(*********************************************************************************************************************************)
(* Notations: miscellaneous notations *)
(*********************************************************************************************************************************)
Require Import Coq.Unicode.Utf8.
Require Import Coq.Classes.RelationClasses.
Require Import Coq.Classes.Morphisms.
Require Import Coq.Setoids.Setoid.
Require Setoid.
Export Coq.Unicode.Utf8.
Export Coq.Classes.RelationClasses.
Export Coq.Classes.Morphisms.
Export Coq.Setoids.Setoid.
Set Printing Width 130. (* Proof General seems to add an extra two columns of overhead *)
Generalizable All Variables.
Reserved Notation "a ~=> b" (at level 70, right associativity).
Reserved Notation "H ===> C" (at level 100).
Reserved Notation "f >>=>> g" (at level 45).
Reserved Notation "a ~~{ C }~~> b" (at level 100).
Reserved Notation "f <--> g" (at level 20).
Reserved Notation "! f" (at level 2).
Reserved Notation "? f" (at level 2).
Reserved Notation "# f" (at level 2).
Reserved Notation "f '⁻¹'" (at level 1).
Reserved Notation "a ≅ b" (at level 70, right associativity).
Reserved Notation "C 'ᵒᴾ'" (at level 1).
Reserved Notation "F \ a" (at level 20).
Reserved Notation "f >>> g" (at level 45).
Reserved Notation "a ~~ b" (at level 54).
Reserved Notation "a ~> b" (at level 70, right associativity).
Reserved Notation "a ≃ b" (at level 70, right associativity).
Reserved Notation "a ≃≃ b" (at level 70, right associativity).
Reserved Notation "a ~~> b" (at level 70, right associativity).
Reserved Notation "F ~~~> G" (at level 70, right associativity).
Reserved Notation "F <~~~> G" (at level 70, right associativity).
Reserved Notation "F <~~⊗~~> G" (at level 70, right associativity).
Reserved Notation "a ⊗ b" (at level 40).
Reserved Notation "a ⊗⊗ b" (at level 40).
Reserved Notation "a ⊕ b" (at level 40).
Reserved Notation "a ⊕⊕ b" (at level 40).
Reserved Notation "f ⋉ A" (at level 40).
Reserved Notation "A ⋊ f" (at level 40).
Reserved Notation "- ⋉ A" (at level 40).
Reserved Notation "A ⋊ -" (at level 40).
Reserved Notation "a *** b" (at level 40).
Reserved Notation "a ---> b" (at level 11, right associativity).
Reserved Notation "a <- b" (at level 100, only parsing).
Reserved Notation "a :: b" (at level 60, right associativity).
Reserved Notation "a ++ b" (at level 60, right associativity).
Reserved Notation "f ○ g" (at level 100).
Reserved Notation "f >>>> g" (at level 45).
Reserved Notation "a >>⊗>> b" (at level 20).
Reserved Notation "f **** g" (at level 40).
Reserved Notation "C × D" (at level 40).
Reserved Notation "C ×× D" (at level 45).
Reserved Notation "C ⁽ºᑭ⁾" (at level 1).
Reserved Notation "F -| G" (at level 75).
Reserved Notation "'ε'".
Reserved Notation "'η'".
Close Scope nat_scope. (* so I can redefine '1' *)
Delimit Scope arrow_scope with arrow.
Delimit Scope biarrow_scope with biarrow.
Delimit Scope garrow_scope with garrow.
Notation "f ○ g" := (fun x => f(g(x))).
Notation "a && b" := (if a then b else false).
Notation "a || b" := (if a then true else b).
Notation "∀ x y z u q , P" := (forall x y z u q , P)
(at level 200, q ident, x ident, y ident, z ident, u ident, right associativity)
: type_scope.
Notation "∀ x y z u q v , P" := (forall x y z u q v , P)
(at level 200, q ident, x ident, y ident, z ident, u ident, v ident, right associativity)
: type_scope.
Notation "∀ x y z u q v a , P" := (forall x y z u q v a , P)
(at level 200, q ident, x ident, y ident, z ident, u ident, v ident, a ident, right associativity)
: type_scope.
Notation "∀ x y z u q v a b , P" := (forall x y z u q v a b , P)
(at level 200, q ident, x ident, y ident, z ident, u ident, v ident, a ident, b ident, right associativity)
: type_scope.
Notation "∀ x y z u q v a b r , P" := (forall x y z u q v a b r , P)
(at level 200, q ident, x ident, y ident, z ident, u ident, v ident, a ident, b ident, r ident, right associativity)
: type_scope.
Notation "∀ x y z u q v a b r s , P" := (forall x y z u q v a b r s , P)
(at level 200, q ident, x ident, y ident, z ident, u ident, v ident, a ident, b ident, r ident, s ident, right associativity)
: type_scope.
Notation "∀ x y z u q v a b r s t , P" := (forall x y z u q v a b r s t , P)
(at level 200, q ident, x ident, y ident, z ident, u ident, v ident, a ident, b ident, r ident, s ident, t ident,
right associativity)
: type_scope.