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authorGravatar Adam Chlipala <adamc@hcoop.net>2009-02-21 14:10:06 -0500
committerGravatar Adam Chlipala <adamc@hcoop.net>2009-02-21 14:10:06 -0500
commit9f20d9299eab7caab6421860b6a54f831af73921 (patch)
tree9e2dcb53a357f93751c3f1e1237a3d0900d02b2d /src/coq/Semantics.v
parentfe5ac0fba7f973b2557c7ae7a6bb9248024ffacd (diff)
Finish semantics for Featherweight Ur
Diffstat (limited to 'src/coq/Semantics.v')
-rw-r--r--src/coq/Semantics.v81
1 files changed, 75 insertions, 6 deletions
diff --git a/src/coq/Semantics.v b/src/coq/Semantics.v
index 19c67a05..2a12df72 100644
--- a/src/coq/Semantics.v
+++ b/src/coq/Semantics.v
@@ -48,6 +48,14 @@ Fixpoint kDen (k : kind) : Type :=
| KRecord k1 => row (kDen k1)
end.
+Fixpoint kDefault (k : kind) : kDen k :=
+ match k return kDen k with
+ | KType => unit
+ | KName => defaultName
+ | KArrow _ k2 => fun _ => kDefault k2
+ | KRecord _ => fun _ => None
+ end.
+
Fixpoint cDen k (c : con kDen k) {struct c} : kDen k :=
match c in con _ k return kDen k with
| CVar _ x => x
@@ -67,7 +75,13 @@ Fixpoint cDen k (c : con kDen k) {struct c} : kDen k :=
| None => None
| Some T => Some (f T)
end
- | CGuarded _ _ _ _ c => cDen c
+ | CGuarded _ _ c1 c2 c =>
+ if badName (fun n => match (cDen c1) n, (cDen c2) n with
+ | Some _, Some _ => false
+ | _, _ => true
+ end)
+ then kDefault _
+ else cDen c
end.
Theorem subs_correct : forall k1 (c1 : con kDen k1) k2 (c2 : _ -> con kDen k2) c2',
@@ -87,11 +101,33 @@ Definition disjoint T (r1 r2 : row T) :=
Definition dvar k (c1 c2 : con kDen (KRecord k)) :=
disjoint (cDen c1) (cDen c2).
+Theorem known_badName : forall T (r1 r2 : row T) T' (v1 v2 : T'),
+ disjoint r1 r2
+ -> (if badName (fun n => match r1 n, r2 n with
+ | Some _, Some _ => false
+ | _, _ => true
+ end)
+ then v1
+ else v2) = v2.
+ intros; match goal with
+ | [ |- context[if ?E then _ else _] ] => destruct E
+ end; firstorder;
+ match goal with
+ | [ H : disjoint _ _, x : name |- _ ] =>
+ generalize (H x);
+ repeat match goal with
+ | [ |- context[match ?E with None => _ | Some _ => _ end] ] => destruct E
+ end; tauto || congruence
+ end.
+Qed.
+
+Hint Rewrite known_badName using solve [ auto ] : Semantics.
+
Scheme deq_mut := Minimality for deq Sort Prop
with disj_mut := Minimality for disj Sort Prop.
Ltac deq_disj_correct scm :=
- let t := repeat progress (simpl; intuition; subst) in
+ let t := repeat progress (simpl; intuition; subst; autorewrite with Semantics) in
let rec use_disjoint' notDone E :=
match goal with
@@ -113,7 +149,7 @@ Ltac deq_disj_correct scm :=
disjoint (cDen c1) (cDen c2))); t;
repeat ((unfold row; apply ext_eq)
|| (match goal with
- | [ H : _ |- _ ] => rewrite H
+ | [ H : _ |- _ ] => rewrite H; []
| [ H : subs _ _ _ |- _ ] => rewrite <- (subs_correct H)
end); t);
unfold disjoint; t;
@@ -124,8 +160,33 @@ Ltac deq_disj_correct scm :=
use_disjoint N1; use_disjoint N2; destruct (name_eq_dec N1 N2)
| [ _ : context[match cDen ?C ?E with Some _ => _ | None => _ end] |- _ ] =>
use_disjoint E; destruct (cDen C E)
+ | [ |- context[if ?E then _ else _] ] => destruct E
end; t).
+Lemma bool_disjoint : forall T (r1 r2 : row T),
+ (forall nm : name,
+ match r1 nm with
+ | Some _ => match r2 nm with
+ | Some _ => false
+ | None => true
+ end
+ | None => true
+ end = true)
+ -> disjoint r1 r2.
+ intros; intro;
+ match goal with
+ | [ H : _, n : name |- _ ] => generalize (H n)
+ end;
+ repeat match goal with
+ | [ |- context[match ?E with Some _ => _ | None => _ end] ] => destruct E
+ end; tauto || discriminate.
+Qed.
+
+Implicit Arguments bool_disjoint [T r1 r2].
+
+Hint Resolve bool_disjoint.
+Hint Unfold dvar.
+
Theorem deq_correct : forall k (c1 c2 : con kDen k),
deq dvar c1 c2
-> cDen c1 = cDen c2.
@@ -138,8 +199,6 @@ Theorem disj_correct : forall k (c1 c2 : con kDen (KRecord k)),
deq_disj_correct disj_mut.
Qed.
-Axiom cheat : forall T, T.
-
Definition tDen (t : con kDen KType) : Set := cDen t.
Theorem name_eq_dec_refl : forall n, name_eq_dec n n = left _ (refl_equal n).
@@ -166,6 +225,8 @@ Qed.
Implicit Arguments cut_disjoint [v r].
+Set Printing All.
+
Fixpoint eDen t (e : exp dvar tDen t) {struct e} : tDen t :=
match e in exp _ _ t return tDen t with
| Var _ x => x
@@ -225,5 +286,13 @@ Fixpoint eDen t (e : exp dvar tDen t) {struct e} : tDen t :=
| _ => fun x => x
end ((eDen e1) n)
- | _ => cheat _
+ | Guarded _ c1 c2 _ e1 =>
+ match badName (fun n => match (cDen c1) n, (cDen c2) n with
+ | Some _, Some _ => false
+ | _, _ => true
+ end)
+ as BN return (if BN return Set then _ else _) with
+ | inleft _ => tt
+ | inright pf => eDen (e1 (bool_disjoint pf))
+ end
end.