lean4-htt/library/init/control/monad.lean
2019-07-12 14:07:33 -07:00

34 lines
1.1 KiB
Text
Raw Blame History

This file contains ambiguous Unicode characters

This file contains Unicode characters that might be confused with other characters. If you think that this is intentional, you can safely ignore this warning. Use the Escape button to reveal them.

/-
Copyright (c) Luke Nelson and Jared Roesch. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Luke Nelson, Jared Roesch, Sebastian Ullrich
-/
prelude
import init.control.applicative
universes u v w
open Function
class HasBind (m : Type u → Type v) :=
(bind : ∀ {α β : Type u}, m α → (α → m β) → m β)
export HasBind (bind)
infixr `>>=` := bind
@[inline] def mcomp {α : Type u} {β δ : Type v} {m : Type v → Type w} [HasBind m] (f : α → m β) (g : β → m δ) : α → m δ :=
fun a => f a >>= g
infixr `>=>` := mcomp
class Monad (m : Type u → Type v) extends Applicative m, HasBind m : Type (max (u+1) v) :=
(map := fun α β f x => x >>= pure ∘ f)
(seq := fun α β f x => f >>= (fun y => y <$> x))
(seqLeft := fun α β x y => x >>= fun a => y >>= fun _ => pure a)
(seqRight := fun α β x y => x >>= fun _ => y)
instance monadInhabited' {α : Type u} {m : Type u → Type v} [Monad m] : Inhabited (α → m α) :=
⟨pure⟩
instance monadInhabited {α : Type u} {m : Type u → Type v} [Monad m] [Inhabited α] : Inhabited (m α) :=
⟨pure $ default _⟩