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feat(function): add unfold hints to function.[h]lean

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Floris van Doorn 2015-05-07 01:23:39 -04:00 committed by Leonardo de Moura
parent 20e62c9623
commit 0a8f4f6dab
2 changed files with 27 additions and 25 deletions
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27
hott/init/function.hlean
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@ -17,41 +17,42 @@ namespace function
variables {A B C D E : Type} variables {A B C D E : Type}
definition compose [reducible] (f : B → C) (g : A → B) : A → C := definition compose [reducible] [unfold-f] (f : B → C) (g : A → B) : A → C :=
λx, f (g x) λx, f (g x)
definition compose_right [reducible] (f : B → B → B) (g : A → B) : B → A → B := definition compose_right [reducible] [unfold-f] (f : B → B → B) (g : A → B) : B → A → B :=
λ b a, f b (g a) λ b a, f b (g a)
definition compose_left [reducible] (f : B → B → B) (g : A → B) : A → B → B := definition compose_left [reducible] [unfold-f] (f : B → B → B) (g : A → B) : A → B → B :=
λ a b, f (g a) b λ a b, f (g a) b
definition id [reducible] (a : A) : A := definition id [reducible] [unfold-f] (a : A) : A :=
a a
definition on_fun [reducible] (f : B → B → C) (g : A → B) : A → A → C := definition on_fun [reducible] [unfold-f] (f : B → B → C) (g : A → B) : A → A → C :=
λx y, f (g x) (g y) λx y, f (g x) (g y)
definition combine [reducible] (f : A → B → C) (op : C → D → E) (g : A → B → D) : A → B → E := definition combine [reducible] [unfold-f] (f : A → B → C) (op : C → D → E) (g : A → B → D)
: A → B → E :=
λx y, op (f x y) (g x y) λx y, op (f x y) (g x y)
definition const [reducible] (B : Type) (a : A) : B → A := definition const [reducible] [unfold-f] (B : Type) (a : A) : B → A :=
λx, a λx, a
definition dcompose [reducible] {B : A → Type} {C : Π {x : A}, B x → Type} definition dcompose [reducible] [unfold-f] {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) := (f : Π {x : A} (y : B x), C y) (g : Πx, B x) : Πx, C (g x) :=
λx, f (g x) λx, f (g x)
definition flip [reducible] {C : A → B → Type} (f : Πx y, C x y) : Πy x, C x y := definition flip [reducible] [unfold-f] {C : A → B → Type} (f : Πx y, C x y) : Πy x, C x y :=
λy x, f x y λy x, f x y
definition app [reducible] {B : A → Type} (f : Πx, B x) (x : A) : B x := definition app [reducible] [unfold-f] {B : A → Type} (f : Πx, B x) (x : A) : B x :=
f x f x
definition curry [reducible] : (A × B → C) → A → B → C := definition curry [reducible] [unfold-f] : (A × B → C) → A → B → C :=
λ f a b, f (a, b) λ f a b, f (a, b)
definition uncurry [reducible] : (A → B → C) → (A × B → C) := definition uncurry [reducible] [unfold-c 5] : (A → B → C) → (A × B → C) :=
λ f p, match p with (a, b) := f a b end λ f p, match p with (a, b) := f a b end
precedence `∘'`:60 precedence `∘'`:60
@ -68,4 +69,4 @@ notation f `-[` op `]-` g := combine f op g
end function end function
-- copy reducible annotations to top-level -- copy reducible annotations to top-level
export [reduce-hints] function export [reduce-hints] [unfold-hints] function

25
library/algebra/function.lean
View file

@ -11,41 +11,42 @@ namespace function
variables {A : Type} {B : Type} {C : Type} {D : Type} {E : Type} variables {A : Type} {B : Type} {C : Type} {D : Type} {E : Type}
definition compose [reducible] (f : B → C) (g : A → B) : A → C := definition compose [reducible] [unfold-f] (f : B → C) (g : A → B) : A → C :=
λx, f (g x) λx, f (g x)
definition compose_right [reducible] (f : B → B → B) (g : A → B) : B → A → B := definition compose_right [reducible] [unfold-f] (f : B → B → B) (g : A → B) : B → A → B :=
λ b a, f b (g a) λ b a, f b (g a)
definition compose_left [reducible] (f : B → B → B) (g : A → B) : A → B → B := definition compose_left [reducible] [unfold-f] (f : B → B → B) (g : A → B) : A → B → B :=
λ a b, f (g a) b λ a b, f (g a) b
definition id [reducible] (a : A) : A := definition id [reducible] [unfold-f] (a : A) : A :=
a a
definition on_fun [reducible] (f : B → B → C) (g : A → B) : A → A → C := definition on_fun [reducible] [unfold-f] (f : B → B → C) (g : A → B) : A → A → C :=
λx y, f (g x) (g y) λx y, f (g x) (g y)
definition combine [reducible] (f : A → B → C) (op : C → D → E) (g : A → B → D) : A → B → E := definition combine [reducible] [unfold-f] (f : A → B → C) (op : C → D → E) (g : A → B → D)
: A → B → E :=
λx y, op (f x y) (g x y) λx y, op (f x y) (g x y)
definition const [reducible] (B : Type) (a : A) : B → A := definition const [reducible] [unfold-f] (B : Type) (a : A) : B → A :=
λx, a λx, a
definition dcompose [reducible] {B : A → Type} {C : Π {x : A}, B x → Type} definition dcompose [reducible] [unfold-f] {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) := (f : Π {x : A} (y : B x), C y) (g : Πx, B x) : Πx, C (g x) :=
λx, f (g x) λx, f (g x)
definition flip [reducible] {C : A → B → Type} (f : Πx y, C x y) : Πy x, C x y := definition flip [reducible] [unfold-f] {C : A → B → Type} (f : Πx y, C x y) : Πy x, C x y :=
λy x, f x y λy x, f x y
definition app [reducible] {B : A → Type} (f : Πx, B x) (x : A) : B x := definition app [reducible] {B : A → Type} (f : Πx, B x) (x : A) : B x :=
f x f x
definition curry [reducible] : (A × B → C) → A → B → C := definition curry [reducible] [unfold-f] : (A × B → C) → A → B → C :=
λ f a b, f (a, b) λ f a b, f (a, b)
definition uncurry [reducible] : (A → B → C) → (A × B → C) := definition uncurry [reducible] [unfold-c 5] : (A → B → C) → (A × B → C) :=
λ f p, match p with (a, b) := f a b end λ f p, match p with (a, b) := f a b end
theorem curry_uncurry (f : A → B → C) : curry (uncurry f) = f := theorem curry_uncurry (f : A → B → C) : curry (uncurry f) = f :=
@ -97,4 +98,4 @@ exists.intro a h
end function end function
-- copy reducible annotations to top-level -- copy reducible annotations to top-level
export [reduce-hints] function export [reduce-hints] [unfold-hints] function