418 lines
14 KiB
Rust
418 lines
14 KiB
Rust
//! LaTeX math-mode parser for the first inline-math slice.
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//!
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//! Framing: `docs/inline-math-slice-framing.md` (rev 3), Q#MS2. This parses
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//! the deliberately small subset the slice renders — characters, groups,
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//! sub/superscripts and fractions — and nothing else. Every other LaTeX
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//! construct is an error, which Q#MS8 turns into "show the raw source".
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//!
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//! The AST is *semantic*, not presentational: `\alpha` resolves to `'α'`
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//! here, but the math-italic mapping (Q#MS2's table) belongs to layout, which
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//! is where a codepoint becomes a glyph. Keeping the split here means the AST
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//! matches what the user wrote, and a future non-italic style context does
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//! not have to unpick a decision the parser baked in.
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/// One node of the slice's math subset (Q#MS2).
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///
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/// Rev 2 of the framing folded `Symbol` into `Char`: both carried a `char`,
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/// and after symbol resolution layout cannot act on the difference.
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#[derive(Clone, Debug, PartialEq, Eq)]
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pub enum MathNode {
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/// A resolved codepoint: `x`, `2`, `+`, `α`.
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Char(char),
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/// A braced group, or the top-level expression.
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Group(Vec<MathNode>),
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/// A base with optional sub- and superscript.
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Script {
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base: Box<MathNode>,
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sub: Option<Box<MathNode>>,
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sup: Option<Box<MathNode>>,
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},
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/// `\frac{num}{den}`.
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Fraction {
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num: Box<MathNode>,
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den: Box<MathNode>,
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},
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}
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/// Why a span could not be parsed. Q#MS8 renders the raw source for all of
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/// these; the variants exist so tests can assert *which* rejection fired.
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#[derive(Clone, Debug, PartialEq, Eq)]
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pub enum MathParseError {
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/// The span held no math (`$$` after delimiter stripping).
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Empty,
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/// A `{` with no matching `}`, or a stray `}`.
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UnbalancedBrace,
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/// A control sequence outside the subset, e.g. `\sqrt`.
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UnknownCommand(String),
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/// `\frac` without two braced arguments.
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MalformedCommand(&'static str),
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/// `^` or `_` with nothing to attach to, or given twice for one base.
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MalformedScript(&'static str),
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/// A `$` inside the span: the delimiters are the caller's business, and
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/// a bare one here means detection handed us something it should not
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/// have (framing acceptance 15 — `$$x$$` degrades through this path).
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UnexpectedDollar,
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}
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/// Greek seed map (Q#MS2). Deliberately partial — growing it is mechanical.
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const GREEK: &[(&str, char)] = &[
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("alpha", 'α'),
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("beta", 'β'),
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("gamma", 'γ'),
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("delta", 'δ'),
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("epsilon", 'ε'),
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("zeta", 'ζ'),
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("eta", 'η'),
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("theta", 'θ'),
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("iota", 'ι'),
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("kappa", 'κ'),
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("lambda", 'λ'),
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("mu", 'μ'),
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("nu", 'ν'),
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("xi", 'ξ'),
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("pi", 'π'),
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("rho", 'ρ'),
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("sigma", 'σ'),
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("tau", 'τ'),
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("upsilon", 'υ'),
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("phi", 'φ'),
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("chi", 'χ'),
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("psi", 'ψ'),
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("omega", 'ω'),
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("Gamma", 'Γ'),
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("Delta", 'Δ'),
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("Theta", 'Θ'),
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("Lambda", 'Λ'),
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("Xi", 'Ξ'),
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("Pi", 'Π'),
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("Sigma", 'Σ'),
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("Upsilon", 'Υ'),
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("Phi", 'Φ'),
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("Psi", 'Ψ'),
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("Omega", 'Ω'),
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];
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/// Parse the *interior* of a math span — delimiters already stripped.
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///
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/// # Errors
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/// Returns [`MathParseError`] for anything outside the Q#MS2 subset.
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pub fn parse(source: &str) -> Result<MathNode, MathParseError> {
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let mut parser = Parser {
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chars: source.chars().collect(),
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pos: 0,
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};
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let nodes = parser.parse_sequence(None)?;
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if parser.pos < parser.chars.len() {
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// Only a stray `}` can stop the top-level sequence early.
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return Err(MathParseError::UnbalancedBrace);
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}
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if nodes.is_empty() {
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return Err(MathParseError::Empty);
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}
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Ok(MathNode::Group(nodes))
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}
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struct Parser {
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chars: Vec<char>,
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pos: usize,
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}
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impl Parser {
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fn peek(&self) -> Option<char> {
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self.chars.get(self.pos).copied()
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}
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fn bump(&mut self) -> Option<char> {
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let ch = self.peek();
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if ch.is_some() {
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self.pos += 1;
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}
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ch
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}
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/// Parse until `close` (or end of input when `None`).
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fn parse_sequence(&mut self, close: Option<char>) -> Result<Vec<MathNode>, MathParseError> {
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let mut out: Vec<MathNode> = Vec::new();
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loop {
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// Whitespace is insignificant in math mode, and it must be
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// skipped HERE rather than inside `parse_atom`: the `^`/`_`
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// dispatch below happens before atoms are read, so leaving a
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// space in front of a marker would make `x ^ 2` parse the caret
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// as a literal character.
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while self.peek().is_some_and(char::is_whitespace) {
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self.pos += 1;
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}
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match self.peek() {
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None => {
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if close.is_some() {
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return Err(MathParseError::UnbalancedBrace);
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}
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return Ok(out);
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}
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Some(ch) if Some(ch) == close => {
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self.pos += 1;
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return Ok(out);
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}
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// A `}` we were not asked to stop at is unbalanced.
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Some('}') => return Err(MathParseError::UnbalancedBrace),
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Some('$') => return Err(MathParseError::UnexpectedDollar),
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Some('^' | '_') => {
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let base = out.pop().ok_or(MathParseError::MalformedScript(
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"sub/superscript with no base",
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))?;
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out.push(self.parse_scripts(base)?);
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}
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Some(_) => {
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let atom = self.parse_atom()?;
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out.push(atom);
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}
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}
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}
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}
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/// One atom: a group, a command, or a single character.
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fn parse_atom(&mut self) -> Result<MathNode, MathParseError> {
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match self.bump() {
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Some('{') => Ok(MathNode::Group(self.parse_sequence(Some('}'))?)),
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Some('\\') => self.parse_command(),
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Some(ch) => Ok(MathNode::Char(ch)),
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None => Err(MathParseError::MalformedCommand("unexpected end of input")),
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}
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}
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fn parse_command(&mut self) -> Result<MathNode, MathParseError> {
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let mut name = String::new();
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while let Some(ch) = self.peek() {
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if ch.is_ascii_alphabetic() {
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name.push(ch);
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self.pos += 1;
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} else {
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break;
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}
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}
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if name.is_empty() {
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// `\$`, `\{` … — an escaped literal.
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return match self.bump() {
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Some(ch) => Ok(MathNode::Char(ch)),
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None => Err(MathParseError::MalformedCommand("trailing backslash")),
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};
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}
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if name == "frac" {
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let num = self.parse_required_group("\\frac numerator")?;
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let den = self.parse_required_group("\\frac denominator")?;
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return Ok(MathNode::Fraction {
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num: Box::new(num),
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den: Box::new(den),
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});
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}
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if let Some((_, ch)) = GREEK.iter().find(|(n, _)| *n == name) {
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return Ok(MathNode::Char(*ch));
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}
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Err(MathParseError::UnknownCommand(name))
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}
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/// A `{…}` argument, skipping leading whitespace.
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fn parse_required_group(&mut self, what: &'static str) -> Result<MathNode, MathParseError> {
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while self.peek().is_some_and(char::is_whitespace) {
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self.pos += 1;
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}
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match self.peek() {
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Some('{') => {
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self.pos += 1;
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Ok(MathNode::Group(self.parse_sequence(Some('}'))?))
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}
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_ => Err(MathParseError::MalformedCommand(what)),
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}
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}
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/// Attach `^`/`_` to `base`, in either order, at most one each.
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fn parse_scripts(&mut self, base: MathNode) -> Result<MathNode, MathParseError> {
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let mut sub: Option<Box<MathNode>> = None;
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let mut sup: Option<Box<MathNode>> = None;
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while let Some(marker @ ('^' | '_')) = self.peek() {
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self.pos += 1;
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let slot = self.parse_script_operand()?;
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match marker {
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'^' if sup.is_some() => {
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return Err(MathParseError::MalformedScript("double superscript"));
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}
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'_' if sub.is_some() => {
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return Err(MathParseError::MalformedScript("double subscript"));
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}
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'^' => sup = Some(Box::new(slot)),
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_ => sub = Some(Box::new(slot)),
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}
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}
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Ok(MathNode::Script {
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base: Box::new(base),
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sub,
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sup,
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})
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}
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/// The operand of `^`/`_`: a braced group, or exactly one atom.
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fn parse_script_operand(&mut self) -> Result<MathNode, MathParseError> {
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while self.peek().is_some_and(char::is_whitespace) {
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self.pos += 1;
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}
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match self.peek() {
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None => Err(MathParseError::MalformedScript("script with no operand")),
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Some('^' | '_') => Err(MathParseError::MalformedScript("script with no operand")),
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Some('}') => Err(MathParseError::MalformedScript("script with no operand")),
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Some(_) => self.parse_atom(),
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}
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}
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}
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#[cfg(test)]
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mod tests {
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use super::*;
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fn ch(c: char) -> MathNode {
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MathNode::Char(c)
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}
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fn group(nodes: Vec<MathNode>) -> MathNode {
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MathNode::Group(nodes)
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}
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#[test]
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fn plain_characters_parse_in_order() {
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assert_eq!(parse("x+1"), Ok(group(vec![ch('x'), ch('+'), ch('1')])));
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}
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#[test]
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fn superscript_and_subscript_attach_to_the_preceding_atom() {
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// Framing acceptance 1.
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assert_eq!(
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parse("x^2"),
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Ok(group(vec![MathNode::Script {
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base: Box::new(ch('x')),
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sub: None,
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sup: Some(Box::new(ch('2'))),
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}]))
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);
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assert_eq!(
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parse("x_i"),
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Ok(group(vec![MathNode::Script {
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base: Box::new(ch('x')),
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sub: Some(Box::new(ch('i'))),
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sup: None,
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}]))
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);
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}
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#[test]
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fn both_scripts_parse_in_either_order() {
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let expected = MathNode::Script {
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base: Box::new(ch('x')),
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sub: Some(Box::new(ch('i'))),
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sup: Some(Box::new(ch('2'))),
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};
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assert_eq!(parse("x_i^2"), Ok(group(vec![expected.clone()])));
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assert_eq!(parse("x^2_i"), Ok(group(vec![expected])));
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}
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#[test]
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fn braced_script_operands_group() {
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assert_eq!(
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parse("x^{i+1}"),
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Ok(group(vec![MathNode::Script {
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base: Box::new(ch('x')),
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sub: None,
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sup: Some(Box::new(group(vec![ch('i'), ch('+'), ch('1')]))),
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}]))
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);
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}
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#[test]
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fn fraction_takes_two_braced_arguments() {
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assert_eq!(
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parse(r"\frac{a}{b}"),
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Ok(group(vec![MathNode::Fraction {
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num: Box::new(group(vec![ch('a')])),
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den: Box::new(group(vec![ch('b')])),
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}]))
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);
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}
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#[test]
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fn fractions_nest() {
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// Framing acceptance 1 and 12's over-tall candidate.
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let inner = MathNode::Fraction {
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num: Box::new(group(vec![ch('a')])),
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den: Box::new(group(vec![ch('b')])),
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};
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assert_eq!(
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parse(r"\frac{\frac{a}{b}}{c}"),
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Ok(group(vec![MathNode::Fraction {
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num: Box::new(group(vec![inner])),
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den: Box::new(group(vec![ch('c')])),
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}]))
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);
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}
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#[test]
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fn greek_seed_resolves_to_codepoints_not_markup() {
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assert_eq!(parse(r"\alpha"), Ok(group(vec![ch('α')])));
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assert_eq!(parse(r"\Gamma"), Ok(group(vec![ch('Γ')])));
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// The AST stays semantic: no italic mapping here (that is layout's,
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// per this module's header and Q#MS2).
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assert_eq!(parse(r"\alpha x"), Ok(group(vec![ch('α'), ch('x')])));
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}
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#[test]
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fn whitespace_is_insignificant() {
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assert_eq!(parse("x ^ 2"), parse("x^2"));
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assert_eq!(parse(r"\frac {a} {b}"), parse(r"\frac{a}{b}"));
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}
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#[test]
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fn subset_violations_are_errors_not_panics() {
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// Framing acceptance 1 and 9.
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assert_eq!(parse(""), Err(MathParseError::Empty));
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assert_eq!(parse(" "), Err(MathParseError::Empty));
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assert_eq!(parse("{a"), Err(MathParseError::UnbalancedBrace));
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assert_eq!(parse("a}"), Err(MathParseError::UnbalancedBrace));
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assert_eq!(
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parse(r"\sqrt{2}"),
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Err(MathParseError::UnknownCommand("sqrt".to_owned()))
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);
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assert!(matches!(
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parse(r"\frac{a}"),
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Err(MathParseError::MalformedCommand(_))
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));
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assert!(matches!(
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parse(r"\frac a b"),
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Err(MathParseError::MalformedCommand(_))
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));
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assert!(matches!(
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parse("^2"),
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Err(MathParseError::MalformedScript(_))
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));
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assert!(matches!(
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parse("x^"),
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Err(MathParseError::MalformedScript(_))
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));
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assert!(matches!(
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parse("x^2^3"),
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Err(MathParseError::MalformedScript(_))
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));
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}
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#[test]
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fn an_interior_dollar_is_rejected_so_display_math_degrades() {
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// Framing acceptance 15: `$$x$$` reaches us as the interior `$x$`
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// (outer delimiters stripped), and must degrade to source rather
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// than half-render. The empty-span path covers `$$` alone.
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assert_eq!(parse("$x$"), Err(MathParseError::UnexpectedDollar));
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assert_eq!(parse(""), Err(MathParseError::Empty));
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}
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#[test]
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fn escaped_literals_survive_as_characters() {
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assert_eq!(parse(r"\{"), Ok(group(vec![ch('{')])));
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assert_eq!(parse(r"\$"), Ok(group(vec![ch('$')])));
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}
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}
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