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(************************************************************************)
(* v * The Coq Proof Assistant / The Coq Development Team *)
(* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
(* \VV/ **************************************************************)
(* // * This file is distributed under the terms of the *)
(* * GNU Lesser General Public License Version 2.1 *)
(************************************************************************)
(*i $Id$ i*)
Require Export Coq.Program.Tactics.
Set Implicit Arguments.
(** Wrap a proposition inside a subset. *)
Notation " {{ x }} " := (tt : { y : unit | x }).
(** A simpler notation for subsets defined on a cartesian product. *)
Notation "{ ( x , y ) : A | P }" :=
(sig (fun anonymous : A => let (x,y) := anonymous in P))
(x ident, y ident, at level 10) : type_scope.
(** Generates an obligation to prove False. *)
Notation " ! " := (False_rect _ _).
(** Abbreviation for first projection and hiding of proofs of subset objects. *)
(** The scope in which programs are typed (not their types). *)
Delimit Scope program_scope with prg.
Notation " ` t " := (proj1_sig t) (at level 10) : core_scope.
Delimit Scope subset_scope with subset.
(* In [subset_scope] to allow masking by redefinitions for particular types. *)
Notation "( x & ? )" := (@exist _ _ x _) : subset_scope.
(** Coerces objects to their support before comparing them. *)
Notation " x '`=' y " := ((x :>) = (y :>)) (at level 70).
(** Quantifying over subsets. *)
(* Notation "'fun' ( x : A | P ) => Q" := *)
(* (fun (x :A|P} => Q) *)
(* (at level 200, x ident, right associativity). *)
(* Notation "'forall' ( x : A | P ), Q" := *)
(* (forall (x : A | P), Q) *)
(* (at level 200, x ident, right associativity). *)
Require Import Coq.Bool.Sumbool.
(** Construct a dependent disjunction from a boolean. *)
Notation "'dec'" := (sumbool_of_bool) (at level 0).
(** The notations [in_right] and [in_left] construct objects of a dependent disjunction. *)
(** These type arguments should be infered from the context. *)
Implicit Arguments left [[A]].
Implicit Arguments right [[B]].
(** Hide proofs and generates obligations when put in a term. *)
Notation left := (left _ _).
Notation right := (right _ _).
(** Extraction directives *)
Extraction Inline proj1_sig.
Extract Inductive unit => "unit" [ "()" ].
Extract Inductive bool => "bool" [ "true" "false" ].
Extract Inductive sumbool => "bool" [ "true" "false" ].
(* Extract Inductive prod "'a" "'b" => " 'a * 'b " [ "(,)" ]. *)
(* Extract Inductive sigT => "prod" [ "" ]. *)
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