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(*         *   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)         *)
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Various syntactic shorthands that are useful with Program. 
Require Export Coq.Program.Tactics.

Set Implicit Arguments.
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.

Declare Scope program_scope.
Delimit Scope program_scope with prg.
Generates an obligation to prove False. 
Notation " ! " := (False_rect _ _) : program_scope.
Abbreviation for first projection and hiding of proofs of subset objects. 
Notation " `  t " := (proj1_sig t) (at level 10, t at next level) : program_scope.
Coerces objects to their support before comparing them. 
Notation " x '`=' y " := ((x :>) = (y :>)) (at level 70) : program_scope.

Require Import Coq.Bool.Sumbool.
Construct a dependent disjunction from a boolean. 
Notation dec := sumbool_of_bool.
The notations in_right and in_left construct objects of a dependent disjunction.
Hide proofs and generates obligations when put in a term. 
Notation in_left := (@left _ _ _).
Notation in_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" [ "" ]. *)
*)