add distinct_decidable, in_decidable to General.v

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

diff --git a/src/General.v b/src/General.v
index ffd0d29..b0266f4 100644 (file)
--- a/src/General.v
+++ b/src/General.v
@@ -301,6 +301,16 @@ Fixpoint unleaves'' {A:Type}(l:list ??A) : Tree ??A :=
     | (a::b) => (unleaves'' b),,(T_Leaf a)
   end.
 
+Lemma mapleaves {T:Type}(t:Tree ??T){Q}{f:T->Q} : leaves (mapOptionTree f t) = map f (leaves t).
+  induction t.
+  destruct a; auto.
+  simpl.
+  rewrite IHt1.
+  rewrite IHt2.
+  rewrite map_app.
+  auto.
+  Qed.
+
 Fixpoint filter {T:Type}(l:list ??T) : list T :=
   match l with
     | nil => nil
@@ -312,6 +322,50 @@ 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).
 
+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.
+  right.
+  unfold not.
+  intros.
+  inversion H.
+  destruct IHlv.
+  left.
+  simpl.
+  auto.
+  set (eqd_dec v a) as dec.
+  destruct dec.
+  subst.
+  left; simpl; auto.
+  right.
+  unfold not; intros.
+  destruct H.
+  subst.
+  apply n0; auto.
+  apply n.
+  apply H.
+  Defined.
+
+Lemma distinct_decidable {VV:Type}{eqdVV:EqDecidable VV} : forall (lv:list VV), sumbool (distinct lv) (not (distinct lv)).
+  intros.
+  induction lv.
+  left; apply distinct_nil.
+  destruct IHlv.
+  set (in_decidable a lv) as dec.
+  destruct dec.
+  right; unfold not; intros.
+  inversion H.
+  subst.
+  apply H2; auto.
+  left.
+  apply distinct_cons; auto.
+  right.
+  unfold not; intros.
+  inversion H.
+  subst.
+  apply n; auto.
+  Defined.
+
 Lemma map_preserves_length {A}{B}(f:A->B)(l:list A) : (length l) = (length (map f l)).
   induction l; auto.
   simpl.
@@ -782,4 +836,16 @@ Notation "'failM'  x" := (uniqM (fun _ => Error x)) (at level 100).
 
 
 
+
+
+Record FreshMonad {T:Type} :=
+{ FMT       :  Type -> Type
+; FMT_Monad :> Monad FMT
+; FMT_fresh :  forall tl:list T, FMT { t:T & @In _ t tl -> False }
+}.
+Implicit Arguments FreshMonad [ ].
+Coercion FMT       : FreshMonad >-> Funclass.
+
+
+
 Variable Prelude_error : forall {A}, string -> A.   Extract Inlined Constant Prelude_error => "Prelude.error".