29 lines
973 B
Text
29 lines
973 B
Text
/-
|
|
Copyright (c) Luke Nelson and Jared Roesch. All rights reserved.
|
|
Released under Apache 2.0 license as described in the file LICENSE.
|
|
Authors: Luke Nelson and Jared Roesch
|
|
-/
|
|
prelude
|
|
import init.applicative init.string init.trace
|
|
universe variables u v
|
|
|
|
class monad (M : Type u → Type v) extends functor M : Type (max u+1 v) :=
|
|
(ret : Π {A : Type u}, A → M A)
|
|
(bind : Π {A B : Type u}, M A → (A → M B) → M B)
|
|
|
|
@[inline] def return {M : Type u → Type v} [monad M] {A : Type u} : A → M A :=
|
|
monad.ret M
|
|
|
|
def fapp {M : Type u → Type v} [monad M] {A B : Type u} (f : M (A → B)) (a : M A) : M B :=
|
|
do g ← f,
|
|
b ← a,
|
|
return (g b)
|
|
|
|
@[inline] instance monad_is_applicative (M : Type u → Type v) [monad M] : applicative M :=
|
|
⟨@fmap _ _, @return _ _, @fapp _ _⟩
|
|
|
|
@[inline] def monad.and_then {A B : Type u} {M : Type u → Type v} [monad M] (a : M A) (b : M B) : M B :=
|
|
do a, b
|
|
|
|
infixl ` >>= `:2 := monad.bind
|
|
infixl ` >> `:2 := monad.and_then
|