update demo

[coq-hetmet.git] / src / HaskFlattener.v

diff --git a/src/HaskFlattener.v b/src/HaskFlattener.v
index 46e6af5..09f7070 100644 (file)
--- a/src/HaskFlattener.v
+++ b/src/HaskFlattener.v
@@ -239,11 +239,11 @@ Section HaskFlattener.
 
   Definition ga_mk_raw {TV}(ec:RawHaskType TV ECKind)(ant suc:Tree ??(RawHaskType TV ★)) : RawHaskType TV ★ :=
     gaTy TV ec
-    (ga_mk_tree' ec (ant,,(mapOptionTreeAndFlatten (unleaves ○ take_arg_types) suc)))
-    (ga_mk_tree' ec (      mapOptionTree                       drop_arg_types  suc) ).
+    (ga_mk_tree' ec ant)
+    (ga_mk_tree' ec suc).
 
-  Definition ga_mk {Γ}(ec:HaskType Γ ECKind )(ant suc:Tree ??(HaskType Γ ★)) : HaskType Γ ★ :=
-    fun TV ite => ga_mk_raw (ec TV ite) (mapOptionTree (fun x => x TV ite) ant) (mapOptionTree (fun x => x TV ite) suc).
+  Definition ga_mk {Γ}(ec:HaskType Γ ECKind)(ant suc:Tree ??(HaskType Γ ★)) : HaskType Γ ★ :=
+    fun TV ite => gaTy TV (ec TV ite) (ga_mk_tree ec ant TV ite) (ga_mk_tree ec suc TV ite).
 
   (*
    *  The story:
@@ -260,7 +260,7 @@ Section HaskFlattener.
     | TCoerc _ t1 t2 t      => TCoerc    (flatten_rawtype t1) (flatten_rawtype t2) (flatten_rawtype t)
     | TArrow                => TArrow
     | TCode     ec e        => let e' := flatten_rawtype e
-                               in  ga_mk_raw ec (unleaves' (take_arg_types e')) [drop_arg_types e']
+                               in  ga_mk_raw ec (unleaves (take_arg_types e')) [drop_arg_types e']
     | TyFunApp  tfc kl k lt => TyFunApp tfc kl k (flatten_rawtype_list _ lt)
     end
     with flatten_rawtype_list {TV}(lk:list Kind)(exp:@RawHaskTypeList TV lk) : @RawHaskTypeList TV lk :=
@@ -852,18 +852,42 @@ Section HaskFlattener.
     apply IHt2.
     Defined.
 
+  Axiom extensionality : forall Γ Q (f g:forall TV, InstantiatedTypeEnv TV Γ -> Q TV),
+    (forall tv ite, f tv ite = g tv ite) -> f=g.
+
   Lemma krunk : forall Γ (ec:HaskTyVar Γ ECKind) t,
     flatten_type (<[ ec |- t ]>)
     = @ga_mk Γ (v2t ec)
-    (mapOptionTree flatten_type (take_arg_types_as_tree Γ t))
+    (mapOptionTree flatten_type (take_arg_types_as_tree t))
     [ flatten_type (drop_arg_types_as_tree   t)].
-
     intros.
     unfold flatten_type at 1.
     simpl.
     unfold ga_mk.
+    apply extensionality.
+    intros.
     unfold v2t.
-    admit. (* BIG HUGE CHEAT FIXME *)
+    unfold ga_mk_raw.
+    unfold ga_mk_tree.
+    rewrite <- mapOptionTree_compose.
+    unfold take_arg_types_as_tree.
+    simpl.
+    replace (flatten_type (drop_arg_types_as_tree t) tv ite)
+      with (drop_arg_types (flatten_rawtype (t tv ite))).
+    replace (unleaves (take_arg_types (flatten_rawtype (t tv ite))))
+      with ((mapOptionTree (fun x : HaskType Γ ★ => flatten_type x tv ite)
+           (unleaves
+              (take_trustme (count_arg_types (t (fun _ : Kind => unit) (ite_unit Γ)))
+                 (fun TV : Kind → Type => take_arg_types ○ t TV))))).
+    reflexivity.
+    unfold flatten_type.
+    clear hetmet_flatten.
+    clear hetmet_unflatten.
+    clear hetmet_id.
+    clear gar.
+    set (t tv ite) as x.
+    admit.
+    admit.
     Qed.
 
   Definition flatten_proof :
@@ -1136,7 +1160,7 @@ Section HaskFlattener.
       simpl.
       destruct lev.
       drop_simplify.
-      set (drop_lev (ec :: nil) (take_arg_types_as_tree Γ t @@@ (ec :: nil))) as empty_tree.
+      set (drop_lev (ec :: nil) (take_arg_types_as_tree t @@@ (ec :: nil))) as empty_tree.
       take_simplify.
       rewrite take_lemma'.
       simpl.
@@ -1149,7 +1173,7 @@ Section HaskFlattener.
       rewrite krunk.
       set (mapOptionTree flatten_leveled_type (drop_lev (ec :: nil) succ)) as succ_host.
       set (mapOptionTree (flatten_type ○ unlev)(take_lev (ec :: nil) succ)) as succ_guest.
-      set (mapOptionTree flatten_type (take_arg_types_as_tree Γ t)) as succ_args.
+      set (mapOptionTree flatten_type (take_arg_types_as_tree t)) as succ_args.
       unfold empty_tree.
       eapply nd_comp; [ eapply nd_rule; eapply RArrange; apply tree_of_nothing | idtac ].
       refine (ga_unkappa' Γ Δ (v2t ec) nil _ _ _ _ ;; _).
@@ -1183,7 +1207,7 @@ Section HaskFlattener.
       clear e.
 
       set (mapOptionTree flatten_leveled_type (drop_lev (ec :: nil) succ)) as succ_host.
-      set (mapOptionTree flatten_type (take_arg_types_as_tree Γ t)) as succ_args.
+      set (mapOptionTree flatten_type (take_arg_types_as_tree t)) as succ_args.
 
       eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; apply RCanR ].
       eapply nd_comp; [ idtac | eapply nd_rule; eapply RLet ].
@@ -1222,6 +1246,20 @@ Section HaskFlattener.
       apply (Prelude_error "found Esc at depth >0 indicating 3-level code; only two-level code is currently supported").
       Defined.
 
+  Definition skolemize_and_flatten_proof :
+    forall  {h}{c},
+      ND  Rule h c ->
+      ND  Rule
+           (mapOptionTree (flatten_judgment ○ skolemize_judgment) h)
+           (mapOptionTree (flatten_judgment ○ skolemize_judgment) c).
+    intros.
+    rewrite mapOptionTree_compose.
+    rewrite mapOptionTree_compose.
+    apply flatten_proof.
+    apply skolemize_proof.
+    apply X.
+    Defined.
+
 
   (* to do: establish some metric on judgments (max length of level of any succedent type, probably), show how to
    * calculate it, and show that the flattening procedure above drives it down by one *)