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|
#![allow(non_snake_case)]
use std::fmt;
use dhall_core::core::*;
/// Reduce an expression to its normal form, performing beta reduction
///
/// `normalize` does not type-check the expression. You may want to type-check
/// expressions before normalizing them since normalization can convert an
/// ill-typed expression into a well-typed expression.
///
/// However, `normalize` will not fail if the expression is ill-typed and will
/// leave ill-typed sub-expressions unevaluated.
///
pub fn normalize<'i, S, T, A>(e: &Expr<'i, S, A>) -> Expr<'i, T, A>
where
S: Clone + fmt::Debug,
T: Clone + fmt::Debug,
A: Clone + fmt::Debug,
{
use dhall_core::BinOp::*;
use dhall_core::Builtin::*;
use dhall_core::Expr::*;
match *e {
Const(k) => Const(k),
Var(v) => Var(v),
Lam(x, ref tA, ref b) => {
let tA2 = normalize(tA);
let b2 = normalize(b);
Lam(x, bx(tA2), bx(b2))
}
Pi(x, ref tA, ref tB) => {
let tA2 = normalize(tA);
let tB2 = normalize(tB);
pi(x, tA2, tB2)
}
App(ref f, ref a) => match normalize::<S, T, A>(f) {
Lam(x, _A, b) => {
// Beta reduce
let vx0 = V(x, 0);
let a2 = shift::<S, S, A>(1, vx0, a);
let b2 = subst::<S, T, A>(vx0, &a2, &b);
let b3 = shift::<S, T, A>(-1, vx0, &b2);
normalize(&b3)
}
f2 => match (f2, normalize::<S, T, A>(a)) {
// fold/build fusion for `List`
(App(box Builtin(ListBuild), _), App(box App(box Builtin(ListFold), _), box e2)) |
(App(box Builtin(ListFold), _), App(box App(box Builtin(ListBuild), _), box e2)) |
// fold/build fusion for `Natural`
(Builtin(NaturalBuild), App(box Builtin(NaturalFold), box e2)) |
(Builtin(NaturalFold), App(box Builtin(NaturalBuild), box e2)) => normalize(&e2),
/*
App (App (App (App NaturalFold (NaturalLit n0)) _) succ') zero ->
normalize (go n0)
where
go !0 = zero
go !n = App succ' (go (n - 1))
App NaturalBuild k
| check -> NaturalLit n
| otherwise -> App f' a'
where
labeled =
normalize (App (App (App k Natural) "Succ") "Zero")
n = go 0 labeled
where
go !m (App (Var "Succ") e') = go (m + 1) e'
go !m (Var "Zero") = m
go !_ _ = internalError text
check = go labeled
where
go (App (Var "Succ") e') = go e'
go (Var "Zero") = True
go _ = False
*/
(Builtin(NaturalIsZero), NaturalLit(n)) => BoolLit(n == 0),
(Builtin(NaturalEven), NaturalLit(n)) => BoolLit(n % 2 == 0),
(Builtin(NaturalOdd), NaturalLit(n)) => BoolLit(n % 2 != 0),
(Builtin(NaturalToInteger), NaturalLit(n)) => IntegerLit(n as isize),
(Builtin(NaturalShow), NaturalLit(n)) => TextLit(n.to_string()),
(App(f@box Builtin(ListBuild), box t), k) => {
let labeled =
normalize::<_, T, _>(&app(app(app(k.clone(), app(
Builtin(self::Builtin::List), t.clone())), "Cons"), "Nil"));
fn list_to_vector<'i, S, A>(v: &mut Vec<Expr<'i, S, A>>, e: Expr<'i, S, A>)
where S: Clone, A: Clone
{
match e {
App(box App(box Var(V("Cons", _)), box x), box e2) => {
v.push(x);
list_to_vector(v, e2)
}
Var(V("Nil", _)) => {}
_ => panic!("internalError list_to_vector"),
}
}
fn check<S, A>(e: &Expr<S, A>) -> bool {
match *e {
App(box App(box Var(V("Cons", _)), _), ref e2) => check(e2),
Var(V("Nil", _)) => true,
_ => false,
}
}
if check(&labeled) {
let mut v = vec![];
list_to_vector(&mut v, labeled);
ListLit(Some(bx(t)), v)
} else {
app(App(f, bx(t)), k)
}
}
(App(box App(box App(box App(box Builtin(ListFold), _), box ListLit(_, xs)), _), cons), nil) => {
let e2: Expr<_, _> = xs.into_iter().rev().fold(nil, |y, ys| // foldr
App(bx(App(cons.clone(), bx(y))), bx(ys))
);
normalize(&e2)
}
(App(f, x_), ListLit(t, ys)) => match *f {
Builtin(ListLength) =>
NaturalLit(ys.len()),
Builtin(ListHead) =>
normalize(&OptionalLit(t, ys.into_iter().take(1).collect())),
Builtin(ListLast) =>
normalize(&OptionalLit(t, ys.into_iter().last().into_iter().collect())),
Builtin(ListReverse) => {
let mut xs = ys;
xs.reverse();
normalize(&ListLit(t, xs))
}
_ => app(App(f, x_), ListLit(t, ys)),
},
/*
App (App ListIndexed _) (ListLit t xs) ->
normalize (ListLit t' (fmap adapt (Data.Vector.indexed xs)))
where
t' = Record (Data.Map.fromList kts)
where
kts = [ ("index", Natural)
, ("value", t)
]
adapt (n, x) = RecordLit (Data.Map.fromList kvs)
where
kvs = [ ("index", NaturalLit (fromIntegral n))
, ("value", x)
]
*/
(App(box App(box App(box App(box Builtin(OptionalFold), _), box OptionalLit(_, xs)), _), just), nothing) => {
let e2: Expr<_, _> = xs.into_iter().fold(nothing, |y, _|
App(just.clone(), bx(y))
);
normalize(&e2)
}
(App(box Builtin(OptionalBuild), _), App(box App(box Builtin(OptionalFold), _), b)) => {
normalize(&b)
}
(App(box Builtin(OptionalBuild), a0), g) => {
let e2: Expr<_, _> = app(app(app(g,
App(bx(Builtin(Optional)), a0.clone())),
Lam("x", a0.clone(),
bx(OptionalLit(Some(a0.clone()), vec![Var(V("x", 0))])))),
OptionalLit(Some(a0), vec![]));
normalize(&e2)
}
(f2, a2) => app(f2, a2),
},
},
Let(f, _, ref r, ref b) => {
let r2 = shift::<_, S, _>(1, V(f, 0), r);
let b2 = subst(V(f, 0), &r2, b);
let b3 = shift::<_, T, _>(-1, V(f, 0), &b2);
normalize(&b3)
}
Annot(ref x, _) => normalize(x),
Builtin(v) => Builtin(v),
BoolLit(b) => BoolLit(b),
BinOp(BoolAnd, ref x, ref y) => with_binop(
BoolAnd,
Expr::bool_lit,
|xn, yn| BoolLit(xn && yn),
normalize(x),
normalize(y),
),
BinOp(BoolOr, ref x, ref y) => with_binop(
BoolOr,
Expr::bool_lit,
|xn, yn| BoolLit(xn || yn),
normalize(x),
normalize(y),
),
BinOp(BoolEQ, ref x, ref y) => with_binop(
BoolEQ,
Expr::bool_lit,
|xn, yn| BoolLit(xn == yn),
normalize(x),
normalize(y),
),
BinOp(BoolNE, ref x, ref y) => with_binop(
BoolNE,
Expr::bool_lit,
|xn, yn| BoolLit(xn != yn),
normalize(x),
normalize(y),
),
BoolIf(ref b, ref t, ref f) => match normalize(b) {
BoolLit(true) => normalize(t),
BoolLit(false) => normalize(f),
b2 => BoolIf(bx(b2), bx(normalize(t)), bx(normalize(f))),
},
NaturalLit(n) => NaturalLit(n),
BinOp(NaturalPlus, ref x, ref y) => with_binop(
NaturalPlus,
Expr::natural_lit,
|xn, yn| NaturalLit(xn + yn),
normalize(x),
normalize(y),
),
BinOp(NaturalTimes, ref x, ref y) => with_binop(
NaturalTimes,
Expr::natural_lit,
|xn, yn| NaturalLit(xn * yn),
normalize(x),
normalize(y),
),
IntegerLit(n) => IntegerLit(n),
DoubleLit(n) => DoubleLit(n),
TextLit(ref t) => TextLit(t.clone()),
BinOp(TextAppend, ref x, ref y) => with_binop(
TextAppend,
Expr::text_lit,
|xt, yt| TextLit(xt + &yt),
normalize(x),
normalize(y),
),
ListLit(ref t, ref es) => {
let t2 = t.as_ref().map(|x| x.as_ref()).map(normalize).map(bx);
let es2 = es.iter().map(normalize).collect();
ListLit(t2, es2)
}
OptionalLit(ref t, ref es) => {
let t2 = t.as_ref().map(|x| x.as_ref()).map(normalize).map(bx);
let es2 = es.iter().map(normalize).collect();
OptionalLit(t2, es2)
}
Record(ref kts) => Record(map_record_value(kts, normalize)),
RecordLit(ref kvs) => RecordLit(map_record_value(kvs, normalize)),
Union(ref kts) => Union(map_record_value(kts, normalize)),
UnionLit(k, ref v, ref kvs) => {
UnionLit(k, bx(normalize(v)), map_record_value(kvs, normalize))
}
Merge(ref _x, ref _y, ref _t) => unimplemented!(),
Field(ref r, x) => match normalize(r) {
RecordLit(kvs) => match kvs.get(x) {
Some(r2) => normalize(r2),
None => {
Field(bx(RecordLit(map_record_value(&kvs, normalize))), x)
}
},
r2 => Field(bx(r2), x),
},
Note(_, ref e) => normalize(e),
Embed(ref a) => Embed(a.clone()),
_ => unimplemented!(),
}
}
fn with_binop<'a, S, A, U, Get, Set>(
op: BinOp,
get: Get,
set: Set,
x: Expr<'a, S, A>,
y: Expr<'a, S, A>,
) -> Expr<'a, S, A>
where
Get: Fn(&Expr<'a, S, A>) -> Option<U>,
Set: FnOnce(U, U) -> Expr<'a, S, A>,
{
if let (Some(xv), Some(yv)) = (get(&x), get(&y)) {
set(xv, yv)
} else {
Expr::BinOp(op, bx(x), bx(y))
}
}
|
