55 lines
2 KiB
Text
55 lines
2 KiB
Text
/-
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Copyright (c) 2016 Microsoft Corporation. All rights reserved.
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Released under Apache 2.0 license as described in the file LICENSE.
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Authors: Leonardo de Moura
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-/
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prelude
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import init.logic init.monad init.alternative init.prod
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definition state (S : Type) (A : Type) := S → A × S
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section
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variables {S A B : Type}
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inline definition state_fmap (f : A → B) (a : state S A) : state S B :=
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λ s, match a s with (a', s') := (f a', s') end
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inline definition state_return (a : A) : state S A :=
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λ s, (a, s)
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inline definition state_bind (a : state S A) (b : A → state S B) : state S B :=
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λ s, match a s with (a', s') := b a' s' end
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definition state_is_monad [instance] (S : Type) : monad (state S) :=
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monad.mk (@state_fmap S) (@state_return S) (@state_bind S)
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end
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namespace state
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inline definition read {S A : Type} : state S S :=
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λ s, (s, s)
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inline definition write {S : Type} : S → state S unit :=
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λ s' s, ((), s')
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end state
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definition stateT (S : Type) (m : Type → Type) [monad m] (A : Type) := S → m (A × S)
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definition stateT_fmap.{l} {S : Type} {m : Type → Type} [monad m] {A B : Type.{l}} (f : A → B) (a : stateT S m A) : stateT S m B :=
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λ s, @monad.bind m _ _ _ (a s) (λ p : A × S, match p with (a', s') := return (f a', s') end)
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definition stateT_return {S : Type} {m : Type → Type} [monad m] {A : Type} (a : A) : stateT S m A :=
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λ s, @monad.ret m _ _ (a, s)
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definition stateT_bind.{l} {S : Type} {m : Type → Type} [monad m] {A B : Type.{l}} (a : stateT S m A) (b : A → stateT S m B) : stateT S m B :=
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λ s, @monad.bind m _ _ _ (a s) (λ p : A × S, match p with (a', s') := b a' s' end)
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definition stateT_is_monad [instance] (S : Type) (m : Type → Type) [monad m] : monad (stateT S m) :=
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monad.mk (@stateT_fmap S m _) (@stateT_return S m _) (@stateT_bind S m _)
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namespace stateT
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definition read {S : Type} {m : Type → Type} [monad m] : stateT S m S :=
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λ s, return (s, s)
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definition write {S : Type} {m : Type → Type} [monad m] : S → stateT S m unit :=
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λ s' s, return ((), s')
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end stateT
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