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-rw-r--r--dhall_normalize/src/normalize.rs286
1 files changed, 286 insertions, 0 deletions
diff --git a/dhall_normalize/src/normalize.rs b/dhall_normalize/src/normalize.rs
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+++ b/dhall_normalize/src/normalize.rs
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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))
+ }
+}
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