Library Coq.Program.Utils


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.

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