# 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.