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|
#![allow(non_snake_case)]
use dhall_core::core::*;
use dhall_generator::dhall_expr;
use std::fmt;
/// Reduce an expression to its weak head normal form, i.e. normalize
/// just enough to get the first constructor of the final expression
/// Is identical to normalize on primitive types, but not on more complex
/// types like functions and records.
/// This allows normalization to be lazy.
pub fn normalize_whnf<S, A>(e: &Expr<S, A>) -> Expr<S, A>
where
S: Clone + fmt::Debug,
A: Clone + fmt::Debug,
{
use dhall_core::BinOp::*;
use dhall_core::Builtin::*;
use dhall_core::Expr::*;
match e {
Let(f, _, r, b) => {
let vf0 = &V(f.clone(), 0);
let r2 = shift::<_, S, _>(1, vf0, r);
let b2 = subst::<_, S, _>(vf0, &r2, b);
let b3 = shift::<_, S, _>(-1, vf0, &b2);
normalize_whnf(&b3)
}
Annot(x, _) => normalize_whnf(x),
Note(_, e) => normalize_whnf(e),
App(f, a) => match (normalize_whnf(f), a) {
(Lam(x, _, b), a) => {
// Beta reduce
let vx0 = &V(x, 0);
let a2 = shift::<S, S, A>(1, vx0, a);
let b2 = subst::<S, S, A>(vx0, &a2, &b);
let b3 = shift::<S, S, A>(-1, vx0, &b2);
normalize_whnf(&b3)
}
(Builtin(b), a) => match (b, normalize_whnf(a)) {
(OptionalSome, a) => OptionalLit(None, vec![a]),
(OptionalNone, a) => OptionalLit(Some(bx(a)), vec![]),
(NaturalIsZero, NaturalLit(n)) => BoolLit(n == 0),
(NaturalEven, NaturalLit(n)) => BoolLit(n % 2 == 0),
(NaturalOdd, NaturalLit(n)) => BoolLit(n % 2 != 0),
(NaturalToInteger, NaturalLit(n)) => IntegerLit(n as isize),
(NaturalShow, NaturalLit(n)) => TextLit(n.to_string()),
(b, App(f, x)) => match (b, normalize_whnf(&f), x) {
// fold/build fusion for `Natural`
(NaturalBuild, Builtin(NaturalFold), x) => {
normalize_whnf(&x)
}
(NaturalFold, Builtin(NaturalBuild), x) => {
normalize_whnf(&x)
}
(b, f, x) => app(Builtin(b), app(f, *x)),
},
(b, a) => app(Builtin(b), a),
},
(App(f, x), y) => match (normalize_whnf(&f), x, y) {
// TODO: use whnf
(Builtin(b), x, y) => match (b, x, normalize::<S, S, A>(&y)) {
(ListLength, _, ListLit(_, ys)) => NaturalLit(ys.len()),
(ListHead, _, ListLit(t, ys)) => {
OptionalLit(t, ys.into_iter().take(1).collect())
}
(ListLast, _, ListLit(t, ys)) => OptionalLit(
t,
ys.into_iter().last().into_iter().collect(),
),
(ListReverse, _, ListLit(t, ys)) => {
let mut xs = ys;
xs.reverse();
ListLit(t, xs)
}
// fold/build fusion for `List`
(
ListBuild,
_,
App(box App(box Builtin(ListFold), _), box e2),
) => normalize_whnf(&e2),
(
ListFold,
_,
App(box App(box Builtin(ListBuild), _), box e2),
) => normalize_whnf(&e2),
// fold/build fusion for `Optional`
(
OptionalBuild,
_,
App(box App(box Builtin(OptionalFold), _), box e2),
) => normalize_whnf(&e2),
(
OptionalFold,
_,
App(box App(box Builtin(OptionalBuild), _), box e2),
) => normalize_whnf(&e2),
(ListBuild, a0, k) => {
let k = bx(k);
let a1 = bx(shift(1, &V("a".into(), 0), &a0));
normalize_whnf(
&dhall_expr!(k (List a0) (λ(a : a0) -> λ(as : List a1) -> [ a ] # as) ([] : List a0)),
)
}
(OptionalBuild, a0, g) => {
let g = bx(g);
normalize_whnf(
&dhall_expr!((g (Optional a0)) (λ(x: a0) -> [x] : Optional a0) ([] : Optional a0)),
)
}
(b, x, y) => app(App(bx(Builtin(b)), x), y),
},
(App(f, x), y, z) => match (normalize_whnf(&f), x, y, z) {
(App(f, x), y, z, w) => {
match (normalize_whnf(&f), x, y, z, w) {
(App(f, x), y, z, w, t) => match (
normalize_whnf(&f),
x,
normalize_whnf(&y),
z,
w,
t,
) {
(
Builtin(ListFold),
_,
ListLit(_, xs),
_,
cons,
nil,
) => {
let e2: Expr<_, _> = xs
.into_iter()
.rev()
.fold((**nil).clone(), |acc, x| {
let x = bx(x);
let acc = bx(acc);
dhall_expr!(cons x acc)
});
normalize_whnf(&e2)
}
(
Builtin(OptionalFold),
_,
OptionalLit(_, xs),
_,
just,
nothing,
) => {
let e2: Expr<_, _> = xs.into_iter().fold(
(**nothing).clone(),
|_, y| {
let y = bx(y);
dhall_expr!(just y)
},
);
normalize_whnf(&e2)
}
(f, x, y, z, w, t) => app(
App(
bx(App(
bx(App(bx(App(bx(f), x)), bx(y))),
z,
)),
w,
),
(**t).clone(),
),
},
(f, x, y, z, w) => app(
App(bx(App(bx(App(bx(f), x)), y)), z),
(**w).clone(),
),
}
}
(f, x, y, z) => {
app(App(bx(App(bx(f), x)), y), (**z).clone())
}
},
(f, x, y) => app(App(bx(f), x), (**y).clone()),
},
(f, a) => app(f, (**a).clone()),
},
BoolIf(b, t, f) => match normalize_whnf(b) {
BoolLit(true) => normalize_whnf(t),
BoolLit(false) => normalize_whnf(f),
b2 => BoolIf(bx(b2), t.clone(), f.clone()),
},
OptionalLit(t, es) => {
if !es.is_empty() {
OptionalLit(None, es.clone())
} else {
OptionalLit(t.clone(), es.clone())
}
}
BinOp(o, x, y) => match (o, normalize_whnf(&x), normalize_whnf(&y)) {
(BoolAnd, BoolLit(x), BoolLit(y)) => BoolLit(x && y),
(BoolOr, BoolLit(x), BoolLit(y)) => BoolLit(x || y),
(BoolEQ, BoolLit(x), BoolLit(y)) => BoolLit(x == y),
(BoolNE, BoolLit(x), BoolLit(y)) => BoolLit(x != y),
(NaturalPlus, NaturalLit(x), NaturalLit(y)) => NaturalLit(x + y),
(NaturalTimes, NaturalLit(x), NaturalLit(y)) => NaturalLit(x * y),
(TextAppend, TextLit(x), TextLit(y)) => TextLit(x + &y),
(ListAppend, ListLit(t1, xs), ListLit(t2, ys)) => {
// Drop type annotation if the result is nonempty
let t = if xs.is_empty() && ys.is_empty() {
t1.or(t2)
} else {
None
};
let xs = xs.into_iter();
let ys = ys.into_iter();
ListLit(t, xs.chain(ys).collect())
}
(o, x, y) => BinOp(*o, bx(x), bx(y)),
},
Field(e, x) => match (normalize_whnf(&e), x) {
(RecordLit(kvs), x) => match kvs.get(&x) {
Some(r) => normalize_whnf(r),
None => Field(bx(RecordLit(kvs)), x.clone()),
},
(e, x) => Field(bx(e), x.clone()),
},
e => e.clone(),
}
}
/// 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<S, T, A>(e: &Expr<S, A>) -> Expr<T, A>
where
S: Clone + fmt::Debug,
T: Clone + fmt::Debug,
A: Clone + fmt::Debug,
{
normalize_whnf(e).map_shallow(
normalize,
|_| unreachable!(),
|x| x.clone(),
|x| x.clone(),
)
}
|
