add an identity production for Arrange

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

diff --git a/src/HaskProofToStrong.v b/src/HaskProofToStrong.v
index 06f97a1..b6e8efe 100644 (file)
--- a/src/HaskProofToStrong.v
+++ b/src/HaskProofToStrong.v
@@ -239,6 +239,7 @@ Section HaskProofToStrong.
  with
           | RLeft   h c ctx r => let case_RLeft  := tt in (fun e => _) (urule2expr _ _ _ r)
           | RRight  h c ctx r => let case_RRight := tt in (fun e => _) (urule2expr _ _ _ r)
+          | RId     a       => let case_RId    := tt in _
           | RCanL   a       => let case_RCanL  := tt in _
           | RCanR   a       => let case_RCanR  := tt in _
           | RuCanL  a       => let case_RuCanL := tt in _
@@ -251,6 +252,9 @@ Section HaskProofToStrong.
           | RComp   a b c f g => let case_RComp  := tt in (fun e1 e2 => _) (urule2expr _ _ _ f) (urule2expr _ _ _ g)
           end); clear urule2expr; intros.
 
+      destruct case_RId.
+        apply X.
+
       destruct case_RCanL.
         simpl; unfold ujudg2exprType; intros.
         simpl in X.
@@ -569,7 +573,6 @@ Section HaskProofToStrong.
   destruct case_RGlobal.
     apply ILeaf; simpl; intros; refine (return ILeaf _ _).
     apply EGlobal.
-    apply wev.
 
   destruct case_RLam.
     apply ILeaf.
@@ -633,7 +636,7 @@ Section HaskProofToStrong.
     apply ileaf in q1'.
     apply ileaf in q2'.
     simpl in *.
-    apply (EApp _ _ _ _ _ _ q1' q2').
+    apply (EApp _ _ _ _ _ _ q2' q1').
 
   destruct case_RLet.
     apply ILeaf.
@@ -715,6 +718,7 @@ Section HaskProofToStrong.
     inversion X; subst; clear X.
 
     apply (@ELetRec _ _ _ _ _ _ _ varstypes).
+    auto.
     apply (@letrec_helper Γ Δ t varstypes).
     rewrite <- pf2 in X1.
     rewrite mapOptionTree_compose.
@@ -758,15 +762,12 @@ Section HaskProofToStrong.
       apply H2.
     Defined.
 
-  Definition closed2expr : forall c (pn:@ClosedSIND _ Rule c), ITree _ judg2exprType c.
-    refine ((
-      fix closed2expr' j (pn:@ClosedSIND _ Rule j) {struct pn} : ITree _ judg2exprType j :=
-      match pn in @ClosedSIND _ _ J return ITree _ judg2exprType J with
-      | cnd_weak             => let case_nil    := tt in INone _ _
-      | cnd_rule h c cnd' r  => let case_rule   := tt in rule2expr _ _ r (closed2expr' _ cnd')
-      | cnd_branch _ _ c1 c2 => let case_branch := tt in IBranch _ _ (closed2expr' _ c1) (closed2expr' _ c2)
-      end)); clear closed2expr'; intros; subst.
-        Defined.
+  Fixpoint closed2expr h j (pn:@SIND _ Rule h j) {struct pn} : ITree _ judg2exprType h -> ITree _ judg2exprType j :=
+    match pn in @SIND _ _ H J return ITree _ judg2exprType H -> ITree _ judg2exprType J with
+    | scnd_weak   _             => let case_nil    := tt in fun _ => INone _ _
+    | scnd_comp   x h c cnd' r  => let case_rule   := tt in fun q => rule2expr _ _ r (closed2expr _ _ cnd' q)
+    | scnd_branch _ _ _ c1 c2   => let case_branch := tt in fun q => IBranch _ _ (closed2expr _ _ c1 q) (closed2expr _ _ c2 q)
+    end.
 
   Lemma manyFresh : forall Γ Σ (ξ0:VV -> LeveledHaskType Γ ★),
     FreshM { vars : _ & { ξ : VV -> LeveledHaskType Γ ★ & Σ = mapOptionTree ξ vars } }.
@@ -804,7 +805,7 @@ Section HaskProofToStrong.
     {zz:ToString VV} : ND Rule [] [Γ > Δ > Σ |- [τ]] ->
     FreshM (???{ ξ : _ & Expr Γ Δ ξ τ}).
     intro pf.
-    set (closedFromSIND _ _ (mkSIND systemfc_all_rules_one_conclusion _ _ _ pf (scnd_weak [])) cnd_weak) as cnd.
+    set (mkSIND systemfc_all_rules_one_conclusion _ _ _ pf (scnd_weak [])) as cnd.
     apply closed2expr in cnd.
     apply ileaf in cnd.
     simpl in *.
@@ -819,6 +820,7 @@ Section HaskProofToStrong.
     refine (return OK _).
     exists ξ.
     apply (ileaf it).
+    apply INone.
     Defined.
 
 End HaskProofToStrong.