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