32 lines
1 KiB
Text
32 lines
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.applicative init.string init.trace
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set_option new_elaborator true
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structure [class] monad (M : Type → Type) extends functor M : Type :=
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(ret : Π {A : Type}, A → M A)
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(bind : Π {A B : Type}, M A → (A → M B) → M B)
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attribute [inline]
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definition return {M : Type → Type} [monad M] {A : Type} : A → M A :=
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monad.ret M
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definition {u} fapp {m : Type → Type} [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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attribute [inline, instance]
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definition monad_is_applicative (m : Type → Type) [monad m] : applicative m :=
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applicative.mk (@fmap _ _) (@return _ _) (@fapp _ _)
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attribute [inline]
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definition monad.and_then {A B : Type} {m : Type → Type} [monad m] (a : m A) (b : m B) : m B :=
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do a, b
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infixl ` >>= `:2 := monad.bind
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infixl ` >> `:2 := monad.and_then
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