# Library Coq.Program.Syntax

Custom notations and implicits for Coq prelude definitions.

Author: Matthieu Sozeau Institution: LRI, CNRS UMR 8623 - University Paris Sud

Haskell-style notations for the unit type and value.

Notation " () " := Datatypes.unit : type_scope.
Notation " () " := tt.

Set maximally inserted implicit arguments for standard definitions.

Implicit Arguments Some [[A]].
Implicit Arguments None [[A]].

Implicit Arguments inl [[A] [B]] [A].
Implicit Arguments inr [[A] [B]] [B].

Implicit Arguments left [[A] [B]] [A].
Implicit Arguments right [[A] [B]] [B].

Implicit Arguments pair [[A] [B]].
Implicit Arguments fst [[A] [B]].
Implicit Arguments snd [[A] [B]].

Require Import Coq.Lists.List.

Implicit Arguments nil [[A]].
Implicit Arguments cons [[A]].

Standard notations for lists.

Notation " [ ] " := nil : list_scope.
Notation " [ x ] " := (cons x nil) : list_scope.
Notation " [ x ; .. ; y ] " := (cons x .. (cons y nil) ..) : list_scope.

Implicit arguments for vectors.

Require Import Bvector.

Implicit Arguments Vnil [[A]] [].
Implicit Arguments Vcons [[A] [n]] [].

Treating n-ary exists

Notation " 'exists' x y , p" := (ex (fun x => (ex (fun y => p))))
(at level 200, x ident, y ident, right associativity) : type_scope.

Notation " 'exists' x y z , p" := (ex (fun x => (ex (fun y => (ex (fun z => p))))))
(at level 200, x ident, y ident, z ident, right associativity) : type_scope.

Notation " 'exists' x y z w , p" := (ex (fun x => (ex (fun y => (ex (fun z => (ex (fun w => p))))))))
(at level 200, x ident, y ident, z ident, w ident, right associativity) : type_scope.

Tactic Notation "exists" constr(x) := exists x.
Tactic Notation "exists" constr(x) constr(y) := exists x ; exists y.
Tactic Notation "exists" constr(x) constr(y) constr(z) := exists x ; exists y ; exists z.
Tactic Notation "exists" constr(x) constr(y) constr(z) constr(w) := exists x ; exists y ; exists z ; exists w.