56 lines
1.6 KiB
Text
56 lines
1.6 KiB
Text
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-- Copyright (c) 2014 Microsoft Corporation. All rights reserved.
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-- Released under Apache 2.0 license as described in the file LICENSE.
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-- Author: Leonardo de Moura
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namespace function
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section
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parameters {A : Type} {B : Type} {C : Type} {D : Type} {E : Type}
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abbreviation compose (f : B → C) (g : A → B) : A → C
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:= λx, f (g x)
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abbreviation id (a : A) : A
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:= a
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abbreviation const (a : A) : B → A
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:= λx, a
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abbreviation on_fun (f : B → B → C) (g : A → B) : A → A → C
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:= λx y, f (g x) (g y)
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abbreviation combine (f : A → B → C) (op : C → D → E) (g : A → B → D) : A → B → E
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:= λx y, op (f x y) (g x y)
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end
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abbreviation dcompose {A : Type} {B : A → Type} {C : Π {x : A}, B x → Type} (f : Π {x : A} (y : B x), C y) (g : Πx, B x) : Πx, C (g x)
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:= λx, f (g x)
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abbreviation flip {A : Type} {B : Type} {C : A → B → Type} (f : Πx y, C x y) : Πy x, C x y
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:= λy x, f x y
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abbreviation app {A : Type} {B : A → Type} (f : Πx, B x) (x : A) : B x
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:= f x
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-- Yet another trick to anotate an expression with a type
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abbreviation is_typeof (A : Type) (a : A) : A
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:= a
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precedence `∘`:60
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precedence `∘'`:60
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precedence `on`:1
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precedence `$`:1
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precedence `-[`:1
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precedence `]-`:1
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precedence `⟨`:1
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infixr ∘ := compose
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infixr ∘' := dcompose
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infixl on := on_fun
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notation `typeof` t `:` T := is_typeof T t
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infixr $ := app
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notation f `-[` op `]-` g := combine f op g
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-- Trick for using any binary function as infix operator
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notation a `⟨` f `⟩` b := f a b
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end
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