diff options
Diffstat (limited to 'theories/Classes/SetoidDec.v')
| -rw-r--r-- | theories/Classes/SetoidDec.v | 18 |
1 files changed, 9 insertions, 9 deletions
diff --git a/theories/Classes/SetoidDec.v b/theories/Classes/SetoidDec.v index cf3d202d..8a069343 100644 --- a/theories/Classes/SetoidDec.v +++ b/theories/Classes/SetoidDec.v @@ -13,7 +13,7 @@ * Institution: LRI, CNRS UMR 8623 - UniversitĂcopyright Paris Sud * 91405 Orsay, France *) -(* $Id: SetoidDec.v 10919 2008-05-11 22:04:26Z msozeau $ *) +(* $Id: SetoidDec.v 11282 2008-07-28 11:51:53Z msozeau $ *) Set Implicit Arguments. Unset Strict Implicit. @@ -27,12 +27,12 @@ Require Export Coq.Classes.SetoidClass. Require Import Coq.Logic.Decidable. -Class [ Setoid A ] => DecidableSetoid := +Class DecidableSetoid A [ Setoid A ] := setoid_decidable : forall x y : A, decidable (x == y). (** The [EqDec] class gives a decision procedure for a particular setoid equality. *) -Class [ Setoid A ] => EqDec := +Class (( s : Setoid A )) => EqDec := equiv_dec : forall x y : A, { x == y } + { x =/= y }. (** We define the [==] overloaded notation for deciding equality. It does not take precedence @@ -75,18 +75,18 @@ Require Import Coq.Arith.Arith. (** The equiv is burried inside the setoid, but we can recover it by specifying which setoid we're talking about. *) -Program Instance eq_setoid : Setoid A := +Program Instance eq_setoid A : Setoid A := equiv := eq ; setoid_equiv := eq_equivalence. -Program Instance nat_eq_eqdec : EqDec (@eq_setoid nat) := +Program Instance nat_eq_eqdec : EqDec (eq_setoid nat) := equiv_dec := eq_nat_dec. Require Import Coq.Bool.Bool. -Program Instance bool_eqdec : EqDec (@eq_setoid bool) := +Program Instance bool_eqdec : EqDec (eq_setoid bool) := equiv_dec := bool_dec. -Program Instance unit_eqdec : EqDec (@eq_setoid unit) := +Program Instance unit_eqdec : EqDec (eq_setoid unit) := equiv_dec x y := in_left. Next Obligation. @@ -95,7 +95,7 @@ Program Instance unit_eqdec : EqDec (@eq_setoid unit) := reflexivity. Qed. -Program Instance prod_eqdec [ ! EqDec (@eq_setoid A), ! EqDec (@eq_setoid B) ] : EqDec (@eq_setoid (prod A B)) := +Program Instance prod_eqdec [ ! EqDec (eq_setoid A), ! EqDec (eq_setoid B) ] : EqDec (eq_setoid (prod A B)) := equiv_dec x y := let '(x1, x2) := x in let '(y1, y2) := y in @@ -110,7 +110,7 @@ Program Instance prod_eqdec [ ! EqDec (@eq_setoid A), ! EqDec (@eq_setoid B) ] : Require Import Coq.Program.FunctionalExtensionality. -Program Instance bool_function_eqdec [ ! EqDec (@eq_setoid A) ] : EqDec (@eq_setoid (bool -> A)) := +Program Instance bool_function_eqdec [ ! EqDec (eq_setoid A) ] : EqDec (eq_setoid (bool -> A)) := equiv_dec f g := if f true == g true then if f false == g false then in_left |