lean4-htt/library/init/applicative.lean

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/-
Copyright (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura
-/
prelude
import init.functor
set_option new_elaborator true
structure [class] {u₁ u₂} applicative (f : Type u₁ → Type u₂) extends functor f : Type (max u₁+1 u₂) :=
(pure : Π {A : Type u₁}, A → f A)
(seq : Π {A B : Type u₁}, f (A → B) → f A → f B)
attribute [inline]
definition pure {f : Type → Type} [applicative f] {A : Type} (a : A) : f A :=
applicative.pure f a
attribute [inline]
definition {u} seq_app {A B : Type u} {f : Type → Type} [applicative f] (g : f (A → B)) (a : f A) : f B :=
applicative.seq g a
infixr ` <*> `:2 := seq_app