chore(hott) add function.hlean to init

hott/init/function.hlean

@@ -0,0 +1,55 @@
+/-
+Copyright (c) 2014 Microsoft Corporation. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Author: Leonardo de Moura
+
+General operations on functions.
+-/
+prelude
+
+namespace function
+
+variables {A : Type} {B : Type} {C : Type} {D : Type} {E : Type}
+
+definition compose [reducible] (f : B → C) (g : A → B) : A → C :=
+λx, f (g x)
+
+definition id [reducible] (a : A) : A :=
+a
+
+definition on_fun (f : B → B → C) (g : A → B) : A → A → C :=
+λx y, f (g x) (g y)
+
+definition combine (f : A → B → C) (op : C → D → E) (g : A → B → D) : A → B → E :=
+λx y, op (f x y) (g x y)
+
+definition const {A : Type} (B : Type) (a : A) : B → A :=
+λx, a
+
+definition 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) :=
+λx, f (g x)
+
+definition flip {A : Type} {B : Type} {C : A → B → Type} (f : Πx y, C x y) : Πy x, C x y :=
+λy x, f x y
+
+definition app {A : Type} {B : A → Type} (f : Πx, B x) (x : A) : B x :=
+f x
+
+precedence `∘`:60
+precedence `∘'`:60
+precedence `on`:1
+precedence `$`:1
+
+variables {f g : A → B}
+
+
+infixr  ∘                 := compose
+infixr  ∘'                 := dcompose
+infixl  on                 := on_fun
+infixr  $                  := app
+notation f `-[` op `]-` g  := combine f op g
+-- Trick for using any binary function as infix operator
+notation a `⟨` f `⟩` b     :=  f a b
+
+end function