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use term::{Term, Notation, abs, app};
use term::Term::*;
use self::Token::*;
use self::CToken::*;
use self::ParseError::*;
use self::Expression::*;
pub use term::Notation::*;
#[derive(Debug, PartialEq)]
pub enum ParseError {
InvalidCharacter((usize, char)),
InvalidExpression,
EmptyExpression
}
#[derive(Debug, PartialEq)]
#[doc(hidden)]
pub enum Token {
Lambda,
Lparen,
Rparen,
Number(usize)
}
#[derive(Debug, PartialEq)]
#[doc(hidden)]
pub enum CToken {
CLambda(String),
CLparen,
CRparen,
CName(String)
}
#[doc(hidden)]
pub fn tokenize_dbr(input: &str) -> Result<Vec<Token>, ParseError> {
let chars = input.chars().enumerate();
let mut tokens = Vec::new();
for (i, c) in chars {
match c {
'\\' | 'λ' => { tokens.push(Lambda) },
'(' => { tokens.push(Lparen) },
')' => { tokens.push(Rparen) },
_ => {
if let Some(n) = c.to_digit(16) {
tokens.push(Number(n as usize))
} else if c.is_whitespace() {
()
} else {
return Err(InvalidCharacter((i, c)))
}
}
}
}
Ok(tokens)
}
#[doc(hidden)]
pub fn tokenize_cla(input: &str) -> Result<Vec<CToken>, ParseError> {
let mut chars = input.chars().enumerate().peekable();
let mut tokens = Vec::new();
let valid_chars = "abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ";
while let Some((i, c)) = chars.next() {
match c {
'\\' | 'λ' => {
let mut name = String::new();
while let Some((i, c)) = chars.next() {
if c == '.' {
break
} else if valid_chars.contains(c) {
name.push(c)
} else {
return Err(InvalidCharacter((i, c)))
}
}
tokens.push(CLambda(name))
},
'(' => { tokens.push(CLparen) },
')' => { tokens.push(CRparen) },
_ => {
if c.is_whitespace() {
()
} else if valid_chars.contains(c) {
let mut name = c.to_string();
while let Some(&(_, c)) = chars.peek() {
if c.is_whitespace() || c == '(' || c == ')' {
break
} else {
name.push(c);
chars.next();
}
}
tokens.push(CName(name))
} else {
return Err(InvalidCharacter((i, c)))
}
}
}
}
Ok(tokens)
}
#[doc(hidden)]
pub fn convert_classic_tokens(tokens: &[CToken]) -> Vec<Token> {
_convert_classic_tokens(tokens, &mut Vec::new(), &mut 0)
}
fn _convert_classic_tokens(tokens: &[CToken], stack: &mut Vec<String>, pos: &mut usize) -> Vec<Token>
{
let mut output = Vec::with_capacity(tokens[*pos..].len());
let mut inner_stack_count = 0;
while let Some(token) = tokens.get(*pos) {
match *token {
CLambda(ref name) => {
output.push(Lambda);
stack.push(name.to_owned());
inner_stack_count += 1;
},
CLparen => {
output.push(Lparen);
*pos += 1;
output.append(&mut _convert_classic_tokens(tokens, stack, pos));
},
CRparen => {
output.push(Rparen);
for _ in 0..inner_stack_count { stack.pop(); }
return output
},
CName(ref name) => {
if let Some(index) = stack.iter().rev().position(|t| t == name) {
output.push(Number(index + 1))
} else {
output.push(Number(stack.len() + 1))
}
}
}
*pos += 1;
}
output
}
#[derive(Debug, PartialEq)]
#[doc(hidden)]
pub enum Expression {
Abstraction,
Sequence(Vec<Expression>),
Variable(usize)
}
#[doc(hidden)]
pub fn get_ast(tokens: &[Token]) -> Result<Expression, ParseError> {
_get_ast(tokens, &mut 0)
}
fn _get_ast(tokens: &[Token], pos: &mut usize) -> Result<Expression, ParseError> {
if tokens.is_empty() { return Err(EmptyExpression) }
let mut expr = Vec::new();
while let Some(token) = tokens.get(*pos) {
match *token {
Lambda => {
expr.push(Abstraction)
},
Number(i) => {
expr.push(Variable(i))
},
Lparen => {
*pos += 1;
let subtree = _get_ast(tokens, pos)?;
expr.push(subtree);
},
Rparen => {
return Ok(Sequence(expr))
}
}
*pos += 1;
}
Ok(Sequence(expr))
}
pub fn parse(input: &str, notation: Notation) -> Result<Term, ParseError> {
let tokens = if notation == DeBruijn {
tokenize_dbr(input)?
} else {
convert_classic_tokens(&tokenize_cla(input)?)
};
let ast = get_ast(&tokens)?;
let exprs = if let Sequence(exprs) = ast {
Ok(exprs)
} else {
Err(InvalidExpression)
};
fold_exprs(&exprs?)
}
#[doc(hidden)]
pub fn fold_exprs(exprs: &[Expression]) -> Result<Term, ParseError> {
let mut depth = 0;
let mut output = Vec::new();
for expr in exprs.iter() {
match *expr {
Variable(i) => output.push(Var(i)),
Abstraction => depth += 1,
Sequence(ref exprs) => {
let subexpr = fold_exprs(exprs)?;
output.push(subexpr)
}
}
}
let mut ret = fold_terms(output)?;
for _ in 0..depth {
ret = abs(ret);
}
Ok(ret)
}
fn fold_terms(mut terms: Vec<Term>) -> Result<Term, ParseError> {
if terms.len() > 1 {
let fst = terms.remove(0);
Ok( terms.into_iter().fold(fst, app) )
} else if terms.len() == 1 {
Ok( terms.pop().unwrap() )
} else {
Err(EmptyExpression)
}
}
#[cfg(test)]
mod tests {
use super::*;
#[test]
fn tokenization_error() {
assert_eq!(tokenize_dbr(&"λλx2"), Err(InvalidCharacter((2, 'x'))));
assert_eq!(tokenize_cla(&"λa.λb a"), Err(InvalidCharacter((5, ' '))));
}
#[test]
fn tokenization_success() {
let quine = "λ 1 ( (λ 1 1) (λ λ λ λ λ 1 4 (3 (5 5) 2) ) ) 1";
let tokens = tokenize_dbr(&quine);
assert!(tokens.is_ok());
assert_eq!(tokens.unwrap(), vec![Lambda, Number(1), Lparen, Lparen, Lambda, Number(1),
Number(1), Rparen, Lparen, Lambda, Lambda, Lambda, Lambda, Lambda, Number(1),
Number(4), Lparen, Number(3), Lparen, Number(5), Number(5), Rparen, Number(2),
Rparen, Rparen, Rparen, Number(1)]);
}
#[test]
fn tokenization_success_classic() {
let blc_dbr = "(λ11)(λλλ1(λλλλ3(λ5(3(λ2(3(λλ3(λ123)))(4(λ4(λ31(21))))))(1(2(λ12))\
(λ4(λ4(λ2(14)))5))))(33)2)(λ1((λ11)(λ11)))";
let blc_cla = format!("{}", parse(&blc_dbr, DeBruijn).unwrap());
let tokens_cla = tokenize_cla(&blc_cla);
let tokens_dbr = tokenize_dbr(&blc_dbr);
assert!(tokens_cla.is_ok());
assert!(tokens_dbr.is_ok());
assert_eq!(convert_classic_tokens(&tokens_cla.unwrap()), tokens_dbr.unwrap());
}
#[test]
fn alternative_lambda_parsing() {
assert_eq!(parse(&r#"\\\2(321)"#, DeBruijn), parse(&"λλλ2(321)", DeBruijn))
}
#[test]
fn succ_ast() {
let tokens = tokenize_dbr(&"λλλ2(321)").unwrap();
let ast = get_ast(&tokens);
assert_eq!(ast,
Ok(Sequence(vec![
Abstraction,
Abstraction,
Abstraction,
Variable(2),
Sequence(vec![
Variable(3),
Variable(2),
Variable(1)
])
])
));
}
#[test]
fn parse_y() {
let y = "λ(λ2(11))(λ2(11))";
assert_eq!(parse(&y, DeBruijn).unwrap(),
abs(
app(
abs(app(Var(2), app(Var(1), Var(1)))),
abs(app(Var(2), app(Var(1), Var(1))))
)
)
);
}
#[test]
fn parse_quine() {
let quine = "λ1((λ11)(λλλλλ14(3(55)2)))1";
assert_eq!(parse(&quine, DeBruijn).unwrap(),
abs(app(app(Var(1), app(abs(app(Var(1), Var(1))), abs!(5, app(app(Var(1),
Var(4)), app(app(Var(3), app(Var(5), Var(5))), Var(2)))))), Var(1)))
);
}
#[test]
fn parse_blc() {
let blc = "(λ11)(λλλ1(λλλλ3(λ5(3(λ2(3(λλ3(λ123)))(4(λ4(λ31(21))))))(1(2(λ12))\
(λ4(λ4(λ2(14)))5))))(33)2)(λ1((λ11)(λ11)))";
assert_eq!(parse(&blc, DeBruijn).unwrap(),
app(app(abs(app(Var(1), Var(1))), abs!(3, app(app(app(Var(1),
abs!(4, app(Var(3), abs(app(app(Var(5), app(Var(3), abs(app(app(Var(2),
app(Var(3), abs!(2, app(Var(3), abs(app(app(Var(1), Var(2)), Var(3))))))), app(Var(4),
abs(app(Var(4), abs(app(app(Var(3), Var(1)), app(Var(2), Var(1))))))))))),
app(app(Var(1), app(Var(2), abs(app(Var(1), Var(2))))), abs(app(app(Var(4),
abs(app(Var(4), abs(app(Var(2), app(Var(1), Var(4))))))), Var(5))))))))),
app(Var(3), Var(3))), Var(2)))), abs(app(Var(1), app(abs(app(Var(1), Var(1))),
abs(app(Var(1), Var(1)))))))
);
}
}