28 lines
967 B
Text
28 lines
967 B
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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structure monad [class] (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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inline definition return {m : Type → Type} [monad m] {A : Type} (a : A) : m A :=
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monad.ret m a
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definition fapp {m : Type → Type} [monad m] {A B : Type} (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 definition monad_is_applicative [instance] (m : Type → Type) [monad m] : applicative m :=
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applicative.mk (@monad.map _ _) (@monad.ret _ _) (@fapp _ _)
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inline 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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