X-Git-Url: http://git.megacz.com/?p=coq-hetmet.git;a=blobdiff_plain;f=src%2FHaskSkolemizer.v;h=b1d65e6ebb3f766b9e1c000062cf1299747cd160;hp=b037bb0457183802a06e59422677bd6c43069ebe;hb=6a7c6977507488245ba4b8cabcf323920c25baef;hpb=b83e779e742413ca84df565263dafbdf9f79920a

diff --git a/src/HaskSkolemizer.v b/src/HaskSkolemizer.v
index b037bb0..b1d65e6 100644
--- a/src/HaskSkolemizer.v
+++ b/src/HaskSkolemizer.v
@@ -9,6 +9,7 @@ Generalizable All Variables.
 Require Import Preamble.
 Require Import General.
 Require Import NaturalDeduction.
+Require Import NaturalDeductionContext.
 Require Import Coq.Strings.String.
 Require Import Coq.Lists.List.
 
@@ -82,19 +83,7 @@ Section HaskSkolemizer.
     end.
 
   (* rules of skolemized proofs *)
-  Definition getΓ (j:Judg) := match j with Γ > _ > _ |- _ => Γ end.
-  Definition getSuc (j:Judg) : Tree ??(LeveledHaskType (getΓ j) ★) :=
-    match j as J return Tree ??(LeveledHaskType (getΓ J) ★) with Γ > _ > _ |- s => s end.
-  Fixpoint getjlev {Γ}(tt:Tree ??(LeveledHaskType Γ ★)) : HaskLevel Γ :=
-    match tt with
-      | T_Leaf None              => nil
-      | T_Leaf (Some (_ @@ lev)) => lev
-      | T_Branch b1 b2 =>
-        match getjlev b1 with
-          | nil => getjlev b2
-          | lev => lev
-        end
-    end.
+  Definition getΓ (j:Judg) := match j with Γ > _ > _ |- _ @ _ => Γ end.
 
   Fixpoint take_trustme {Γ}
     (n:nat)
@@ -136,14 +125,14 @@ Section HaskSkolemizer.
     destruct (eqd_dec ([tx],,take_arg_types_as_tree te) (take_arg_types_as_tree (tx ---> te))).
       rewrite <- e.
       simpl.
-      apply RId.
+      apply AId.
     unfold take_arg_types_as_tree.
       Opaque take_arg_types_as_tree.
       simpl.
       destruct (count_arg_types (te (fun _ : Kind => unit) (ite_unit Γ))).
       simpl.
       replace (tx) with (fun (TV : Kind → Type) (ite : InstantiatedTypeEnv TV Γ) => tx TV ite).
-      apply RCanR.
+      apply ACanR.
         apply phoas_extensionality.
         reflexivity.
     apply (Prelude_error "should not be possible").
@@ -157,14 +146,14 @@ Section HaskSkolemizer.
     destruct (eqd_dec ([tx],,take_arg_types_as_tree te) (take_arg_types_as_tree (tx ---> te))).
       rewrite <- e.
       simpl.
-      apply RId.
+      apply AId.
     unfold take_arg_types_as_tree.
       Opaque take_arg_types_as_tree.
       simpl.
       destruct (count_arg_types (te (fun _ : Kind => unit) (ite_unit Γ))).
       simpl.
       replace (tx) with (fun (TV : Kind → Type) (ite : InstantiatedTypeEnv TV Γ) => tx TV ite).
-      apply RuCanR.
+      apply AuCanR.
         apply phoas_extensionality.
         reflexivity.
     apply (Prelude_error "should not be possible").
@@ -184,13 +173,13 @@ Section HaskSkolemizer.
   | SFlat  : forall h c, Rule h c -> SRule h c
   | SBrak  : forall Γ Δ t ec Σ l,
     SRule
-    [Γ > Δ > Σ,,(take_arg_types_as_tree t @@@ (ec::l)) |- [ drop_arg_types_as_tree t        @@ (ec::l) ]]
-    [Γ > Δ > Σ                                  |- [<[ec |- t]>              @@      l  ]]
+    [Γ > Δ > Σ,,(take_arg_types_as_tree t @@@ (ec::l)) |- [ drop_arg_types_as_tree t        ] @ (ec::l)]
+    [Γ > Δ > Σ                                  |- [<[ec |- t]>                ] @l]
 
   | SEsc   : forall Γ Δ t ec Σ l,
     SRule
-    [Γ > Δ > Σ                                  |- [<[ec |- t]>              @@      l  ]]
-    [Γ > Δ > Σ,,(take_arg_types_as_tree t @@@ (ec::l)) |- [ drop_arg_types_as_tree t        @@ (ec::l) ]]
+    [Γ > Δ > Σ                                  |- [<[ec |- t]>                ] @l]
+    [Γ > Δ > Σ,,(take_arg_types_as_tree t @@@ (ec::l)) |- [ drop_arg_types_as_tree t         ] @ (ec::l)]
     .
 
   Definition take_arg_types_as_tree' {Γ}(lt:LeveledHaskType Γ ★) :=
@@ -201,11 +190,9 @@ Section HaskSkolemizer.
 
   Definition skolemize_judgment (j:Judg) : Judg :=
     match j with
-      Γ > Δ > Σ₁ |- Σ₂ =>
-        match getjlev Σ₂ with
-          | nil => j
-          | lev => Γ > Δ > Σ₁,,(mapOptionTreeAndFlatten take_arg_types_as_tree' Σ₂) |- mapOptionTree drop_arg_types_as_tree' Σ₂
-        end
+      | Γ > Δ > Σ₁ |- Σ₂ @ nil       => j
+        | Γ > Δ > Σ₁ |- Σ₂ @ lev => 
+          Γ > Δ > Σ₁,,(mapOptionTreeAndFlatten take_arg_types_as_tree Σ₂ @@@ lev) |- mapOptionTree drop_arg_types_as_tree Σ₂ @ lev
     end.
 
   Definition check_hof : forall {Γ}(t:HaskType Γ ★),
@@ -232,7 +219,7 @@ Section HaskSkolemizer.
     intros.
 
     refine (match X as R in Rule H C with
-      | RArrange Γ Δ a b x d           => let case_RArrange := tt      in _
+      | RArrange Γ Δ a b x l d         => let case_RArrange := tt      in _
       | RNote    Γ Δ Σ τ l n           => let case_RNote := tt         in _
       | RLit     Γ Δ l     _           => let case_RLit := tt          in _
       | RVar     Γ Δ σ           lev   => let case_RVar := tt          in _
@@ -245,9 +232,11 @@ Section HaskSkolemizer.
       | RAbsCo   Γ Δ Σ κ σ  σ₁ σ₂  lev => let case_RAbsCo := tt        in _
       | RApp     Γ Δ Σ₁ Σ₂ tx te lev   => let case_RApp := tt          in _
       | RLet     Γ Δ Σ₁ Σ₂ σ₁ σ₂ lev   => let case_RLet := tt          in _
+      | RCut     Γ Δ Σ Σ₁ Σ₁₂ Σ₂ Σ₃ l  => let case_RCut := tt          in _
+      | RLeft    Γ Δ Σ₁ Σ₂  Σ     l    => let case_RLeft := tt in _
+      | RRight   Γ Δ Σ₁ Σ₂  Σ     l    => let case_RRight := tt in _
       | RWhere   Γ Δ Σ₁ Σ₂ Σ₃ σ₁ σ₂ lev => let case_RWhere := tt          in _
-      | RJoin    Γ p lri m x q         => let case_RJoin := tt in _
-      | RVoid    _ _                   => let case_RVoid := tt   in _
+      | RVoid    _ _           l       => let case_RVoid := tt   in _
       | RBrak    Γ Δ t ec succ lev     => let case_RBrak := tt         in _
       | REsc     Γ Δ t ec succ lev     => let case_REsc := tt          in _
       | RCase    Γ Δ lev tc Σ avars tbranches alts => let case_RCase := tt         in _
@@ -256,7 +245,7 @@ Section HaskSkolemizer.
 
       destruct case_RArrange.
         simpl.
-        destruct (getjlev x).
+        destruct l. 
         apply nd_rule.
         apply SFlat.
         apply RArrange.
@@ -264,7 +253,7 @@ Section HaskSkolemizer.
         apply nd_rule.
         apply SFlat.
         apply RArrange.
-        apply RRight.
+        apply ARight.
         apply d.
 
       destruct case_RBrak.
@@ -301,7 +290,7 @@ Section HaskSkolemizer.
         rewrite H.
         rewrite H0.
         simpl.
-        eapply nd_comp; [ idtac | eapply nd_rule; eapply SFlat; eapply RArrange; apply RuCanL ].
+        eapply nd_comp; [ idtac | eapply nd_rule; eapply SFlat; eapply RArrange; apply AuCanL ].
         apply nd_rule.
         apply SFlat.
         apply RLit.
@@ -316,7 +305,7 @@ Section HaskSkolemizer.
         rewrite H.
         rewrite H0.
         simpl.
-        eapply nd_comp; [ idtac | eapply nd_rule; apply SFlat; eapply RArrange; apply RuCanR ].
+        eapply nd_comp; [ idtac | eapply nd_rule; apply SFlat; eapply RArrange; apply AuCanR ].
         apply nd_rule.
         apply SFlat.
         apply RVar.
@@ -331,7 +320,7 @@ Section HaskSkolemizer.
         rewrite H.
         rewrite H0.
         simpl.
-        eapply nd_comp; [ idtac | eapply nd_rule; apply SFlat; eapply RArrange; apply RuCanR ].
+        eapply nd_comp; [ idtac | eapply nd_rule; apply SFlat; eapply RArrange; apply AuCanR ].
         apply nd_rule.
         apply SFlat.
         apply RGlobal.
@@ -347,9 +336,9 @@ Section HaskSkolemizer.
         apply nd_rule.
           apply SFlat.
           apply RArrange.
-          eapply RComp.
-          eapply RCossa.
-          eapply RLeft.
+          eapply AComp.
+          eapply AuAssoc.
+          eapply ALeft.
           apply take_arrange.
 
       destruct case_RCast.
@@ -361,16 +350,6 @@ Section HaskSkolemizer.
         apply γ.
         apply (Prelude_error "found RCast at level >0").
 
-      destruct case_RJoin.
-        simpl.
-        destruct (getjlev x).
-        destruct (getjlev q).
-        apply nd_rule.
-        apply SFlat.
-        apply RJoin.
-        apply (Prelude_error "found RJoin at level >0").
-        apply (Prelude_error "found RJoin at level >0").
-
       destruct case_RApp.
         simpl.
         destruct lev.
@@ -385,14 +364,14 @@ Section HaskSkolemizer.
         rewrite H0.
         simpl.
         eapply nd_comp.
-        eapply nd_prod; [ idtac | eapply nd_rule; eapply SFlat; eapply RArrange; eapply RCanR ].
+        eapply nd_prod; [ idtac | eapply nd_rule; eapply SFlat; eapply RArrange; eapply ACanR ].
         eapply nd_rule.
         eapply SFlat.
         eapply RArrange.
-        eapply RLeft.
+        eapply ALeft.
         eapply take_unarrange.
 
-        eapply nd_comp; [ idtac | eapply nd_rule; apply SFlat; eapply RArrange; apply RAssoc ].
+        eapply nd_comp; [ idtac | eapply nd_rule; apply SFlat; eapply RArrange; apply AAssoc ].
         eapply nd_rule; eapply SFlat; apply RWhere.
 
       destruct case_RLet.
@@ -408,17 +387,17 @@ Section HaskSkolemizer.
         rewrite H0.
 
         eapply nd_comp.
-        eapply nd_prod; [ eapply nd_rule; eapply SFlat; eapply RArrange; eapply RCanR | eapply nd_id ].
+        eapply nd_prod; [ eapply nd_rule; eapply SFlat; eapply RArrange; eapply ACanR | eapply nd_id ].
 
         set (@RLet Γ Δ Σ₁ (Σ₂,,(take_arg_types_as_tree σ₂ @@@ (h::lev))) σ₁ (drop_arg_types_as_tree σ₂) (h::lev)) as q.
-        eapply nd_comp; [ idtac | eapply nd_rule; apply SFlat; eapply RArrange; apply RAssoc ].
+        eapply nd_comp; [ idtac | eapply nd_rule; apply SFlat; eapply RArrange; apply AAssoc ].
         eapply nd_comp; [ idtac | eapply nd_rule; eapply SFlat; eapply q ].
         apply nd_prod.
           apply nd_id.
           apply nd_rule.
           eapply SFlat.
           eapply RArrange.
-          eapply RCossa.
+          eapply AuAssoc.
 
       destruct case_RWhere.
         simpl.
@@ -433,19 +412,105 @@ Section HaskSkolemizer.
         rewrite H0.
 
         eapply nd_comp.
-        eapply nd_prod; [ apply nd_id | eapply nd_rule; eapply SFlat; eapply RArrange; eapply RCanR ].
-        eapply nd_comp; [ idtac | eapply nd_rule; eapply SFlat; eapply RArrange; eapply RAssoc ].
-        eapply nd_comp; [ idtac | eapply nd_rule; eapply SFlat; eapply RArrange; eapply RLeft; eapply RAssoc ].
+        eapply nd_prod; [ apply nd_id | eapply nd_rule; eapply SFlat; eapply RArrange; eapply ACanR ].
+        eapply nd_comp; [ idtac | eapply nd_rule; eapply SFlat; eapply RArrange; eapply AAssoc ].
+        eapply nd_comp; [ idtac | eapply nd_rule; eapply SFlat; eapply RArrange; eapply ALeft; eapply AAssoc ].
         eapply nd_comp; [ idtac | eapply nd_rule; eapply SFlat; eapply RWhere ].
         apply nd_prod; [ idtac | eapply nd_id ].
         eapply nd_rule; apply SFlat; eapply RArrange.
-        eapply RComp.
-        eapply RCossa.
-        apply RLeft.
-        eapply RCossa.
+        eapply AComp.
+        eapply AuAssoc.
+        apply ALeft.
+        eapply AuAssoc.
+
+      destruct case_RCut.
+        simpl; destruct l; [ apply nd_rule; apply SFlat; apply RCut | idtac ].
+        set (mapOptionTreeAndFlatten take_arg_types_as_tree Σ₃) as Σ₃''.
+        set (mapOptionTree drop_arg_types_as_tree Σ₃) as Σ₃'''.
+        set (mapOptionTreeAndFlatten take_arg_types_as_tree Σ₁₂) as Σ₁₂''.
+        set (mapOptionTree drop_arg_types_as_tree Σ₁₂) as Σ₁₂'''.
+        destruct (decide_tree_empty (Σ₁₂'' @@@ (h::l)));
+          [ idtac | apply (Prelude_error "used RCut on a variable with function type") ].
+        destruct (eqd_dec Σ₁₂ Σ₁₂'''); [ idtac | apply (Prelude_error "used RCut on a variable with function type") ].
+        rewrite <- e.
+        clear e.
+        destruct s.
+        eapply nd_comp.
+          eapply nd_prod.
+          eapply nd_rule.
+          eapply SFlat.
+          eapply RArrange.
+          eapply AComp.
+          eapply ALeft.
+          eapply arrangeCancelEmptyTree with (q:=x).
+          apply e.
+          apply ACanR.
+          apply nd_id.
+        eapply nd_comp; [ idtac | eapply nd_rule; eapply SFlat; eapply RArrange; eapply AAssoc ].
+        eapply nd_comp; [ idtac | eapply nd_rule; eapply SFlat; eapply RArrange; eapply ALeft; eapply AAssoc ].
+        eapply nd_comp; [ idtac | eapply nd_rule; eapply SFlat; eapply RCut ].
+        apply nd_prod.
+        apply nd_id.
+        eapply nd_rule.
+          eapply SFlat.
+          eapply RArrange.
+          eapply AComp.
+          eapply AuAssoc.
+          eapply ALeft.
+          eapply AComp.
+          eapply AuAssoc.
+          eapply ALeft.
+          eapply AId.
+
+      destruct case_RLeft.
+        simpl; destruct l; [ apply nd_rule; apply SFlat; apply RLeft | idtac ].
+        set (mapOptionTreeAndFlatten take_arg_types_as_tree Σ₂) as Σ₂'.
+        set (mapOptionTreeAndFlatten take_arg_types_as_tree Σ) as Σ'.
+        set (mapOptionTree drop_arg_types_as_tree Σ₂) as Σ₂''.
+        set (mapOptionTree drop_arg_types_as_tree Σ) as Σ''.
+        destruct (decide_tree_empty (Σ' @@@ (h::l)));
+          [ idtac | apply (Prelude_error "used RLeft on a variable with function type") ].
+        destruct (eqd_dec Σ Σ''); [ idtac | apply (Prelude_error "used RLeft on a variable with function type") ].
+        rewrite <- e.
+        clear Σ'' e.
+        destruct s.
+        set (arrangeUnCancelEmptyTree _ _ e) as q.
+        eapply nd_comp; [ idtac | eapply nd_rule; eapply SFlat; eapply RArrange; eapply ALeft; eapply ARight; eapply q ].
+        eapply nd_comp; [ idtac | eapply nd_rule; eapply SFlat; eapply RArrange; eapply ALeft; eapply AuCanL; eapply q ].
+        eapply nd_comp; [ idtac | eapply nd_rule; eapply SFlat; eapply RArrange; eapply AAssoc ].
+        apply nd_rule.
+        eapply SFlat.
+        eapply RLeft.
+        
+      destruct case_RRight.
+        simpl; destruct l; [ apply nd_rule; apply SFlat; apply RRight | idtac ].
+        set (mapOptionTreeAndFlatten take_arg_types_as_tree Σ₂) as Σ₂'.
+        set (mapOptionTreeAndFlatten take_arg_types_as_tree Σ) as Σ'.
+        set (mapOptionTree drop_arg_types_as_tree Σ₂) as Σ₂''.
+        set (mapOptionTree drop_arg_types_as_tree Σ) as Σ''.
+        destruct (decide_tree_empty (Σ' @@@ (h::l)));
+          [ idtac | apply (Prelude_error "used RRight on a variable with function type") ].
+        destruct (eqd_dec Σ Σ''); [ idtac | apply (Prelude_error "used RRight on a variable with function type") ].
+        rewrite <- e.
+        clear Σ'' e.
+        destruct s.
+        set (arrangeUnCancelEmptyTree _ _ e) as q.
+        eapply nd_comp; [ idtac | eapply nd_rule; eapply SFlat; eapply RArrange; eapply ALeft; eapply ALeft; eapply q ].
+        eapply nd_comp; [ idtac | eapply nd_rule; eapply SFlat; eapply RArrange; eapply ALeft; eapply AuCanR ].
+        eapply nd_comp; [ idtac | eapply nd_rule; eapply SFlat; eapply RArrange; eapply AAssoc ].
+        eapply nd_comp; [ idtac | eapply nd_rule; eapply SFlat; eapply RArrange; eapply ALeft; eapply AExch ].  (* yuck *)
+        eapply nd_comp; [ idtac | eapply nd_rule; eapply SFlat; eapply RArrange; eapply AuAssoc ].
+        eapply nd_rule.
+        eapply SFlat.
+        apply RRight.
 
       destruct case_RVoid.
         simpl.
+        destruct l.
+        apply nd_rule.
+        apply SFlat.
+        apply RVoid.
+        eapply nd_comp; [ idtac | eapply nd_rule; eapply SFlat; eapply RArrange; eapply AuCanL ].
         apply nd_rule.
         apply SFlat.
         apply RVoid.
@@ -474,17 +539,16 @@ Section HaskSkolemizer.
       destruct case_RLetRec.
         simpl.
         destruct t.
-        destruct (getjlev (y @@@ nil)).
         apply nd_rule.
         apply SFlat.
         apply (@RLetRec Γ Δ lri x y nil).
         apply (Prelude_error "RLetRec at depth>0").
-        apply (Prelude_error "RLetRec at depth>0").
 
       destruct case_RCase.
         simpl.
         apply (Prelude_error "CASE: BIG FIXME").
         Defined.
+
   Transparent take_arg_types_as_tree.
 
 End HaskSkolemizer.