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//! Derivative parsing: diff(), partial(), Leibniz notation, prime notation.
use super::*;
impl TextParser {
/// Parses `diff(expr, var)` or `diff(expr, var, order)` into `ExprKind::Derivative`.
pub(super) fn parse_diff_function(&mut self) -> ParseResult<Expression> {
self.consume(Token::LParen)?;
let expr = self.parse_expression()?;
self.consume(Token::Comma)?;
let var = self.expect_identifier("variable name")?;
let order = if self.check(&Token::Comma) {
self.next();
self.expect_positive_integer("derivative order")?
} else {
1
};
self.consume(Token::RParen)?;
Ok(ExprKind::Derivative {
expr: Box::new(expr),
var,
order,
}
.into())
}
/// Parses `partial(expr, var[, order_or_var2[, ...]])` into `ExprKind::PartialDerivative`.
///
/// - `partial(f, x)` → first partial w.r.t. x
/// - `partial(f, x, 2)` → second partial w.r.t. x
/// - `partial(f, x, y)` → mixed partial ∂²f/∂x∂y (nested)
pub(super) fn parse_partial_function(&mut self) -> ParseResult<Expression> {
self.consume(Token::LParen)?;
let expr = self.parse_expression()?;
self.consume(Token::Comma)?;
let first_var = self.expect_identifier("variable name")?;
if !self.check(&Token::Comma) {
self.consume(Token::RParen)?;
return Ok(ExprKind::PartialDerivative {
expr: Box::new(expr),
var: first_var,
order: 1,
}
.into());
}
self.next(); // consume comma
// Peek: integer → nth-order partial; identifier → mixed partial
if let Some(token) = self.peek() {
match &token.value {
Token::Integer(n) => {
let order = *n as u32;
self.next();
let result = self.parse_additional_partials(
ExprKind::PartialDerivative {
expr: Box::new(expr),
var: first_var,
order,
}
.into(),
)?;
self.consume(Token::RParen)?;
return Ok(result);
}
Token::Identifier(_) => {
let second_var = self.expect_identifier("variable name")?;
let inner: Expression = ExprKind::PartialDerivative {
expr: Box::new(expr),
var: second_var,
order: 1,
}
.into();
let wrapped: Expression = ExprKind::PartialDerivative {
expr: Box::new(inner),
var: first_var,
order: 1,
}
.into();
let result = self.parse_additional_partials_simple(wrapped)?;
self.consume(Token::RParen)?;
return Ok(result);
}
_ => {
let span = token.span;
return Err(ParseError::unexpected_token(
vec!["integer order or variable name"],
format!("{}", token.value),
Some(span),
));
}
}
}
self.consume(Token::RParen)?;
Ok(ExprKind::PartialDerivative {
expr: Box::new(expr),
var: first_var,
order: 1,
}
.into())
}
/// Accumulate additional `, var[, order]` pairs for nth-order partials.
fn parse_additional_partials(&mut self, mut result: Expression) -> ParseResult<Expression> {
while self.check(&Token::Comma) {
self.next();
let var = self.expect_identifier("variable name")?;
let ord = if self.check(&Token::Comma) {
if let Some(t) = self.peek_ahead(1) {
if matches!(t.value, Token::Integer(_)) {
self.next(); // comma
self.expect_positive_integer("derivative order")?
} else {
1
}
} else {
1
}
} else {
1
};
result = ExprKind::PartialDerivative {
expr: Box::new(result),
var,
order: ord,
}
.into();
}
Ok(result)
}
/// Accumulate additional `, var` pairs for mixed partials (order always 1).
fn parse_additional_partials_simple(
&mut self,
mut result: Expression,
) -> ParseResult<Expression> {
while self.check(&Token::Comma) {
self.next();
let var = self.expect_identifier("variable name")?;
result = ExprKind::PartialDerivative {
expr: Box::new(result),
var,
order: 1,
}
.into();
}
Ok(result)
}
/// Tries to parse Leibniz derivative notation: `dy/dx`, `d2y/dx2`, `d(expr)/dx`.
///
/// Returns `None` if the identifier doesn't match the pattern or lookahead fails.
pub(super) fn try_parse_leibniz_derivative(
&mut self,
name: &str,
) -> ParseResult<Option<Expression>> {
// Must start with 'd'
if !name.starts_with('d') {
return Ok(None);
}
// Special case: d(expr)/dx — operator form
if name == "d" && self.check(&Token::LParen) {
return self.try_parse_operator_derivative();
}
if name.len() < 2 {
return Ok(None);
}
// Lookahead: next must be `/` followed by identifier starting with `d`
let is_slash = self
.peek()
.map(|t| matches!(t.value, Token::Slash))
.unwrap_or(false);
if !is_slash {
return Ok(None);
}
let denom_name = self
.peek_ahead(1)
.and_then(|t| {
if let Token::Identifier(s) = &t.value {
Some(s.clone())
} else {
None
}
})
.unwrap_or_default();
if !denom_name.starts_with('d') || denom_name.len() < 2 {
return Ok(None);
}
// Parse numerator: d[order]<func_name>
let after_d = &name[1..];
let (num_order, func_name) = split_order_prefix(after_d);
if func_name.is_empty() {
return Ok(None);
}
// Parse denominator: d<var>[order]
let after_d_denom = &denom_name[1..];
let (denom_order, var_name) = split_order_suffix(after_d_denom);
if var_name.is_empty() {
return Ok(None);
}
// Orders must match (or numerator has no explicit order = 1)
let order = if num_order > 0 && denom_order > 0 {
if num_order != denom_order {
return Ok(None); // Mismatched orders, not a valid derivative
}
num_order
} else if num_order > 0 {
num_order
} else if denom_order > 0 {
denom_order
} else {
1
};
// Commit: consume `/` and denominator identifier
self.next(); // Slash
self.next(); // denominator identifier
Ok(Some(
ExprKind::Derivative {
expr: Box::new(Expression::variable(func_name.to_string()).into()),
var: var_name.to_string(),
order,
}
.into(),
))
}
/// Tries to parse `d(expr)/dx` or `d(expr)/d(var)` operator-form derivative.
///
/// Called when we've consumed identifier `d` and the next token is `(`.
/// Returns `None` if the pattern doesn't match (falls back to function call).
fn try_parse_operator_derivative(&mut self) -> ParseResult<Option<Expression>> {
// We need: ( expr ) / d<var> or ( expr ) / d ( var )
// Lookahead to verify the /d pattern before committing
// Save position for backtrack
let saved_pos = self.pos;
// Parse the parenthesized expression
self.next(); // consume (
let expr = match self.parse_expression() {
Ok(e) => e,
Err(_) => {
self.pos = saved_pos;
return Ok(None);
}
};
if self.consume(Token::RParen).is_err() {
self.pos = saved_pos;
return Ok(None);
}
// Expect /
if !self.check(&Token::Slash) {
self.pos = saved_pos;
return Ok(None);
}
self.next(); // consume /
// Expect d<var> or d(<var>)
let var = if let Some(token) = self.peek() {
match &token.value {
Token::Identifier(s) if s.starts_with('d') && s.len() > 1 => {
let v = s[1..].to_string();
self.next();
v
}
Token::Identifier(s) if s == "d" => {
self.next(); // consume d
// Expect (var)
if self.consume(Token::LParen).is_err() {
self.pos = saved_pos;
return Ok(None);
}
let v = match self.expect_identifier("variable") {
Ok(v) => v,
Err(_) => {
self.pos = saved_pos;
return Ok(None);
}
};
if self.consume(Token::RParen).is_err() {
self.pos = saved_pos;
return Ok(None);
}
v
}
_ => {
self.pos = saved_pos;
return Ok(None);
}
}
} else {
self.pos = saved_pos;
return Ok(None);
};
Ok(Some(
ExprKind::Derivative {
expr: Box::new(expr),
var,
order: 1,
}
.into(),
))
}
/// Parses prime notation: `y'`, `y''`, `y'''`.
///
/// The derivative variable is left empty since prime notation doesn't specify it.
pub(super) fn parse_prime_derivative(&mut self, name: String) -> ParseResult<Expression> {
let mut order = 0u32;
while self.check(&Token::Apostrophe) {
self.next();
order += 1;
}
Ok(ExprKind::Derivative {
expr: Box::new(self.identifier_to_expression(name)),
var: String::new(),
order,
}
.into())
}
/// Consumes an identifier token and returns its name, or errors with context.
pub(super) fn expect_identifier(&mut self, context: &str) -> ParseResult<String> {
if let Some(token) = self.next() {
if let Token::Identifier(name) = token.value {
return Ok(name);
}
return Err(ParseError::unexpected_token(
vec![context],
format!("{}", token.value),
Some(token.span),
));
}
Err(ParseError::unexpected_eof(
vec![context],
Some(self.current_span()),
))
}
/// Consumes an integer token and returns it as u32, or errors with context.
pub(super) fn expect_positive_integer(&mut self, context: &str) -> ParseResult<u32> {
if let Some(token) = self.next() {
if let Token::Integer(n) = token.value {
if n > 0 {
return Ok(n as u32);
}
}
return Err(ParseError::unexpected_token(
vec![context],
format!("{}", token.value),
Some(token.span),
));
}
Err(ParseError::unexpected_eof(
vec![context],
Some(self.current_span()),
))
}
}