--- /dev/null
+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.
+
+(******************************************************************************)
+(* Preamble *)
+(******************************************************************************)
+
+Reserved Notation "a -~- b" (at level 10).
+Reserved Notation "a ** b" (at level 10).
+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 "a ;; b" (at level 45).
+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 "pf1 === pf2" (at level 80).
+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 40).
+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 : κ ⇒ 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 "'★'".
+
+Notation "a +++ b" := (append a b) (at level 100).
+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).
+
+(* 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.
projects / coq-categories.git / blobdiff