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authorGravatar msozeau <msozeau@85f007b7-540e-0410-9357-904b9bb8a0f7>2008-12-14 16:34:43 +0000
committerGravatar msozeau <msozeau@85f007b7-540e-0410-9357-904b9bb8a0f7>2008-12-14 16:34:43 +0000
commitc74f11d65b693207cdfa6d02f697e76093021be7 (patch)
treeb32866140d9f5ecde0bb719c234c6603d44037a8 /theories/Classes/EquivDec.v
parent2f63108dccc104fe32344d88b35193d34a88f743 (diff)
Generalized binding syntax overhaul: only two new binders: `() and `{},
guessing the binding name by default and making all generalized variables implicit. At the same time, continue refactoring of Record/Class/Inductive etc.., getting rid of [VernacRecord] definitively. The AST is not completely satisfying, but leaning towards Record/Class as restrictions of inductive (Arnaud, anyone ?). Now, [Class] declaration bodies are either of the form [meth : type] or [{ meth : type ; ... }], distinguishing singleton "definitional" classes and inductive classes based on records. The constructor syntax is accepted ([meth1 : type1 | meth1 : type2]) but raises an error immediately, as support for defining a class by a general inductive type is not there yet (this is a bugfix!). git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@11679 85f007b7-540e-0410-9357-904b9bb8a0f7
Diffstat (limited to 'theories/Classes/EquivDec.v')
-rw-r--r--theories/Classes/EquivDec.v30
1 files changed, 14 insertions, 16 deletions
diff --git a/theories/Classes/EquivDec.v b/theories/Classes/EquivDec.v
index b530cc098..91c417ce3 100644
--- a/theories/Classes/EquivDec.v
+++ b/theories/Classes/EquivDec.v
@@ -1,4 +1,3 @@
-(* -*- coq-prog-args: ("-emacs-U" "-nois") -*- *)
(************************************************************************)
(* v * The Coq Proof Assistant / The Coq Development Team *)
(* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
@@ -15,8 +14,7 @@
(* $Id$ *)
-Set Implicit Arguments.
-Unset Strict Implicit.
+Set Manual Implicit Arguments.
(** Export notations. *)
@@ -29,12 +27,12 @@ Require Import Coq.Logic.Decidable.
Open Scope equiv_scope.
-Class [ equiv : Equivalence A ] => DecidableEquivalence :=
+Class DecidableEquivalence `(equiv : Equivalence A) :=
setoid_decidable : forall x y : A, decidable (x === y).
(** The [EqDec] class gives a decision procedure for a particular setoid equality. *)
-Class [ equiv : Equivalence A ] => EqDec :=
+Class EqDec A R {equiv : Equivalence R} :=
equiv_dec : forall x y : A, { x === y } + { x =/= y }.
(** We define the [==] overloaded notation for deciding equality. It does not take precedence
@@ -54,7 +52,7 @@ Open Local Scope program_scope.
(** Invert the branches. *)
-Program Definition nequiv_dec [ EqDec A ] (x y : A) : { x =/= y } + { x === y } := swap_sumbool (x == y).
+Program Definition nequiv_dec `{EqDec A} (x y : A) : { x =/= y } + { x === y } := swap_sumbool (x == y).
(** Overloaded notation for inequality. *)
@@ -62,10 +60,10 @@ Infix "<>" := nequiv_dec (no associativity, at level 70) : equiv_scope.
(** Define boolean versions, losing the logical information. *)
-Definition equiv_decb [ EqDec A ] (x y : A) : bool :=
+Definition equiv_decb `{EqDec A} (x y : A) : bool :=
if x == y then true else false.
-Definition nequiv_decb [ EqDec A ] (x y : A) : bool :=
+Definition nequiv_decb `{EqDec A} (x y : A) : bool :=
negb (equiv_decb x y).
Infix "==b" := equiv_decb (no associativity, at level 70).
@@ -77,15 +75,15 @@ Require Import Coq.Arith.Peano_dec.
(** The equiv is burried inside the setoid, but we can recover it by specifying which setoid we're talking about. *)
-Program Instance nat_eq_eqdec : ! EqDec nat eq :=
+Program Instance nat_eq_eqdec : EqDec nat eq :=
equiv_dec := eq_nat_dec.
Require Import Coq.Bool.Bool.
-Program Instance bool_eqdec : ! EqDec bool eq :=
+Program Instance bool_eqdec : EqDec bool eq :=
equiv_dec := bool_dec.
-Program Instance unit_eqdec : ! EqDec unit eq :=
+Program Instance unit_eqdec : EqDec unit eq :=
equiv_dec x y := in_left.
Next Obligation.
@@ -94,7 +92,7 @@ Program Instance unit_eqdec : ! EqDec unit eq :=
reflexivity.
Qed.
-Program Instance prod_eqdec [ EqDec A eq, EqDec B eq ] :
+Program Instance prod_eqdec `(EqDec A eq, EqDec B eq) :
! EqDec (prod A B) eq :=
equiv_dec x y :=
let '(x1, x2) := x in
@@ -106,8 +104,8 @@ Program Instance prod_eqdec [ EqDec A eq, EqDec B eq ] :
Solve Obligations using unfold complement, equiv ; program_simpl.
-Program Instance sum_eqdec [ EqDec A eq, EqDec B eq ] :
- ! EqDec (sum A B) eq :=
+Program Instance sum_eqdec `(EqDec A eq, EqDec B eq) :
+ EqDec (sum A B) eq :=
equiv_dec x y :=
match x, y with
| inl a, inl b => if a == b then in_left else in_right
@@ -121,7 +119,7 @@ Program Instance sum_eqdec [ EqDec A eq, EqDec B eq ] :
Require Import Coq.Program.FunctionalExtensionality.
-Program Instance bool_function_eqdec [ EqDec A eq ] : ! EqDec (bool -> A) eq :=
+Program Instance bool_function_eqdec `(EqDec A eq) : ! EqDec (bool -> A) eq :=
equiv_dec f g :=
if f true == g true then
if f false == g false then in_left
@@ -138,7 +136,7 @@ Program Instance bool_function_eqdec [ EqDec A eq ] : ! EqDec (bool -> A) eq :=
Require Import List.
-Program Instance list_eqdec [ eqa : EqDec A eq ] : ! EqDec (list A) eq :=
+Program Instance list_eqdec `(eqa : EqDec A eq) : ! EqDec (list A) eq :=
equiv_dec :=
fix aux (x : list A) y { struct x } :=
match x, y with