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use term::*;
use term::Term::*;
use self::Closure::*;
use self::Expression::*;
use std::collections::VecDeque;
#[derive(Debug, PartialEq, Clone)]
enum Closure {
Depth(usize),
TermInEnv(Term, Environment)
}
#[derive(Debug, PartialEq)]
enum Expression {
Evaluation(Closure),
Application(Box<Expression>, Term, Environment)
}
type Environment = VecDeque<Closure>;
fn whnf(term: Term, mut env: Environment) -> Expression {
match term {
Var(i) => match env.remove(i - 1) {
Some(Depth(i)) => Evaluation(Depth(i)),
Some(TermInEnv(t, e)) => whnf(t, e),
None => unreachable!()
},
Abs(t) => Evaluation(TermInEnv(Abs(t), env)),
App(lhs, rhs) => match whnf(*lhs, env.clone()) {
Evaluation(TermInEnv(Abs(lhs2), mut env2)) => {
env2.push_front(TermInEnv(*rhs, env));
whnf(*lhs2, env2)
},
expr => Application(Box::new(expr), *rhs, env)
}
}
}
fn reduce(depth: usize, exp: Expression) -> Term {
match exp {
Application(lhs, rhs, env) => app(reduce(depth, *lhs), nf(depth, rhs, env)),
Evaluation(TermInEnv(Abs(term), mut env)) => {
env.push_front(Depth(depth));
abs(nf(depth + 1, *term, env))
},
Evaluation(TermInEnv(term, _)) => term,
Evaluation(Depth(i)) => Var(depth - i)
}
}
fn nf(depth: usize, term: Term, env: Environment) -> Term {
reduce(depth, whnf(term, env))
}
pub fn normalize(term: Term) -> Term {
nf(0, term, VecDeque::new())
}
pub const SHOW_REDUCTIONS: bool = false;
impl Term {
pub fn beta_once(&mut self) {
match *self {
Var(_) => (),
Abs(_) => self.unabs_ref_mut().unwrap().beta_once(),
App(_, _) => {
if self.lhs_ref().unwrap().unabs_ref().is_ok() {
let copy = self.clone();
let reduced = copy.eval().unwrap();
if SHOW_REDUCTIONS { println!(" {} reduces to {}", self, reduced) };
*self = reduced;
} else {
self.lhs_ref_mut().unwrap().beta_once();
self.rhs_ref_mut().unwrap().beta_once()
}
}
}
}
pub fn beta_full(&mut self) {
loop {
if SHOW_REDUCTIONS { println!("reducing {}", self) }
let tmp = self.clone();
self.beta_once();
if *self == tmp { break }
}
if SHOW_REDUCTIONS { println!(" doesn't reduce") }
}
}
pub fn beta_full(mut term: Term) -> Term {
term.beta_full();
term
}
pub fn beta_once(mut term: Term) -> Term {
term.beta_once();
term
}
#[cfg(test)]
mod test {
#[test]
fn weak_head_normal_form() {
}
}