(*********************************************************************************************************************************) (* Preamble: miscellaneous notations *) (*********************************************************************************************************************************) Require Import Coq.Unicode.Utf8. Require Import Coq.Classes.RelationClasses. Require Import Coq.Classes.Morphisms. Require Import Coq.Setoids.Setoid. Require Setoid. Require Import Coq.Strings.String. 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 40). Reserved Notation "a ;; b" (at level 45). Reserved Notation "a -~- b" (at level 10). Reserved Notation "pf1 === pf2" (at level 80). Reserved Notation "?? x" (at level 1). Reserved Notation "a ,, b" (at level 50). Reserved Notation "!! f" (at level 3). Reserved Notation "!` x" (at level 2). Reserved Notation "`! x" (at level 2). 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 "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 "[# f #]" (at level 2). Reserved Notation "a ---> b" (at level 11, right associativity). Reserved Notation "a <- b" (at level 100, only parsing). Reserved Notation "G |= S" (at level 75). Reserved Notation "F -| G" (at level 75). Reserved Notation "a :: b" (at level 60, right associativity). Reserved Notation "a ++ b" (at level 60, right associativity). Reserved Notation "<[ t @]>" (at level 30). Reserved Notation "<[ t @ n ]>" (at level 30). Reserved Notation "<[ e ]>" (at level 30). Reserved Notation "'Λ' x : t :-> e" (at level 9, right associativity, x ident). Reserved Notation "R ==> R' " (at level 55, right associativity). Reserved Notation "f ○ g" (at level 100). Reserved Notation "a ==[ n ]==> b" (at level 20). Reserved Notation "a ==[ h | c ]==> b" (at level 20). Reserved Notation "H /⋯⋯/ C" (at level 70). Reserved Notation "a |== b @@ c" (at level 100). Reserved Notation "f >>>> g" (at level 45). Reserved Notation "a >>[ n ]<< b" (at level 100). 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 "'<[' a '|-' t ']>'" (at level 35). Reserved Notation "Γ '∌' x" (at level 10). Reserved Notation "Γ '∌∌' x" (at level 10). Reserved Notation "Γ '∋∋' x : a ∼ b" (at level 10, x at level 99). Reserved Notation "Γ '∋' x : c" (at level 10, x at level 99). Reserved Notation "a ⇛ b" (at level 55, right associativity). Reserved Notation "φ₁ →→ φ₂" (at level 11, right associativity). Reserved Notation "a '⊢ᴛy' b : c" (at level 20, b at level 99, c at level 80). Reserved Notation "a '⊢ᴄᴏ' b : c ∼ d" (at level 20, b at level 99). Reserved Notation "Γ '+' x : c" (at level 50, x at level 99). Reserved Notation "Γ '++' x : a ∼ b" (at level 50, x at level 99). Reserved Notation "φ₁ ∼∼ φ₂ ⇒ φ₃" (at level 11, φ₂ at level 99, right associativity). Reserved Notation "Γ > past : present '⊢ᴇ' succedent" (at level 52, past at level 99, present at level 50, succedent at level 50). Reserved Notation "'η'". Reserved Notation "'ε'". Reserved Notation "'★'". 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 "?? T" := (option T). Notation "a && b" := (if a then b else false). Notation "a || b" := (if a then true else b). (* these are handy since Coq's pattern matching syntax isn't integrated with its abstraction binders (like Haskell and ML) *) Notation "'⟨' x ',' y '⟩'" := ((x,y)) (at level 100). Notation "'Λ' '⟨' x ',' y '⟩' e" := (fun xy => match xy with (a,b) => (fun x y => e) a b end) (at level 100). Notation "'Λ' '⟨' x ',' '⟨' y ',' z '⟩' '⟩' e" := (fun xyz => match xyz with (a,bc) => match bc with (b,c) => (fun x y z => e) a b c end end) (at level 100). Notation "'Λ' '⟨' '⟨' x ',' y '⟩' ',' z '⟩' e" := (fun xyz => match xyz with (ab,c) => match ab with (a,b) => (fun x y z => e) a b c end end) (at level 100). 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.