diff options
Diffstat (limited to 'theories/FSets/FSetCompat.v')
| -rw-r--r-- | theories/FSets/FSetCompat.v | 60 |
1 files changed, 31 insertions, 29 deletions
diff --git a/theories/FSets/FSetCompat.v b/theories/FSets/FSetCompat.v index b1769da3..736c85da 100644 --- a/theories/FSets/FSetCompat.v +++ b/theories/FSets/FSetCompat.v @@ -1,10 +1,12 @@ -(***********************************************************************) -(* v * The Coq Proof Assistant / The Coq Development Team *) -(* <O___,, * INRIA-Rocquencourt & LRI-CNRS-Orsay *) -(* \VV/ *************************************************************) -(* // * This file is distributed under the terms of the *) -(* * GNU Lesser General Public License Version 2.1 *) -(***********************************************************************) +(************************************************************************) +(* * The Coq Proof Assistant / The Coq Development Team *) +(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *) +(* <O___,, * (see CREDITS file for the list of authors) *) +(* \VV/ **************************************************************) +(* // * This file is distributed under the terms of the *) +(* * GNU Lesser General Public License Version 2.1 *) +(* * (see LICENSE file for the text of the license) *) +(************************************************************************) (** * Compatibility functors between FSetInterface and MSetInterface. *) @@ -165,13 +167,13 @@ End Backport_WSets. (** * From new Sets to new ones *) Module Backport_Sets - (E:OrderedType.OrderedType) - (M:MSetInterface.Sets with Definition E.t := E.t - with Definition E.eq := E.eq - with Definition E.lt := E.lt) - <: FSetInterface.S with Module E:=E. + (O:OrderedType.OrderedType) + (M:MSetInterface.Sets with Definition E.t := O.t + with Definition E.eq := O.eq + with Definition E.lt := O.lt) + <: FSetInterface.S with Module E:=O. - Include Backport_WSets E M. + Include Backport_WSets O M. Implicit Type s : t. Implicit Type x y : elt. @@ -182,21 +184,21 @@ Module Backport_Sets Definition min_elt_1 : forall s x, min_elt s = Some x -> In x s := M.min_elt_spec1. Definition min_elt_2 : forall s x y, - min_elt s = Some x -> In y s -> ~ E.lt y x + min_elt s = Some x -> In y s -> ~ O.lt y x := M.min_elt_spec2. Definition min_elt_3 : forall s, min_elt s = None -> Empty s := M.min_elt_spec3. Definition max_elt_1 : forall s x, max_elt s = Some x -> In x s := M.max_elt_spec1. Definition max_elt_2 : forall s x y, - max_elt s = Some x -> In y s -> ~ E.lt x y + max_elt s = Some x -> In y s -> ~ O.lt x y := M.max_elt_spec2. Definition max_elt_3 : forall s, max_elt s = None -> Empty s := M.max_elt_spec3. - Definition elements_3 : forall s, sort E.lt (elements s) + Definition elements_3 : forall s, sort O.lt (elements s) := M.elements_spec2. Definition choose_3 : forall s s' x y, - choose s = Some x -> choose s' = Some y -> Equal s s' -> E.eq x y + choose s = Some x -> choose s' = Some y -> Equal s s' -> O.eq x y := M.choose_spec3. Definition lt_trans : forall s s' s'', lt s s' -> lt s' s'' -> lt s s'' := @StrictOrder_Transitive _ _ M.lt_strorder. @@ -211,7 +213,7 @@ Module Backport_Sets [ apply EQ | apply LT | apply GT ]; auto. Defined. - Module E := E. + Module E := O. End Backport_Sets. @@ -342,13 +344,13 @@ End Update_WSets. (** * From old Sets to new ones. *) Module Update_Sets - (E:Orders.OrderedType) - (M:FSetInterface.S with Definition E.t := E.t - with Definition E.eq := E.eq - with Definition E.lt := E.lt) - <: MSetInterface.Sets with Module E:=E. + (O:Orders.OrderedType) + (M:FSetInterface.S with Definition E.t := O.t + with Definition E.eq := O.eq + with Definition E.lt := O.lt) + <: MSetInterface.Sets with Module E:=O. - Include Update_WSets E M. + Include Update_WSets O M. Implicit Type s : t. Implicit Type x y : elt. @@ -359,21 +361,21 @@ Module Update_Sets Definition min_elt_spec1 : forall s x, min_elt s = Some x -> In x s := M.min_elt_1. Definition min_elt_spec2 : forall s x y, - min_elt s = Some x -> In y s -> ~ E.lt y x + min_elt s = Some x -> In y s -> ~ O.lt y x := M.min_elt_2. Definition min_elt_spec3 : forall s, min_elt s = None -> Empty s := M.min_elt_3. Definition max_elt_spec1 : forall s x, max_elt s = Some x -> In x s := M.max_elt_1. Definition max_elt_spec2 : forall s x y, - max_elt s = Some x -> In y s -> ~ E.lt x y + max_elt s = Some x -> In y s -> ~ O.lt x y := M.max_elt_2. Definition max_elt_spec3 : forall s, max_elt s = None -> Empty s := M.max_elt_3. - Definition elements_spec2 : forall s, sort E.lt (elements s) + Definition elements_spec2 : forall s, sort O.lt (elements s) := M.elements_3. Definition choose_spec3 : forall s s' x y, - choose s = Some x -> choose s' = Some y -> Equal s s' -> E.eq x y + choose s = Some x -> choose s' = Some y -> Equal s s' -> O.eq x y := M.choose_3. Instance lt_strorder : StrictOrder lt. @@ -407,6 +409,6 @@ Module Update_Sets Lemma compare_spec : forall s s', CompSpec eq lt s s' (compare s s'). Proof. intros; unfold compare; destruct M.compare; auto. Qed. - Module E := E. + Module E := O. End Update_Sets. |