designcraft/crates/engine/src/dtd.rs

//! Document Type Definitions: element declarations (content models) and required attributes, and
//! validation of an XML document against them (Structure ▸ Validate).

use std::collections::HashMap;

/// A content particle: a name, a sequence, a choice, or one of those repeated (`?`, `*`, `+`).
#[derive(Clone, Debug, PartialEq)]
enum Cp {
    Name(String),
    Seq(Vec<Cp>),
    Choice(Vec<Cp>),
    Rep(Box<Cp>, char),
}

#[derive(Clone, Debug, PartialEq)]
enum Model {
    Empty,
    Any,
    /// `(#PCDATA | a | b)*`: text and these elements in any order.
    Mixed(Vec<String>),
    Children(Cp),
}

/// A parsed DTD.
#[derive(Clone, Debug, Default)]
pub struct Dtd {
    elements: Vec<(String, Model)>,
    /// Element → its `#REQUIRED` attributes.
    required: HashMap<String, Vec<String>>,
}

/// A problem found by validation: where (an element path such as `Root/story[2]`) and what.
#[derive(Clone, Debug, PartialEq, serde::Serialize)]
pub struct Problem {
    pub path: String,
    pub message: String,
}

impl Dtd {
    /// Declared element names, in order.
    pub fn element_names(&self) -> impl Iterator<Item = &str> {
        self.elements.iter().map(|(n, _)| n.as_str())
    }

    fn model(&self, name: &str) -> Option<&Model> {
        self.elements.iter().find(|(n, _)| n == name).map(|(_, m)| m)
    }
}

/// Markup declarations (`<!…>`) with comments removed and quoted strings kept whole.
fn declarations(src: &str) -> Vec<String> {
    let mut out = Vec::new();
    let mut rest = src;
    while let Some(i) = rest.find("<!") {
        rest = &rest[i..];
        if rest.starts_with("<!--") {
            rest = rest.find("-->").map_or("", |j| &rest[j + 3..]);
            continue;
        }
        let mut quote = None;
        let mut end = rest.len();
        for (k, c) in rest.char_indices().skip(2) {
            match (quote, c) {
                (Some(q), c) if c == q => quote = None,
                (None, '"' | '\'') => quote = Some(c),
                (None, '>') => {
                    end = k;
                    break;
                }
                _ => {}
            }
        }
        out.push(rest[2..end].to_string());
        rest = rest.get(end + 1..).unwrap_or("");
    }
    out
}

fn tokens(s: &str) -> Vec<String> {
    let mut out = Vec::new();
    let mut cur = String::new();
    for c in s.chars() {
        if c.is_whitespace() || "(),|?*+".contains(c) {
            if !cur.is_empty() {
                out.push(std::mem::take(&mut cur));
            }
            if !c.is_whitespace() {
                out.push(c.to_string());
            }
        } else {
            cur.push(c);
        }
    }
    if !cur.is_empty() {
        out.push(cur);
    }
    out
}

/// How deeply groups may nest in a content model; parsing, matching (`ends`) and printing (`show`)
/// recurse once per level.
const MAX_CONTENT_MODEL_DEPTH: usize = 64;

/// Parse a content particle from `t[*i..]`, inside `depth` enclosing groups.
fn particle(t: &[String], i: &mut usize, depth: usize) -> Result<Cp, String> {
    let base = match t.get(*i).map(String::as_str) {
        Some("(") => {
            if depth >= MAX_CONTENT_MODEL_DEPTH {
                return Err(format!("content model nested more than {MAX_CONTENT_MODEL_DEPTH} levels"));
            }
            *i += 1;
            let mut items = vec![particle(t, i, depth + 1)?];
            let mut sep = None;
            loop {
                match t.get(*i).map(String::as_str) {
                    Some(")") => {
                        *i += 1;
                        break;
                    }
                    Some(s @ ("," | "|")) => {
                        if sep.is_some_and(|p| p != s) {
                            return Err("mixed `,` and `|` in one group".into());
                        }
                        sep = Some(if s == "," { "," } else { "|" });
                        *i += 1;
                        items.push(particle(t, i, depth + 1)?);
                    }
                    other => return Err(format!("unexpected `{}` in a content model", other.unwrap_or("end"))),
                }
            }
            if sep == Some("|") { Cp::Choice(items) } else { Cp::Seq(items) }
        }
        Some(n) if !"),|?*+".contains(n) => {
            *i += 1;
            Cp::Name(n.to_string())
        }
        other => return Err(format!("unexpected `{}` in a content model", other.unwrap_or("end"))),
    };
    Ok(match t.get(*i).map(String::as_str) {
        Some(r @ ("?" | "*" | "+")) => {
            *i += 1;
            Cp::Rep(Box::new(base), r.chars().next().unwrap_or('*'))
        }
        _ => base,
    })
}

fn parse_model(s: &str) -> Result<Model, String> {
    let s = s.trim();
    match s {
        "EMPTY" => return Ok(Model::Empty),
        "ANY" => return Ok(Model::Any),
        _ => {}
    }
    if s.contains("#PCDATA") {
        let t = tokens(&s.replace("#PCDATA", " #PCDATA "));
        return Ok(Model::Mixed(t.into_iter().filter(|x| !"()|*".contains(x.as_str()) && x != "#PCDATA").collect()));
    }
    let t = tokens(s);
    let mut i = 0;
    let cp = particle(&t, &mut i, 0)?;
    if i != t.len() {
        return Err(format!("unexpected `{}` after the content model", t[i]));
    }
    Ok(Model::Children(cp))
}

const MAX_PARAMETER_ENTITY_EXPANSION: usize = 16 * 1024 * 1024;
/// How deeply parameter entities may nest: a reference in the DTD is level 1, a reference in its
/// value level 2, and so on.
const MAX_PARAMETER_ENTITY_DEPTH: usize = 64;

/// Expand `%name;` references, one level per round, until a round changes nothing.
fn expand_parameter_entities(src: &str, ents: &[(String, String)]) -> Result<String, String> {
    let mut entities = HashMap::new();
    for (name, value) in ents {
        entities.entry(name.as_str()).or_insert(value.as_str());
    }
    let limit = MAX_PARAMETER_ENTITY_EXPANSION.max(src.len());
    let append = |out: &mut String, value: &str| -> Result<(), String> {
        if value.len() > limit.saturating_sub(out.len()) {
            return Err(format!("parameter entities expand to more than {limit} bytes"));
        }
        out.push_str(value);
        Ok(())
    };
    let too_deep = || format!("parameter entities refer to themselves or nest deeper than {MAX_PARAMETER_ENTITY_DEPTH} levels");
    let mut text = src.to_string();
    // The round after the deepest level changes nothing, hence one more round than levels.
    for _ in 0..=MAX_PARAMETER_ENTITY_DEPTH {
        let mut out = String::with_capacity(text.len());
        let mut rest = text.as_str();
        let mut changed = false;
        while let Some(i) = rest.find('%') {
            let (prefix, reference) = rest.split_at(i);
            append(&mut out, prefix)?;
            // `find` points to an ASCII `%`, so both split positions are UTF-8 boundaries.
            rest = reference.split_at(1).1;
            // A name has no whitespace and no `%` (`parse` ends a name at whitespace), whatever its
            // length: the search for the closing `;` stops at the first of those, so the searches of
            // a round never overlap and a round stays linear in the text.
            let end =
                rest.bytes().position(|b| matches!(b, b';' | b'%') || b.is_ascii_whitespace()).filter(|&k| rest.as_bytes().get(k) == Some(&b';'));
            if let Some(end) = end
                && let Some(value) = rest.get(..end).and_then(|name| entities.get(name))
            {
                // A value that is its own reference (`<!ENTITY % a "%a;">`) never gets anywhere.
                if reference.get(..end + 2) == Some(*value) {
                    return Err(too_deep());
                }
                append(&mut out, value)?;
                changed = true;
                rest = rest.split_at(end + 1).1;
                continue;
            }
            append(&mut out, "%")?;
        }
        append(&mut out, rest)?;
        text = out;
        if !changed {
            return Ok(text);
        }
    }
    Err(too_deep())
}

/// Parse a DTD (its element and attribute-list declarations; parameter entities are expanded).
pub fn parse(src: &str) -> Result<Dtd, String> {
    // Parameter entities first, then expand references and read the declarations again.
    let mut ents: Vec<(String, String)> = Vec::new();
    for d in declarations(src) {
        if let Some(rest) = d.strip_prefix("ENTITY") {
            let rest = rest.trim_start();
            if let Some(rest) = rest.strip_prefix('%') {
                let rest = rest.trim_start();
                let name: String = rest.chars().take_while(|c| !c.is_whitespace()).collect();
                let val = rest[name.len()..].trim();
                let q = val.chars().next().unwrap_or('"');
                if let Some(v) = val.strip_prefix(q).and_then(|v| v.find(q).map(|e| &v[..e])) {
                    ents.push((name, v.to_string()));
                }
            }
        }
    }
    let text = expand_parameter_entities(src, &ents)?;
    let mut dtd = Dtd::default();
    for d in declarations(&text) {
        if let Some(rest) = d.strip_prefix("ELEMENT") {
            let rest = rest.trim_start();
            let name: String = rest.chars().take_while(|c| !c.is_whitespace()).collect();
            let model = parse_model(&rest[name.len()..]).map_err(|e| format!("<!ELEMENT {name}>: {e}"))?;
            dtd.elements.push((name, model));
        } else if let Some(rest) = d.strip_prefix("ATTLIST") {
            // name (attr type default)*; only `#REQUIRED` matters here.
            let mut words = Vec::new();
            let mut cur = String::new();
            let mut quote = None;
            let mut group = 0;
            for c in rest.chars() {
                match (quote, c) {
                    (Some(q), c) if c == q => {
                        quote = None;
                        cur.push(c);
                    }
                    (Some(_), c) => cur.push(c),
                    (None, '"' | '\'') => {
                        quote = Some(c);
                        cur.push(c);
                    }
                    (None, '(') => {
                        group += 1;
                        cur.push(c);
                    }
                    (None, ')') => {
                        group -= 1;
                        cur.push(c);
                    }
                    (None, c) if c.is_whitespace() && group == 0 => {
                        if !cur.is_empty() {
                            words.push(std::mem::take(&mut cur));
                        }
                    }
                    (None, c) => cur.push(c),
                }
            }
            if !cur.is_empty() {
                words.push(cur);
            }
            let Some((el, attrs)) = words.split_first() else { continue };
            let mut k = 0;
            while k + 2 < attrs.len() {
                let name = &attrs[k];
                let default = attrs.get(k + 2).map(String::as_str).unwrap_or("");
                if default == "#REQUIRED" {
                    dtd.required.entry(el.clone()).or_default().push(name.clone());
                }
                k += if default == "#FIXED" { 4 } else { 3 };
            }
        }
    }
    if dtd.elements.is_empty() {
        return Err("no element declarations".into());
    }
    Ok(dtd)
}

/// What `ends` has worked out for one sequence of children: the end positions of a group (by the
/// address of its node, which lives as long as the model) from a position.
type EndsMemo = HashMap<(usize, usize), Vec<usize>>;

/// End positions after `cp` matches a prefix of `seq[i..]`.
///
/// The positions of each group are worked out once per start position (`memo`): nested repetitions
/// such as `((a*)*)*` ask the inner group for the same positions again and again, which is
/// exponential in their depth without it.
fn ends(cp: &Cp, seq: &[&str], i: usize, memo: &mut EndsMemo) -> Vec<usize> {
    if let Cp::Name(n) = cp {
        return if seq.get(i) == Some(&n.as_str()) { vec![i + 1] } else { vec![] };
    }
    let key = (std::ptr::from_ref(cp) as usize, i);
    if let Some(done) = memo.get(&key) {
        return done.clone();
    }
    let mut out: Vec<usize> = match cp {
        Cp::Name(_) => vec![],
        // Keep the positions after each item a set: as a list of every path, `(a?, a?, …)` doubles per item.
        Cp::Seq(items) => {
            let mut at = vec![i];
            for c in items {
                let mut next = Vec::new();
                for p in at {
                    next.extend(ends(c, seq, p, memo));
                }
                next.sort_unstable();
                next.dedup();
                at = next;
            }
            at
        }
        Cp::Choice(items) => {
            let mut all = Vec::new();
            for c in items {
                all.extend(ends(c, seq, i, memo));
            }
            all
        }
        Cp::Rep(c, r) => {
            let mut all = if *r == '+' { vec![] } else { vec![i] };
            let mut frontier = ends(c, seq, i, memo);
            if *r == '?' {
                all.extend(frontier);
            } else {
                while !frontier.is_empty() {
                    let new: Vec<usize> = frontier.iter().copied().filter(|p| !all.contains(p)).collect();
                    all.extend(&new);
                    let mut next = Vec::new();
                    for p in new.into_iter().filter(|&p| p > i) {
                        next.extend(ends(c, seq, p, memo).into_iter().filter(|p| !all.contains(p)));
                    }
                    // Two paths to one position are one position: kept apart they multiply per round.
                    next.sort_unstable();
                    next.dedup();
                    frontier = next;
                }
            }
            all
        }
    };
    out.sort_unstable();
    out.dedup();
    memo.insert(key, out.clone());
    out
}

fn show(cp: &Cp) -> String {
    match cp {
        Cp::Name(n) => n.clone(),
        Cp::Seq(v) => format!("({})", v.iter().map(show).collect::<Vec<_>>().join(", ")),
        Cp::Choice(v) => format!("({})", v.iter().map(show).collect::<Vec<_>>().join(" | ")),
        Cp::Rep(c, r) => format!("{}{r}", show(c)),
    }
}

/// An element of the document being validated.
struct Node {
    name: String,
    attrs: Vec<String>,
    children: Vec<Node>,
    text: bool,
}

fn read_tree(xml: &str) -> Result<Node, String> {
    use quick_xml::events::Event;
    let mut r = quick_xml::Reader::from_str(xml);
    let mut stack: Vec<Node> = Vec::new();
    let node = |e: &quick_xml::events::BytesStart| Node {
        name: String::from_utf8_lossy(e.name().as_ref()).to_string(),
        attrs: e.attributes().flatten().map(|a| String::from_utf8_lossy(a.key.as_ref()).to_string()).collect(),
        children: vec![],
        text: false,
    };
    loop {
        match r.read_event().map_err(|e| e.to_string())? {
            Event::Start(e) => stack.push(node(&e)),
            Event::Empty(e) => {
                let n = node(&e);
                match stack.last_mut() {
                    Some(p) => p.children.push(n),
                    None => return Ok(n),
                }
            }
            Event::End(_) => {
                let n = stack.pop().ok_or("unbalanced end tag")?;
                match stack.last_mut() {
                    Some(p) => p.children.push(n),
                    None => return Ok(n),
                }
            }
            Event::Text(t) => {
                if let Some(p) = stack.last_mut()
                    && !t.iter().all(u8::is_ascii_whitespace)
                {
                    p.text = true;
                }
            }
            Event::CData(_) | Event::GeneralRef(_) => {
                if let Some(p) = stack.last_mut() {
                    p.text = true;
                }
            }
            Event::Eof => return Err("no root element".into()),
            _ => {}
        }
    }
}

fn check(dtd: &Dtd, n: &Node, path: &str, out: &mut Vec<Problem>) {
    let mut problem = |m: String| out.push(Problem { path: path.to_string(), message: m });
    match dtd.model(&n.name) {
        None => problem(format!("`{}` isn't declared in the DTD", n.name)),
        Some(Model::Any) => {}
        Some(Model::Empty) => {
            if n.text || !n.children.is_empty() {
                problem(format!("`{}` should be empty", n.name));
            }
        }
        Some(Model::Mixed(allowed)) => {
            for c in &n.children {
                if !allowed.contains(&c.name) {
                    problem(format!("`{}` isn't allowed in `{}`", c.name, n.name));
                }
            }
        }
        Some(Model::Children(cp)) => {
            if n.text {
                problem(format!("`{}` can't contain text", n.name));
            }
            let seq: Vec<&str> = n.children.iter().map(|c| c.name.as_str()).collect();
            if !ends(cp, &seq, 0, &mut EndsMemo::new()).contains(&seq.len()) {
                let got = if seq.is_empty() { "nothing".to_string() } else { seq.join(", ") };
                problem(format!("`{}` contains {got}; the DTD asks for {}", n.name, show(cp)));
            }
        }
    }
    for a in dtd.required.get(&n.name).into_iter().flatten() {
        if !n.attrs.contains(a) {
            problem(format!("`{}` is missing the required attribute `{a}`", n.name));
        }
    }
    let mut seen: HashMap<&str, usize> = HashMap::new();
    for c in &n.children {
        let k = seen.entry(c.name.as_str()).or_default();
        *k += 1;
        check(dtd, c, &format!("{path}/{}[{k}]", c.name), out);
    }
}

/// Validate `xml` against `dtd`; an empty list when it's valid.
pub fn validate(dtd: &Dtd, xml: &str) -> Vec<Problem> {
    match read_tree(xml) {
        Ok(root) => {
            let mut out = Vec::new();
            let path = root.name.clone();
            check(dtd, &root, &path, &mut out);
            out
        }
        Err(e) => vec![Problem { path: String::new(), message: format!("not well-formed XML: {e}") }],
    }
}

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

    const DTD: &str = r##"<!-- an article -->
<!ENTITY % inline "#PCDATA | em | term">
<!ELEMENT Root (story+, figure*)>
<!ELEMENT story (title, (para | list)*)>
<!ELEMENT title (%inline;)*>
<!ELEMENT para (%inline;)*>
<!ELEMENT list (para+)>
<!ELEMENT em (#PCDATA)>
<!ELEMENT term (#PCDATA)>
<!ELEMENT figure EMPTY>
<!ATTLIST figure href CDATA #REQUIRED alt CDATA "a > b" kind (photo|chart) "photo">"##;

    #[test]
    fn content_models_and_required_attributes() {
        let dtd = parse(DTD).unwrap();
        assert_eq!(dtd.element_names().count(), 8);
        let ok = r#"<Root><story><title>T <em>x</em></title><para>a</para><list><para>b</para></list></story><figure href="a.png"/></Root>"#;
        assert_eq!(validate(&dtd, ok), vec![]);
        let bad = r#"<Root><story><para>no title</para></story><figure/><figure href="b"><em>x</em></figure><aside/></Root>"#;
        let p = validate(&dtd, bad);
        let msgs: Vec<String> = p.iter().map(|p| format!("{}: {}", p.path, p.message)).collect();
        assert!(msgs.iter().any(|m| m.starts_with("Root/story[1]: `story` contains para; the DTD asks for (title, (para | list)*)")), "{msgs:?}");
        assert!(msgs.iter().any(|m| m == "Root/figure[1]: `figure` is missing the required attribute `href`"), "{msgs:?}");
        assert!(msgs.iter().any(|m| m == "Root/figure[2]: `figure` should be empty"), "{msgs:?}");
        assert!(msgs.iter().any(|m| m == "Root/aside[1]: `aside` isn't declared in the DTD"), "{msgs:?}");
        // The root's model fails too (aside isn't in it).
        assert!(msgs.iter().any(|m| m.starts_with("Root: ")), "{msgs:?}");
        // Text where only elements are allowed; an element not in a mixed model.
        let p = validate(&dtd, "<Root><story>loose<title><list/></title></story></Root>");
        assert!(p.iter().any(|p| p.message == "`story` can't contain text"), "{p:?}");
        assert!(p.iter().any(|p| p.message == "`list` isn't allowed in `title`"), "{p:?}");
        assert!(parse("<!ELEMENT a (b, c | d)>").is_err());
        assert!(parse("just text").is_err());
    }

    #[test]
    fn repetition_matches_like_a_regular_expression() {
        let dtd = parse("<!ELEMENT r ((a, b?)+, c*)><!ELEMENT a EMPTY><!ELEMENT b EMPTY><!ELEMENT c EMPTY>").unwrap();
        for (xml, ok) in [
            ("<r><a/></r>", true),
            ("<r><a/><b/><a/><c/><c/></r>", true),
            ("<r><a/><a/><b/></r>", true),
            ("<r><b/></r>", false),
            ("<r><a/><b/><b/></r>", false),
            ("<r><a/><c/><a/></r>", false),
            ("<r/>", false),
        ] {
            assert_eq!(validate(&dtd, xml).is_empty(), ok, "{xml}");
        }
    }

    #[test]
    fn parameter_entity_bomb_is_rejected() {
        let mut src = String::new();
        for i in (0..10).rev() {
            let value = if i == 0 { "x".to_string() } else { format!("%e{};", i - 1).repeat(8) };
            src.push_str(&format!("<!ENTITY % e{i} \"{value}\">\n"));
        }
        src.push_str("<!ELEMENT root (%e9;)>");
        match parse(&src) {
            Err(error) => assert!(error.contains("parameter entities expand"), "{error}"),
            Ok(_) => panic!("parameter entity expansion bomb was accepted"),
        }
    }

    /// `n` parameter entities, `e{i}` referring to `e{i-1}` and `e0` being `x`, declared in ascending
    /// or descending order, and an element `root` whose model uses the last one.
    fn entity_chain(n: usize, ascending: bool) -> String {
        let mut order: Vec<usize> = (0..n).collect();
        if !ascending {
            order.reverse();
        }
        let mut src = String::new();
        for i in order {
            let value = if i == 0 { "x".to_string() } else { format!("%e{};", i - 1) };
            src.push_str(&format!("<!ENTITY % e{i} \"{value}\">\n"));
        }
        src.push_str(&format!("<!ELEMENT root (%e{};)><!ELEMENT x EMPTY>", n - 1));
        src
    }

    #[test]
    fn parameter_entity_reverse_chain_expands_completely() {
        let dtd = parse(&entity_chain(20, false)).unwrap();
        assert_eq!(validate(&dtd, "<root><x/></root>"), vec![]);
    }

    #[test]
    fn parameter_entity_ascending_chain_expands_completely() {
        // With `e0` declared first, replacing the entities in declaration order resolves one level per pass.
        let dtd = parse(&entity_chain(20, true)).unwrap();
        assert_eq!(validate(&dtd, "<root><x/></root>"), vec![]);
    }

    #[test]
    fn parameter_entity_cycle_is_refused() {
        // Two entities that refer to each other, and one whose value is its own reference.
        for src in ["<!ENTITY % a \"%b;\"><!ENTITY % b \"%a;\"><!ELEMENT root (%a;)>", "<!ENTITY % a \"%a;\"><!ELEMENT root (%a;)>"] {
            match parse(src) {
                Err(error) => assert!(error.contains("refer to themselves"), "{src}: {error}"),
                Ok(dtd) => panic!("a cycle was accepted ({src}): {:?}", dtd.model("root")),
            }
        }
    }

    #[test]
    fn parameter_entity_chain_deeper_than_the_limit_is_refused() {
        for ascending in [true, false] {
            for n in [65, 70] {
                match parse(&entity_chain(n, ascending)) {
                    Err(error) => assert!(error.contains("deeper than 64 levels"), "{n}, {ascending}: {error}"),
                    Ok(dtd) => panic!("a chain of {n} ({ascending}) was accepted: {:?}", dtd.model("root")),
                }
            }
            let dtd = parse(&entity_chain(64, ascending)).unwrap();
            assert_eq!(validate(&dtd, "<root><x/></root>"), vec![], "{ascending}");
        }
    }

    #[test]
    fn parameter_entity_name_scan_stops_at_the_next_percent() {
        // A name never contains `%`, so the search for the closing `;` stops at the next one: the
        // searches of a run of `%` don't overlap and a round stays linear. (Looking past the next
        // `%` would expand this reference to an entity that is named `a%b`.)
        let entities = [("a%b".to_string(), "X".to_string())];
        assert_eq!(expand_parameter_entities("%a%b;", &entities), Ok("%a%b;".to_string()));
        // A run of `%` around a real reference still finds it.
        let entities = [("model".to_string(), "EMPTY".to_string())];
        assert_eq!(expand_parameter_entities("%%%model;%%", &entities), Ok("%%EMPTY%%".to_string()));
    }

    #[test]
    fn parameter_entity_with_a_long_name_expands() {
        // A name can be any length: the search for the closing `;` has no window.
        let name = "n".repeat(300);
        let dtd = parse(&format!("<!ENTITY % {name} \"EMPTY\"><!ELEMENT root %{name};>")).unwrap();
        assert_eq!(dtd.model("root"), Some(&Model::Empty));
    }

    #[test]
    fn percent_in_text_without_a_reference_is_left_alone() {
        // `100% sure` (a space ends the search) and a `%` followed by 1 MiB without a `;` are text.
        let text = format!("100% sure, %{}", "a".repeat(1 << 20));
        let entities = [("a".to_string(), "X".to_string())];
        assert_eq!(expand_parameter_entities(&text, &entities), Ok(text.clone()));
    }

    /// `a` inside `levels` groups, each repeated: `((a)*)*…`.
    fn nested_repetitions(levels: usize) -> String {
        format!("{}a{}", "(".repeat(levels), ")*".repeat(levels))
    }

    #[test]
    fn nested_repetitions_validate_without_going_exponential() {
        // Ten levels over 100 children: each level asked the one below for the same positions again
        // and again, about 10^14 steps without the memo of `ends`.
        let dtd = parse(&format!("<!ELEMENT root {}><!ELEMENT a EMPTY><!ELEMENT b EMPTY>", nested_repetitions(10))).unwrap();
        assert_eq!(validate(&dtd, &format!("<root>{}</root>", "<a/>".repeat(100))), vec![]);
        let problems = validate(&dtd, &format!("<root>{}<b/></root>", "<a/>".repeat(100)));
        assert_eq!(problems.len(), 1, "{problems:?}");
    }

    #[test]
    fn repetition_of_a_sequence_of_optional_elements_validates() {
        // `(a, a?, a?, a?, a?, a?)*` over 90 children: every way to split the children among the
        // repetitions reaches the same positions, and the paths used to be kept apart in each round.
        let dtd = parse("<!ELEMENT r (a, a?, a?, a?, a?, a?)*><!ELEMENT a EMPTY><!ELEMENT b EMPTY>").unwrap();
        assert_eq!(validate(&dtd, &format!("<r>{}</r>", "<a/>".repeat(90))), vec![]);
        let problems = validate(&dtd, &format!("<r>{}<b/></r>", "<a/>".repeat(90)));
        assert_eq!(problems.len(), 1, "{problems:?}");
    }

    #[test]
    fn parameter_entity_first_declaration_wins() {
        let dtd = parse("<!ENTITY % model \"EMPTY\"><!ENTITY % model \"ANY\"><!ELEMENT root %model;>").unwrap();
        assert_eq!(dtd.model("root"), Some(&Model::Empty));
    }

    #[test]
    fn parameter_entity_unknown_and_lone_percent_are_preserved() {
        let src = "%nothing; <!ELEMENT root EMPTY> %";
        let dtd = parse(src).unwrap();
        assert_eq!(dtd.model("root"), Some(&Model::Empty));
        assert_eq!(expand_parameter_entities("%nothing; %", &[]), Ok("%nothing; %".to_string()));
    }

    #[test]
    fn parameter_entity_many_flat_declarations_parse() {
        let mut src = String::new();
        for i in 0..5000 {
            src.push_str(&format!("<!ENTITY % e{i} \"x\">\n"));
        }
        src.push_str("<!ELEMENT root (%e0;, %e2499;, %e4999;)><!ELEMENT x EMPTY>");
        let dtd = parse(&src).unwrap();
        assert_eq!(validate(&dtd, "<root><x/><x/><x/></root>"), vec![]);
    }

    /// An element `root` whose content model is `a` inside `depth` nested groups.
    fn nested_model(depth: usize) -> String {
        format!("<!ELEMENT root {}a{}><!ELEMENT a EMPTY>", "(".repeat(depth), ")".repeat(depth))
    }

    #[test]
    fn content_model_nested_100000_deep_is_refused() {
        // One recursion per `(` overflowed the stack: an abort, not a panic.
        match parse(&nested_model(100_000)) {
            Err(error) => assert!(error.contains("nested more than 64 levels"), "{error}"),
            Ok(_) => panic!("a content model nested 100000 deep was accepted"),
        }
    }

    #[test]
    fn content_model_nesting_limit() {
        let dtd = parse(&nested_model(64)).unwrap();
        assert_eq!(validate(&dtd, "<root><a/></root>"), vec![]);
        assert_eq!(validate(&dtd, "<root/>").len(), 1);
        match parse(&nested_model(65)) {
            Err(error) => assert_eq!(error, "<!ELEMENT root>: content model nested more than 64 levels"),
            Ok(_) => panic!("a content model nested 65 deep was accepted"),
        }
    }

    #[test]
    fn sequence_of_40_optional_elements_validates() {
        // Keeping every path through the sequence meant 2^40 positions here.
        let dtd = parse(&format!("<!ELEMENT r ({})><!ELEMENT a EMPTY>", ["a?"; 40].join(", "))).unwrap();
        assert_eq!(validate(&dtd, &format!("<r>{}</r>", "<a/>".repeat(40))), vec![]);
        let problems = validate(&dtd, &format!("<r>{}</r>", "<a/>".repeat(41)));
        assert_eq!(problems.len(), 1, "{problems:?}");
        assert!(problems[0].message.starts_with("`r` contains a, a, a"), "{problems:?}");
    }
}