diff options
author | letouzey <letouzey@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2006-05-30 13:43:15 +0000 |
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committer | letouzey <letouzey@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2006-05-30 13:43:15 +0000 |
commit | 493367ccdfe146d4f898bb49f1ff43ead382dbf9 (patch) | |
tree | 666293128093cd5b39a64851caf1cd6852319ac6 /theories/FSets/FMapWeakList.v | |
parent | af354d63a814b0855eefda81852029d72b3544db (diff) |
* suite de la revision des wrappers Make
* quelques unfold E.eq en cas de changement de la semantique des foncteurs
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@8876 85f007b7-540e-0410-9357-904b9bb8a0f7
Diffstat (limited to 'theories/FSets/FMapWeakList.v')
-rw-r--r-- | theories/FSets/FMapWeakList.v | 171 |
1 files changed, 106 insertions, 65 deletions
diff --git a/theories/FSets/FMapWeakList.v b/theories/FSets/FMapWeakList.v index bfa97d0b2..dc034bf83 100644 --- a/theories/FSets/FMapWeakList.v +++ b/theories/FSets/FMapWeakList.v @@ -878,83 +878,124 @@ Module Make (X: DecidableType) <: S with Module E:=X. Module Raw := Raw X. Module E := X. - Definition key := X.t. + Definition key := E.t. Record slist (elt:Set) : Set := {this :> Raw.t elt; NoDup : NoDupA (@Raw.PX.eqk elt) this}. Definition t (elt:Set) := slist elt. - Section Elt. +Section Elt. Variable elt elt' elt'':Set. Implicit Types m : t elt. - - Definition empty := Build_slist (Raw.empty_NoDup elt). - Definition is_empty m := Raw.is_empty m.(this). - Definition add x e m := Build_slist (Raw.add_NoDup m.(NoDup) x e). - Definition find x m := Raw.find x m.(this). - Definition remove x m := Build_slist (Raw.remove_NoDup m.(NoDup) x). - Definition mem x m := Raw.mem x m.(this). + Implicit Types x y : key. + Implicit Types e : elt. + + Definition empty : t elt := Build_slist (Raw.empty_NoDup elt). + Definition is_empty m : bool := Raw.is_empty m.(this). + Definition add x e m : t elt := Build_slist (Raw.add_NoDup m.(NoDup) x e). + Definition find x m : option elt := Raw.find x m.(this). + Definition remove x m : t elt := Build_slist (Raw.remove_NoDup m.(NoDup) x). + Definition mem x m : bool := Raw.mem x m.(this). Definition map f m : t elt' := Build_slist (Raw.map_NoDup m.(NoDup) f). - Definition mapi f m : t elt' := Build_slist (Raw.mapi_NoDup m.(NoDup) f). + Definition mapi (f:key->elt->elt') m : t elt' := Build_slist (Raw.mapi_NoDup m.(NoDup) f). Definition map2 f m (m':t elt') : t elt'' := - Build_slist (Raw.map2_NoDup f m.(NoDup) m'.(NoDup)). - Definition elements m := @Raw.elements elt m.(this). - Definition fold A f m i := @Raw.fold elt A f m.(this) i. - Definition equal cmp m m' := @Raw.equal elt cmp m.(this) m'.(this). - - Definition MapsTo x e m := Raw.PX.MapsTo x e m.(this). - Definition In x m := Raw.PX.In x m.(this). - Definition Empty m := Raw.Empty m.(this). - Definition Equal cmp m m' := @Raw.Equal elt cmp m.(this) m'.(this). + Build_slist (Raw.map2_NoDup f m.(NoDup) m'.(NoDup)). + Definition elements m : list (key*elt) := @Raw.elements elt m.(this). + Definition fold (A:Set)(f:key->elt->A->A) m (i:A) : A := @Raw.fold elt A f m.(this) i. + Definition equal cmp m m' : bool := @Raw.equal elt cmp m.(this) m'.(this). + + Definition MapsTo x e m : Prop := Raw.PX.MapsTo x e m.(this). + Definition In x m : Prop := Raw.PX.In x m.(this). + Definition Empty m : Prop := Raw.Empty m.(this). + Definition Equal cmp m m' : Prop := @Raw.Equal elt cmp m.(this) m'.(this). + + Definition eq_key : (key*elt) -> (key*elt) -> Prop := @Raw.PX.eqk elt. + Definition eq_key_elt : (key*elt) -> (key*elt) -> Prop:= @Raw.PX.eqke elt. + + Lemma MapsTo_1 : forall m x y e, E.eq x y -> MapsTo x e m -> MapsTo y e m. + Proof. intros m; exact (@Raw.PX.MapsTo_eq elt m.(this)). Qed. + + Lemma mem_1 : forall m x, In x m -> mem x m = true. + Proof. intros m; exact (@Raw.mem_1 elt m.(this) m.(NoDup)). Qed. + Lemma mem_2 : forall m x, mem x m = true -> In x m. + Proof. intros m; exact (@Raw.mem_2 elt m.(this) m.(NoDup)). Qed. + + Lemma empty_1 : Empty empty. + Proof. exact (@Raw.empty_1 elt). Qed. + + Lemma is_empty_1 : forall m, Empty m -> is_empty m = true. + Proof. intros m; exact (@Raw.is_empty_1 elt m.(this)). Qed. + Lemma is_empty_2 : forall m, is_empty m = true -> Empty m. + Proof. intros m; exact (@Raw.is_empty_2 elt m.(this)). Qed. + + Lemma add_1 : forall m x y e, E.eq x y -> MapsTo y e (add x e m). + Proof. intros m; exact (@Raw.add_1 elt m.(this)). Qed. + Lemma add_2 : forall m x y e e', ~ E.eq x y -> MapsTo y e m -> MapsTo y e (add x e' m). + Proof. intros m; exact (@Raw.add_2 elt m.(this)). Qed. + Lemma add_3 : forall m x y e e', ~ E.eq x y -> MapsTo y e (add x e' m) -> MapsTo y e m. + Proof. intros m; exact (@Raw.add_3 elt m.(this)). Qed. + + Lemma remove_1 : forall m x y, E.eq x y -> ~ In y (remove x m). + Proof. intros m; exact (@Raw.remove_1 elt m.(this) m.(NoDup)). Qed. + Lemma remove_2 : forall m x y e, ~ E.eq x y -> MapsTo y e m -> MapsTo y e (remove x m). + Proof. intros m; exact (@Raw.remove_2 elt m.(this) m.(NoDup)). Qed. + Lemma remove_3 : forall m x y e, MapsTo y e (remove x m) -> MapsTo y e m. + Proof. intros m; exact (@Raw.remove_3 elt m.(this) m.(NoDup)). Qed. + + Lemma find_1 : forall m x e, MapsTo x e m -> find x m = Some e. + Proof. intros m; exact (@Raw.find_1 elt m.(this) m.(NoDup)). Qed. + Lemma find_2 : forall m x e, find x m = Some e -> MapsTo x e m. + Proof. intros m; exact (@Raw.find_2 elt m.(this)). Qed. + + Lemma elements_1 : forall m x e, MapsTo x e m -> InA eq_key_elt (x,e) (elements m). + Proof. intros m; exact (@Raw.elements_1 elt m.(this)). Qed. + Lemma elements_2 : forall m x e, InA eq_key_elt (x,e) (elements m) -> MapsTo x e m. + Proof. intros m; exact (@Raw.elements_2 elt m.(this)). Qed. + Lemma elements_3 : forall m, NoDupA eq_key (elements m). + Proof. intros m; exact (@Raw.elements_3 elt m.(this) m.(NoDup)). Qed. + + Lemma fold_1 : forall m (A : Set) (i : A) (f : key -> elt -> A -> A), + fold f m i = fold_left (fun a p => f (fst p) (snd p) a) (elements m) i. + Proof. intros m; exact (@Raw.fold_1 elt m.(this)). Qed. + + Lemma equal_1 : forall m m' cmp, Equal cmp m m' -> equal cmp m m' = true. + Proof. intros m m'; exact (@Raw.equal_1 elt m.(this) m.(NoDup) m'.(this) m'.(NoDup)). Qed. + Lemma equal_2 : forall m m' cmp, equal cmp m m' = true -> Equal cmp m m'. + Proof. intros m m'; exact (@Raw.equal_2 elt m.(this) m.(NoDup) m'.(this) m'.(NoDup)). Qed. - Definition eq_key (p p':key*elt) := X.eq (fst p) (fst p'). + End Elt. - Definition eq_key_elt (p p':key*elt) := - X.eq (fst p) (fst p') /\ (snd p) = (snd p'). - - Definition MapsTo_1 m := @Raw.PX.MapsTo_eq elt m.(this). - - Definition mem_1 m := @Raw.mem_1 elt m.(this) m.(NoDup). - Definition mem_2 m := @Raw.mem_2 elt m.(this) m.(NoDup). - - Definition empty_1 := @Raw.empty_1. - - Definition is_empty_1 m := @Raw.is_empty_1 elt m.(this). - Definition is_empty_2 m := @Raw.is_empty_2 elt m.(this). - - Definition add_1 m := @Raw.add_1 elt m.(this). - Definition add_2 m := @Raw.add_2 elt m.(this). - Definition add_3 m := @Raw.add_3 elt m.(this). - - Definition remove_1 m := @Raw.remove_1 elt m.(this) m.(NoDup). - Definition remove_2 m := @Raw.remove_2 elt m.(this) m.(NoDup). - Definition remove_3 m := @Raw.remove_3 elt m.(this) m.(NoDup). + Lemma map_1 : forall (elt elt':Set)(m: t elt)(x:key)(e:elt)(f:elt->elt'), + MapsTo x e m -> MapsTo x (f e) (map f m). + Proof. intros elt elt' m; exact (@Raw.map_1 elt elt' m.(this)). Qed. + Lemma map_2 : forall (elt elt':Set)(m: t elt)(x:key)(f:elt->elt'), + In x (map f m) -> In x m. + Proof. intros elt elt' m; exact (@Raw.map_2 elt elt' m.(this)). Qed. + + Lemma mapi_1 : forall (elt elt':Set)(m: t elt)(x:key)(e:elt) + (f:key->elt->elt'), MapsTo x e m -> + exists y, E.eq y x /\ MapsTo x (f y e) (mapi f m). + Proof. intros elt elt' m; exact (@Raw.mapi_1 elt elt' m.(this)). Qed. + Lemma mapi_2 : forall (elt elt':Set)(m: t elt)(x:key) + (f:key->elt->elt'), In x (mapi f m) -> In x m. + Proof. intros elt elt' m; exact (@Raw.mapi_2 elt elt' m.(this)). Qed. + + Lemma map2_1 : forall (elt elt' elt'':Set)(m: t elt)(m': t elt') + (x:key)(f:option elt->option elt'->option elt''), + In x m \/ In x m' -> + find x (map2 f m m') = f (find x m) (find x m'). + Proof. + intros elt elt' elt'' m m' x f; + exact (@Raw.map2_1 elt elt' elt'' f m.(this) m.(NoDup) m'.(this) m'.(NoDup) x). + Qed. + Lemma map2_2 : forall (elt elt' elt'':Set)(m: t elt)(m': t elt') + (x:key)(f:option elt->option elt'->option elt''), + In x (map2 f m m') -> In x m \/ In x m'. + Proof. + intros elt elt' elt'' m m' x f; + exact (@Raw.map2_2 elt elt' elt'' f m.(this) m.(NoDup) m'.(this) m'.(NoDup) x). + Qed. - Definition find_1 m := @Raw.find_1 elt m.(this) m.(NoDup). - Definition find_2 m := @Raw.find_2 elt m.(this). - - Definition elements_1 m := @Raw.elements_1 elt m.(this). - Definition elements_2 m := @Raw.elements_2 elt m.(this). - Definition elements_3 m := @Raw.elements_3 elt m.(this) m.(NoDup). - - Definition fold_1 m := @Raw.fold_1 elt m.(this). - - Definition map_1 m := @Raw.map_1 elt elt' m.(this). - Definition map_2 m := @Raw.map_2 elt elt' m.(this). - - Definition mapi_1 m := @Raw.mapi_1 elt elt' m.(this). - Definition mapi_2 m := @Raw.mapi_2 elt elt' m.(this). - - Definition map2_1 m (m':t elt') x f := - @Raw.map2_1 elt elt' elt'' f m.(this) m.(NoDup) m'.(this) m'.(NoDup) x. - Definition map2_2 m (m':t elt') x f := - @Raw.map2_2 elt elt' elt'' f m.(this) m.(NoDup) m'.(this) m'.(NoDup) x. - - Definition equal_1 m m' := @Raw.equal_1 elt m.(this) m.(NoDup) m'.(this) m'.(NoDup). - Definition equal_2 m m' := @Raw.equal_2 elt m.(this) m.(NoDup) m'.(this) m'.(NoDup). - - End Elt. End Make. - |