HaskFlattener: support escapifying multi-leaf contexts

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

diff --git a/src/HaskFlattener.v b/src/HaskFlattener.v
index ed3ca43..a5f4261 100644 (file)
--- a/src/HaskFlattener.v
+++ b/src/HaskFlattener.v
@@ -722,24 +722,116 @@ Section HaskFlattener.
       apply IHsucc2.
     Defined.
 
+  Definition arrange_empty_tree : forall {T}{A}(q:Tree A)(t:Tree ??T),
+    t = mapTree (fun _:A => None) q ->
+    Arrange t [].
+    intros T A q.
+    induction q; intros.
+      simpl in H.
+      rewrite H.
+      apply RId.
+    simpl in *.
+    destruct t; try destruct o; inversion H.
+      set (IHq1 _ H1) as x1.
+      set (IHq2 _ H2) as x2.
+      eapply RComp.
+        eapply RRight.
+        rewrite <- H1.
+        apply x1.
+      eapply RComp.
+        apply RCanL.
+        rewrite <- H2.
+        apply x2.
+      Defined.
+
+(*  Definition unarrange_empty_tree : forall {T}{A}(t:Tree ??T)(q:Tree A),
+    t = mapTree (fun _:A => None) q ->
+    Arrange [] t.
+  Defined.*)
+
+  Definition decide_tree_empty : forall {T:Type}(t:Tree ??T),
+    sum { q:Tree unit & t = mapTree (fun _ => None) q } unit.
+    intro T.
+    refine (fix foo t :=
+      match t with
+        | T_Leaf x => _
+        | T_Branch b1 b2 => let b1' := foo b1 in let b2' := foo b2 in _
+      end).
+    intros.
+    destruct x.
+    right; apply tt.
+    left.
+      exists (T_Leaf tt).
+      auto.
+    destruct b1'.
+    destruct b2'.
+    destruct s.
+    destruct s0.
+    subst.
+    left.
+    exists (x,,x0).
+    reflexivity.
+    right; auto.
+    right; auto.
+    Defined.
+
   Definition arrange_esc : forall Γ Δ ec succ t,
    ND Rule
      [Γ > Δ > mapOptionTree (flatten_leveled_type ) succ |- [t @@  nil]]
      [Γ > Δ > mapOptionTree (flatten_leveled_type ) (drop_lev (ec :: nil) succ),,
       [(@ga_mk _ (v2t ec) [] (mapOptionTree (flatten_type ○ unlev) (take_lev (ec :: nil) succ))) @@  nil] |- [t @@  nil]].
     intros.
-    unfold drop_lev.
     set (@arrange _ succ (levelMatch (ec::nil))) as q.
+    set (@drop_lev Γ (ec::nil) succ) as q'.
+    assert (@drop_lev Γ (ec::nil) succ=q') as H.
+      reflexivity.
+    unfold drop_lev in H.
+    unfold mkDropFlags in H.
+    rewrite H in q.
+    clear H.
     set (arrangeMap _ _ flatten_leveled_type q) as y.
     eapply nd_comp.
     eapply nd_rule.
     eapply RArrange.
     apply y.
-    idtac.
     clear y q.
 
+    set (mapOptionTree flatten_leveled_type (dropT (mkFlags (liftBoolFunc false (bnot ○ levelMatch (ec :: nil))) succ))) as q.
+    destruct (decide_tree_empty q); [ idtac | apply (Prelude_error "escapifying open code not yet supported") ].
+    destruct s.
+
+    simpl.
+    eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; apply RExch ].
+    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 q'' ].
+    clear q''.
+    eapply nd_comp; [ apply nd_rlecnac | idtac ].
+    apply nd_prod.
+    apply nd_rule.
+    apply RArrange.
+    eapply RComp; [ idtac | apply RCanR ].
+    apply RLeft.
+    apply (@arrange_empty_tree _ _ _ _ e).
+    
+    eapply nd_comp.
+      eapply nd_rule.
+      eapply (@RVar Γ Δ t nil).
+    apply nd_rule.
+      apply RArrange.
+      eapply RComp.
+      apply RuCanL.
+      apply RRight.
+      apply RWeak.
+(*
+    eapply decide_tree_empty.
+
+    simpl.
+    set (dropT (mkFlags (liftBoolFunc false (bnot ○ levelMatch (ec :: nil))) succ)) as escapified.
+    destruct (decide_tree_empty escapified).
+
     induction succ.
     destruct a.
+      unfold drop_lev.
       destruct l.
       simpl.
       unfold mkDropFlags; simpl.
@@ -763,6 +855,7 @@ Section HaskFlattener.
         apply RLeft.
         apply RWeak.
       apply (Prelude_error "escapifying code with multi-leaf antecedents is not supported").
+*)
       Defined.
 
   Lemma mapOptionTree_distributes
@@ -771,32 +864,6 @@ Section HaskFlattener.
     reflexivity.
     Qed.
 
-  Definition decide_tree_empty : forall {T:Type}(t:Tree ??T),
-    sum { q:Tree unit & t = mapTree (fun _ => None) q } unit.
-    intro T.
-    refine (fix foo t :=
-      match t with
-        | T_Leaf x => _
-        | T_Branch b1 b2 => let b1' := foo b1 in let b2' := foo b2 in _
-      end).
-    intros.
-    destruct x.
-    right; apply tt.
-    left.
-      exists (T_Leaf tt).
-      auto.
-    destruct b1'.
-    destruct b2'.
-    destruct s.
-    destruct s0.
-    subst.
-    left.
-    exists (x,,x0).
-    reflexivity.
-    right; auto.
-    right; auto.
-    Defined.
-
   Lemma unlev_relev : forall {Γ}(t:Tree ??(HaskType Γ ★)) lev, mapOptionTree unlev (t @@@ lev) = t.
     intros.
     induction t.