into())]
        );
        assert_eq!(
            one("accent", vec![word("upper")], "ёж"),
            vec![Value::Str("Ёж".into())]
        );
        assert_eq!(
            one("accent", vec![word("apostrophe")], "ёж"),
            vec![Value::Str("ёж".into())]
        );
        assert_eq!(
            one("accent", vec![word("bogus")], "замо\u{301}к"),
            vec![Value::Null]
        );
        // widths by grapheme: the acute takes no cell
        assert_eq!(one("gc", vec![], "замо\u{301}к"), vec![Value::Int(5)]);
        assert_eq!(one("cc", vec![], "замо\u{301}к"), vec![Value::Int(6)]);
        assert_eq!(
            one("rpad", vec![Arg::Lit(Value::Int(7))], "замо\u{301}к"),
            vec![Value::Str("замо\u{301}к  ".into())]
        );
        assert_eq!(
            one("translit", vec![word("scholarly")], "щу\u{301}ка"),
            vec![Value::Str("šču\u{301}ka".into())]
        );
        assert_eq!(
            one("translit", vec![], "Москва"),
            vec![Value::Str("Moskva".into())]
        );
        assert!(known_scalar("translit") && known_scalar("accent") && known_scalar("gc"));
    }

    #[test]
    fn vowels_counts_the_letters() {
        let v = |w: &str| scalar("vowels", vec![], w);
        assert_eq!(v("молоко"), vec![Value::Int(3)]);
        assert_eq!(v("стрх"), vec![Value::Int(0)]);
        assert_eq!(v("Ёж"), vec![Value::Int(1)]);
        assert_eq!(v("kefir"), vec![Value::Int(2)]);
        assert_eq!(
            scalar("vowels", vec![word("ы")], "сыры"),
            vec![Value::Int(2)]
        );
    }

    #[test]
    fn normalization_forms() {
        let nfd = |w: &str| scalar("nfd", vec![], w);
        let nfc = |w: &str| scalar("nfc", vec![], w);
        assert_eq!(nfd("й"), vec![Value::Str("и\u{306}".into())]);
        assert_eq!(nfc("и\u{306}"), vec![Value::Str("й".into())]);
        assert_eq!(nfd("ёж"), vec![Value::Str("е\u{308}ж".into())]);
        // no precomposed Cyrillic vowel with an acute: two code
        // points under either form
        assert_eq!(nfc("о\u{301}")[0].to_string().chars().count(), 2);
        assert_eq!(nfd("о\u{301}")[0].to_string().chars().count(), 2);
        assert_eq!(
            apply_scalar(&call("nfc", vec![]), Value::Null, &|_| None),
            vec![Value::Null]
        );
        assert!(known_scalar("nfc") && known_scalar("nfd"));
    }
}