remove magic flatten/unflatten identifiers

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

diff --git a/src/HaskFlattener.v b/src/HaskFlattener.v
index d822dd6..59636bf 100644 (file)
--- a/src/HaskFlattener.v
+++ b/src/HaskFlattener.v
@@ -161,9 +161,6 @@ Section HaskFlattener.
   (*******************************************************************************)
 
 
-  Context (hetmet_flatten : WeakExprVar).
-  Context (hetmet_unflatten : WeakExprVar).
-  Context (hetmet_id      : WeakExprVar).
   Context {unitTy : forall TV, RawHaskType TV ECKind  -> RawHaskType TV ★                                          }.
   Context {prodTy : forall TV, RawHaskType TV ECKind  -> RawHaskType TV ★  -> RawHaskType TV ★ -> RawHaskType TV ★ }.
   Context {gaTy   : forall TV, RawHaskType TV ECKind  -> RawHaskType TV ★ -> RawHaskType TV ★  -> RawHaskType TV ★ }.
@@ -272,6 +269,8 @@ Section HaskFlattener.
   ; ga_second    : ∀ Γ Δ ec l a b x, ND Rule [] [Γ > Δ >      [@ga_mk Γ ec a b @@l] |- [@ga_mk Γ ec (x,,a) (x,,b) ]@l ]
   ; ga_lit       : ∀ Γ Δ ec l lit  , ND Rule [] [Γ > Δ >                          [] |- [@ga_mk Γ ec [] [literalType lit] ]@l ]
   ; ga_curry     : ∀ Γ Δ ec l a b c, ND Rule [] [Γ > Δ > [@ga_mk Γ ec (a,,[b]) [c] @@ l] |- [@ga_mk Γ ec a [b ---> c] ]@ l ]
+  ; ga_loopl     : ∀ Γ Δ ec l x y z, ND Rule [] [Γ > Δ > [@ga_mk Γ ec (z,,x) (z,,y) @@ l] |- [@ga_mk Γ ec x y ]@ l ]
+  ; ga_loopr     : ∀ Γ Δ ec l x y z, ND Rule [] [Γ > Δ > [@ga_mk Γ ec (x,,z) (y,,z) @@ l] |- [@ga_mk Γ ec x y ]@ l ]
   ; ga_comp      : ∀ Γ Δ ec l a b c, ND Rule [] [Γ > Δ > [@ga_mk Γ ec a b @@ l],,[@ga_mk Γ ec b c @@ l] |- [@ga_mk Γ ec a c ]@l ] 
   ; ga_apply     : ∀ Γ Δ ec l a a' b c,
                  ND Rule [] [Γ > Δ > [@ga_mk Γ ec a [b ---> c] @@ l],,[@ga_mk Γ ec a' [b] @@ l] |- [@ga_mk Γ ec (a,,a') [c] ]@l ]
@@ -288,7 +287,7 @@ Section HaskFlattener.
     ND Rule [ Γ > Δ > ant |- [x]@lev ] [ Γ > Δ > ant      |- [y]@lev ].
     intros.
     eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; eapply ACanR ].
-    eapply nd_comp; [ idtac | eapply nd_rule; apply RLet ].
+    eapply nd_comp; [ idtac | apply RLet ].
     eapply nd_comp; [ apply nd_rlecnac | idtac ].
     apply nd_prod.
     apply nd_id.
@@ -304,7 +303,7 @@ Section HaskFlattener.
       [ Γ > Δ > a                           |- [@ga_mk _ ec y z ]@lev ]
       [ Γ > Δ > a,,[@ga_mk _ ec x y @@ lev] |- [@ga_mk _ ec x z ]@lev ].
     intros.
-    eapply nd_comp; [ idtac | eapply nd_rule; eapply RLet ].
+    eapply nd_comp; [ idtac | eapply RLet ].
     eapply nd_comp; [ apply nd_rlecnac | idtac ].
     apply nd_prod.
     apply nd_id.
@@ -327,7 +326,7 @@ Section HaskFlattener.
       [ Γ > Δ > a                           |- [@ga_mk _ ec x y ]@lev ]
       [ Γ > Δ > a,,[@ga_mk _ ec y z @@ lev] |- [@ga_mk _ ec x z ]@lev ].
     intros.
-    eapply nd_comp; [ idtac | eapply nd_rule; eapply RLet ].
+    eapply nd_comp; [ idtac | eapply RLet ].
     eapply nd_comp; [ apply nd_rlecnac | idtac ].
     apply nd_prod.
     apply nd_id.
@@ -348,7 +347,7 @@ Section HaskFlattener.
             [ Γ > Δ > Σ                    |- [@ga_mk Γ ec (a,,c) (b,,c) ]@lev ].
     intros.
     eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; eapply ACanR ].
-    eapply nd_comp; [ idtac | eapply nd_rule; apply RLet ].
+    eapply nd_comp; [ idtac | apply RLet ].
     eapply nd_comp; [ apply nd_rlecnac | idtac ].
     apply nd_prod.
     apply nd_id.
@@ -371,7 +370,7 @@ Section HaskFlattener.
      [ Γ > Δ > Σ                    |- [@ga_mk Γ ec (c,,a) (c,,b) ]@lev ].
     intros.
     eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; eapply ACanR ].
-    eapply nd_comp; [ idtac | eapply nd_rule; apply RLet ].
+    eapply nd_comp; [ idtac | apply RLet ].
     eapply nd_comp; [ apply nd_rlecnac | idtac ].
     apply nd_prod.
     apply nd_id.
@@ -394,12 +393,12 @@ Section HaskFlattener.
      [Γ > Δ > Σ,,[@ga_mk Γ ec [] a @@ l] |- [@ga_mk Γ ec x       b ]@l ].
      intros.
      eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; eapply AExch ].
-     eapply nd_comp; [ idtac | eapply nd_rule; eapply RLet ].
+     eapply nd_comp; [ idtac | eapply RLet ].
      eapply nd_comp; [ apply nd_llecnac | idtac ].
      apply nd_prod.
      apply ga_first.
 
-     eapply nd_comp; [ idtac | eapply nd_rule; eapply RLet ].
+     eapply nd_comp; [ idtac | eapply RLet ].
      eapply nd_comp; [ apply nd_llecnac | idtac ].
      apply nd_prod.
      apply postcompose.
@@ -450,14 +449,14 @@ Section HaskFlattener.
           set (mapOptionTree (flatten_type ○ unlev) (take_lev (ec :: lev) b)) as b' in *.
           set (mapOptionTree (flatten_type ○ unlev) (take_lev (ec :: lev) c)) as c' in *.
           eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; apply ACanL ].
-          eapply nd_comp; [ idtac | eapply nd_rule; apply
+          eapply nd_comp; [ idtac | apply
              (@RLet Γ Δ [] [] (@ga_mk _ (v2t ec) a' b') (@ga_mk _ (v2t ec) a' c')) ].
           eapply nd_comp; [ apply nd_llecnac | idtac ].
           apply nd_prod.
           apply r2'.
           eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; apply AuCanR ].
           eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; apply ACanL ].
-          eapply nd_comp; [ idtac | eapply nd_rule;  apply RLet ].
+          eapply nd_comp; [ idtac | apply RLet ].
           eapply nd_comp; [ apply nd_llecnac | idtac ].
           eapply nd_prod.
           apply r1'.
@@ -537,13 +536,13 @@ Section HaskFlattener.
     intro pfb.
     apply secondify with (c:=a)  in pfb.
     apply firstify  with (c:=[])  in pfa.
-    eapply nd_comp; [ idtac | eapply nd_rule; eapply RLet ].
+    eapply nd_comp; [ idtac | eapply RLet ].
     eapply nd_comp; [ eapply nd_llecnac | idtac ].
     apply nd_prod.
     apply pfa.
     clear pfa.
 
-    eapply nd_comp; [ idtac | eapply nd_rule; eapply RLet ].
+    eapply nd_comp; [ idtac | eapply RLet ].
     eapply nd_comp; [ apply nd_llecnac | idtac ].
     apply nd_prod.
     eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; eapply ACanL ].
@@ -576,7 +575,7 @@ Section HaskFlattener.
     eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; eapply AExch ].
     simpl.
     eapply nd_comp; [ apply nd_llecnac | idtac ].
-    eapply nd_comp; [ idtac | eapply nd_rule; eapply RLet ].
+    eapply nd_comp; [ idtac | eapply RLet ].
     apply nd_prod.
     Focus 2.
     apply nd_id.
@@ -643,7 +642,7 @@ Section HaskFlattener.
     simpl.
     eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; apply AExch ].
     set (fun z z' => @RLet Γ Δ z (mapOptionTree flatten_leveled_type q') t z' nil) as q''.
-    eapply nd_comp; [ idtac | eapply nd_rule; apply RLet ].
+    eapply nd_comp; [ idtac | apply RLet ].
     clear q''.
     eapply nd_comp; [ apply nd_rlecnac | idtac ].
     apply nd_prod.
@@ -775,9 +774,6 @@ Section HaskFlattener.
                  (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.
@@ -830,11 +826,9 @@ Section HaskFlattener.
       | RAppCo   Γ Δ Σ κ σ₁ σ₂ γ σ lev => let case_RAppCo := tt        in _
       | 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 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 _
+      | 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 _
       | 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 _
@@ -888,6 +882,7 @@ Section HaskFlattener.
       rename l into g.
       rename σ into l.
       destruct l as [|ec lev]; simpl. 
+        (*
         destruct (eqd_dec (g:CoreVar) (hetmet_flatten:CoreVar)).
           set (flatten_type (g wev)) as t.
           set (RGlobal _ Δ nil (mkGlobal Γ t hetmet_id)) as q.
@@ -902,6 +897,7 @@ Section HaskFlattener.
           apply nd_rule.
           apply q.
           apply INil.
+          *)
         unfold flatten_leveled_type. simpl.
           apply nd_rule; rewrite globals_do_not_have_code_types.
           apply RGlobal.
@@ -958,59 +954,6 @@ Section HaskFlattener.
   Notation "!<[@]> x" := (mapOptionTree flatten_leveled_type x) (at level 1).
 *)
 
-    destruct case_RLet.
-      simpl.
-      destruct lev as [|ec lev]; simpl; [ apply nd_rule; apply RLet; auto | idtac ].
-      repeat drop_simplify.
-      repeat take_simplify.
-      simpl.
-
-      set (mapOptionTree (flatten_type ○ unlev) (take_lev (ec :: lev) Σ₁)) as Σ₁'.
-      set (mapOptionTree (flatten_type ○ unlev) (take_lev (ec :: lev) Σ₂)) as Σ₂'.
-      set (mapOptionTree flatten_leveled_type (drop_lev (ec :: lev) Σ₁)) as Σ₁''.
-      set (mapOptionTree flatten_leveled_type (drop_lev (ec :: lev) Σ₂)) as Σ₂''.
-
-      eapply nd_comp.
-      eapply nd_prod; [ idtac | apply nd_id ].
-      eapply boost.
-      apply (ga_first _ _ _ _ _ _ Σ₂').
-
-      eapply nd_comp; [ idtac | eapply nd_rule; eapply RLet ].
-      apply nd_prod.
-      apply nd_id.
-      eapply nd_comp; [ eapply nd_rule; eapply RArrange; eapply ACanL | idtac ].
-      eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; eapply AExch (* okay *)].
-      apply precompose.
-
-    destruct case_RWhere.
-      simpl.
-      destruct lev as [|ec lev]; simpl; [ apply nd_rule; apply RWhere; auto | idtac ].
-      repeat take_simplify.
-      repeat drop_simplify.
-      simpl.
-
-      set (mapOptionTree (flatten_type ○ unlev) (take_lev (ec :: lev) Σ₁)) as Σ₁'.
-      set (mapOptionTree (flatten_type ○ unlev) (take_lev (ec :: lev) Σ₂)) as Σ₂'.
-      set (mapOptionTree (flatten_type ○ unlev) (take_lev (ec :: lev) Σ₃)) as Σ₃'.
-      set (mapOptionTree flatten_leveled_type (drop_lev (ec :: lev) Σ₁)) as Σ₁''.
-      set (mapOptionTree flatten_leveled_type (drop_lev (ec :: lev) Σ₂)) as Σ₂''.
-      set (mapOptionTree flatten_leveled_type (drop_lev (ec :: lev) Σ₃)) as Σ₃''.
-
-      eapply nd_comp.
-      eapply nd_prod; [ eapply nd_id | idtac ].
-      eapply (first_nd _ _ _ _ _ _ Σ₃').
-      eapply nd_comp.
-      eapply nd_prod; [ eapply nd_id | idtac ].
-      eapply (second_nd _ _ _ _ _ _ Σ₁').
-
-      eapply nd_comp; [ idtac | eapply nd_rule; eapply RWhere ].
-      apply nd_prod; [ idtac | apply nd_id ].
-      eapply nd_comp; [ idtac | eapply precompose' ].
-      apply nd_rule.
-      apply RArrange.
-      apply ALeft.
-      apply ACanL.
-
     destruct case_RCut.
       simpl.
       destruct l as [|ec lev]; simpl.
@@ -1022,41 +965,50 @@ Section HaskFlattener.
         rewrite <- IHΣ₁₂1.
         rewrite <- IHΣ₁₂2.
         reflexivity.
-      simpl.
-      repeat drop_simplify.
-      simpl.
-      repeat take_simplify.
+      simpl; repeat drop_simplify.
+      simpl; repeat take_simplify.
       simpl.
       set (drop_lev (ec :: lev) (Σ₁₂ @@@ (ec :: lev))) as x1.
       rewrite take_lemma'.
       rewrite mapOptionTree_compose.
       rewrite mapOptionTree_compose.
       rewrite mapOptionTree_compose.
+      rewrite mapOptionTree_compose.
       rewrite unlev_relev.
       rewrite <- mapOptionTree_compose.
       rewrite <- mapOptionTree_compose.
+      rewrite <- mapOptionTree_compose.
       eapply nd_comp; [ idtac | eapply nd_rule; eapply RCut ]. 
       apply nd_prod.
       apply nd_id.
       eapply nd_comp.
       eapply nd_rule.
       eapply RArrange.
+      eapply ALeft.
       eapply ARight.
       unfold x1.
       rewrite drop_to_nothing.
       apply arrangeCancelEmptyTree with (q:=(mapTree (fun _ : ??(HaskType Γ ★) => tt) Σ₁₂)).
-      admit. (* OK *)
-      eapply nd_comp; [ eapply nd_rule; eapply RArrange; eapply ACanL | idtac ].
+        induction Σ₁₂; try destruct a; auto.
+        simpl.
+        rewrite <- IHΣ₁₂1 at 2.
+        rewrite <- IHΣ₁₂2 at 2.
+        reflexivity.
+      eapply nd_comp; [ eapply nd_rule; eapply RArrange; eapply ALeft; eapply ACanL | idtac ].
       set (mapOptionTree flatten_type Σ₁₂) as a.
       set (mapOptionTree (flatten_type ○ unlev) (take_lev (ec :: lev) Σ₁)) as b.
       set (mapOptionTree flatten_leveled_type (drop_lev (ec :: lev) Σ₂)) as c.
       set (mapOptionTree (flatten_type ○ unlev) (take_lev (ec :: lev) Σ₂)) as d.
+      set (mapOptionTree flatten_leveled_type (drop_lev (ec :: lev) Σ)) as e.
+      set (mapOptionTree (flatten_type ○ unlev) (take_lev (ec :: lev) Σ)) as f.
       eapply nd_comp; [ idtac | eapply nd_rule; eapply RCut ].
       eapply nd_comp; [ apply nd_llecnac | idtac ].
       apply nd_prod.
       simpl.
-      eapply ga_first.
-      eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; eapply AExch ].
+      eapply secondify.
+      apply ga_first.
+      eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; eapply ALeft; eapply AExch ].
+      eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; eapply AuAssoc ].
       simpl.
       apply precompose.
 
@@ -1081,7 +1033,11 @@ Section HaskFlattener.
         eapply RArrange.
         eapply ARight.
         apply arrangeUnCancelEmptyTree with (q:=(mapTree (fun _ : ??(HaskType Γ ★) => tt) Σ)).
-        admit (* FIXME *).
+          induction Σ; try destruct a; auto.
+          simpl.
+          rewrite <- IHΣ1 at 2.
+          rewrite <- IHΣ2 at 2.
+          reflexivity.
         idtac.
         eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; eapply AuCanL ].
         apply boost.
@@ -1116,7 +1072,11 @@ Section HaskFlattener.
         eapply RArrange.
         eapply ALeft.
         apply arrangeUnCancelEmptyTree with (q:=(mapTree (fun _ : ??(HaskType Γ ★) => tt) Σ)).
-        admit (* FIXME *).
+          induction Σ; try destruct a; auto.
+          simpl.
+          rewrite <- IHΣ1 at 2.
+          rewrite <- IHΣ2 at 2.
+          reflexivity.
         idtac.
         eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; eapply AuCanR ].
         apply boost.
@@ -1132,10 +1092,13 @@ Section HaskFlattener.
 
     destruct case_RVoid.
       simpl.
-      apply nd_rule.
       destruct l.
+      apply nd_rule.
       apply RVoid.
-      apply (Prelude_error "RVoid at level >0").
+      drop_simplify.
+      take_simplify.
+      simpl.
+      apply ga_id.
         
     destruct case_RAppT.
       simpl. destruct lev; simpl.
@@ -1206,7 +1169,31 @@ Section HaskFlattener.
         rewrite IHy1.
         rewrite IHy2.
         reflexivity.
-      apply (Prelude_error "LetRec not supported inside brackets yet (FIXME)").
+      repeat drop_simplify.
+      repeat take_simplify.
+      simpl.
+      rewrite drop_to_nothing.
+      eapply nd_comp.
+        eapply nd_rule.
+        eapply RArrange.
+        eapply AComp.
+        eapply ARight.
+        apply arrangeCancelEmptyTree with (q:=y).
+          induction y; try destruct a; auto.
+          simpl.
+          rewrite <- IHy1.
+          rewrite <- IHy2.
+          reflexivity.
+        apply ACanL.
+        rewrite take_lemma'.
+        set (mapOptionTree (flatten_type ○ unlev) (take_lev (h :: lev) lri)) as lri'.
+        set (mapOptionTree flatten_leveled_type (drop_lev (h :: lev) lri)) as lri''.
+        replace (mapOptionTree (flatten_type ○ unlev) (y @@@ (h :: lev))) with (mapOptionTree flatten_type y).
+        apply boost.
+        apply ga_loopl.
+        rewrite <- mapOptionTree_compose.
+        simpl.
+        reflexivity.
 
     destruct case_RCase.
       simpl.
@@ -1272,7 +1259,7 @@ Section HaskFlattener.
       eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; apply AuCanR ].
       eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; apply AuCanR ].
       eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; apply ACanL ].
-      eapply nd_comp; [ idtac | eapply nd_rule; eapply RLet ].
+      eapply nd_comp; [ idtac | eapply RLet ].
       eapply nd_comp; [ apply nd_llecnac | idtac ].
       apply nd_prod; [ idtac | eapply boost ].
       induction x.