X-Git-Url: http://git.megacz.com/?a=blobdiff_plain;f=src%2FGeneral.v;h=96ac1baf758f6721787292c58d588c4e66f8a3c9;hb=32436fdf380f7f2efc7a70896268509e7b3e0d6f;hp=685619ff1e646ebf75eb4bff45c744fe2994d62b;hpb=8f00501ac48984925832279f7d67302c09a570ec;p=coq-hetmet.git

diff --git a/src/General.v b/src/General.v
index 685619f..96ac1ba 100644
--- a/src/General.v
+++ b/src/General.v
@@ -41,6 +41,13 @@ Notation "[ q ]"    := (@T_Leaf (option _) (Some q))            : tree_scope.
 Notation "[ ]"      := (@T_Leaf (option _) None)                : tree_scope.
 Notation "[]"       := (@T_Leaf (option _) None)                : tree_scope.
 
+Fixpoint InT {A} (a:A) (t:Tree ??A) {struct t} : Prop :=
+  match t with
+    | T_Leaf None     => False
+    | T_Leaf (Some x) => x = a
+    | T_Branch b1 b2  => InT a b1 \/ InT a b2
+  end.
+
 Open Scope tree_scope.
 
 Fixpoint mapTree {a b:Type}(f:a->b)(t:@Tree a) : @Tree b :=
@@ -52,7 +59,7 @@ Fixpoint mapOptionTree {a b:Type}(f:a->b)(t:@Tree ??a) : @Tree ??b :=
   match t with 
     | T_Leaf None     => T_Leaf None
     | T_Leaf (Some x) => T_Leaf (Some (f x))
-    | T_Branch l r => T_Branch (mapOptionTree f l) (mapOptionTree f r)
+    | T_Branch l r    => T_Branch (mapOptionTree f l) (mapOptionTree f r)
   end.
 Fixpoint mapTreeAndFlatten {a b:Type}(f:a->@Tree b)(t:@Tree a) : @Tree b :=
   match t with 
@@ -341,6 +348,11 @@ Inductive distinct {T:Type} : list T -> Prop :=
 | distinct_nil  : distinct nil
 | distinct_cons : forall a ax, (@In _ a ax -> False) -> distinct ax -> distinct (a::ax).
 
+Inductive distinctT {T:Type} : Tree ??T -> Prop :=
+| distinctT_nil  : distinctT []
+| distinctT_leaf : forall t, distinctT [t]
+| distinctT_cons : forall t1 t2, (forall v, InT v t1 -> InT v t2 -> False) -> distinctT (t1,,t2).
+
 Lemma in_decidable {VV:Type}{eqdVV:EqDecidable VV} : forall (v:VV)(lv:list VV), sumbool (In v lv) (not (In v lv)).
   intros.
   induction lv.
@@ -385,6 +397,10 @@ Lemma distinct_decidable {VV:Type}{eqdVV:EqDecidable VV} : forall (lv:list VV),
   apply n; auto.
   Defined.
 
+Lemma distinctT_decidable {VV:Type}{eqdVV:EqDecidable VV} : forall (lv:Tree ??VV), sumbool (distinctT lv) (not (distinctT lv)).
+  admit.
+  Defined.
+
 Lemma map_preserves_length {A}{B}(f:A->B)(l:list A) : (length l) = (length (map f l)).
   induction l; auto.
   simpl.
@@ -868,3 +884,33 @@ Coercion FMT       : FreshMonad >-> Funclass.
 
 
 Variable Prelude_error : forall {A}, string -> A.   Extract Inlined Constant Prelude_error => "Prelude.error".
+
+
+
+
+Ltac eqd_dec_refl X :=
+  destruct (eqd_dec X X) as [eqd_dec1 | eqd_dec2];
+    [ clear eqd_dec1 | set (eqd_dec2 (refl_equal _)) as eqd_dec2'; inversion eqd_dec2' ].
+
+Lemma unleaves_injective : forall T (t1 t2:list T), unleaves t1 = unleaves t2 -> t1 = t2.
+  intros T.
+  induction t1; intros.
+  destruct t2.
+  auto.
+  inversion H.
+  destruct t2.
+  inversion H.
+  simpl in H.
+  inversion H.
+  set (IHt1 _ H2) as q.
+  rewrite q.
+  reflexivity.
+  Qed.
+
+Lemma fst_zip : forall T Q n (v1:vec T n)(v2:vec Q n), vec_map (@fst _ _) (vec_zip v1 v2) = v1.
+  admit.
+  Defined.
+
+Lemma snd_zip : forall T Q n (v1:vec T n)(v2:vec Q n), vec_map (@snd _ _) (vec_zip v1 v2) = v2.
+  admit.
+  Defined.