Stateをさわってみる

haskellのStateモナドへの理解を深めるために、Stateモナドを真似て実装をなぞりつつ気づいたことをまとめたお話になります。

スライド中で紹介している実装はこちら：
https://github.com/pnlybubbles-gomibako/counter-haskell

Transcript

1. StateΛ͞ΘͬͯΈΔ pnly (@pn1y) on Haskell
2. Who am I … • ΆΜΓ͌ • Twitter: @pn1y • ෺ཧֶՊ 3೥ • Web԰΍ͬͯ·͢ • ਺ֶŷţƄŜŢŘ…
3. ൃදͷ్தͰ΋ͲΜͲΜ ποίϛ͓ئ͍͠·͢
4. ͜͜Ͱ͸ • ໨తɿঢ়ଶΛ͏·͘ѻ͍͍ͨ • StateϞφυࣗମΛ͞ΘΔͱ͍͏ΑΓɺStateϞ φυͷ΍͍ͬͯΔ͜ͱΛ໛฿ͯ͠ཧղΛਂΊΔ • ྫΛ༻͍ͨ۩ମతͳ࣮૷Λϕʔεʹͨ͠࿩ • ҰൠԽʹؔͯ͠͸͋·Γ৮Ε·ͤΜ
5. State == ঢ়ଶ • ʲঢ়ଶʳ෺ࣄ͕ɺͦͷ࣌ʹͦ͏ͳ͍ͬͯΔɺ ͋Γ͞·ɻ • Haskellʹ͓͚Δʮͦͷ࣌ʯͬͯͳʹʁ • func(A)ͷ࣌ɺfunc(B)ͷ࣌ɺͷΑ͏ͳҾ਺͕ҧ ͏”࣌”
6. HaskellͰঢ়ଶΛ”දݱ”͢Δ • ঢ়ଶͱ͍͏ͱ࣌ʑࠁʑͱมΘΓͦ͏ͳ΋ͷ • ͔͠͠Haskell͸͢΂ͯ७ਮͳͷͰImmutable • ͦ΋ͦ΋Haskellʹ͓͚Δ࣌ؒͷ֓೦͸ʁ • Ҿ਺ͷҧ͍Ͱঢ়ଶΛ”දݱ”ͯ͠ΈΔ
7. - ঢ়ଶͷྫ - Stack
8. Stack type Stack = [Integer] push :: Integer -> Stack -> (Integer, Stack) push c cs = (c, c:cs) pop :: Stack -> (Integer, Stack) pop (c:cs) = (c, cs) ݹ͍Stack ৽͍͠Stack ݹ͍Stack ৽͍͠Stack Ҿ਺Ͱલͷ”ঢ়ଶ”Λ༩͑ɺ࣍ͷ”ঢ়ଶ”Λ࡞Δ
9. Stackʹର͢Δجຊతͳૢ࡞ push :: Integer -> Stack -> (Integer, Stack) ݹ͍Stack (ૢ࡞ͷ݁Ռ, ৽͍͠Stack) ͜ͷૢ࡞ΛStackʹର͢Δ”ঢ়ଶͷߋ৽”ͱ͢Δ
10. Stackͷίʔυશମ type Stack = [Integer] push :: Integer -> Stack -> (Integer, Stack) push c cs = (c, c:cs) pop :: Stack -> (Integer, Stack) pop (c:cs) = (c, cs) main = do let stack = [1, 2, 3, 4, 5] let (i1, stack1) = pop stack let (i2, stack2) = pop stack1 let (i3, stack3) = push (i1 + i2) stack2 print (i3, stack3)
11. 2ͭpopͯ͠଍͠ࢉͯ͠push type Stack = [Integer] calc :: (Integer -> Integer -> Integer) -> Stack -> (Integer, Stack) calc op stack = (i3, stack3) where (i1, stack1) = pop stack (i2, stack2) = pop stack1 (i3, stack3) = push (op i1 i2) stack2 main = do let stack = [1, 2, 3, 4, 5] print $ calc (+) stack
12. 2ͭpopͯ͠଍͠ࢉͯ͠push calc :: (Integer -> Integer -> Integer) -> Stack -> (Integer, Stack) Stackͷૢ࡞
13. ͳΜ͔ඒ͘͠ͳ͍ͱ͜Ζ main = do let stack = [1, 2, 3, 4, 5] let (i1, stack1) = pop stack let (i2, stack2) = pop stack1 print (i2, stack2) ࣍ͷૢ࡞Λ͢ΔͨΊʹ͸લͷঢ়ଶΛ৯Θͤͳ͍ͱ͍͚ͳ͍
14. ૢ࡞Λ࿈࠯ͤ͞Δͱ͖ʹલͷ ঢ়ଶΛ҉໧తʹ౉͍ͨ͠
15. લͷૢ࡞ͱ࣍ͷૢ࡞Λܨ͙ bind :: (Stack -> (Integer, Stack)) -> (Integer -> (Stack -> (Integer, Stack))) -> (Stack -> (Integer, Stack)) લͷૢ࡞ ࣍ͷૢ࡞ લͷૢ࡞ͱ࣍ͷૢ࡞Λ࿈࠯ͤͨ͞ૢ࡞
16. લͷૢ࡞ͱ࣍ͷૢ࡞Λܨ͙ bind :: (Stack -> (Integer, Stack)) -> (Integer -> (Stack -> (Integer, Stack))) -> (Stack -> (Integer, Stack)) લͷૢ࡞ͷ݁Ռ લͷૢ࡞ͷ݁ՌΛࡐྉʹɺ࣍ͷૢ࡞Λ࡞Δ
17. bindͷ࣮૷ bind method lambda stack = (i', s') where (i, s) = method stack (i', s') = lambda i s લͷૢ࡞Λద༻ ࣍ͷૢ࡞Λద༻ ݁Ռ͔Β࣍ͷૢ࡞Λ࡞Δؔ਺
18. calcΛbindͰॻ͖׵͑Δ calc op stack = (i3, stack3) where (i1, stack1) = pop stack (i2, stack2) = pop stack1 (i3, stack3) = push (op i1 i2) stack2 calc op = pop `bind` \i1 -> pop `bind` \i2 -> push (op i1 i2) calc :: (Integer -> Integer -> Integer) -> Stack -> (Integer, Stack) εοΩϦ😁
19. bindͰมΘͬͨ͜ͱ • ̎ͭͷStackʹର͢Δૢ࡞Λܨ͙͜ͱ͕Ͱ͖ͨ • Ұ࣌ม਺Λ࡞Δ͜ͱແ͘ɺલͷঢ়ଶΛ࣍ͷૢ ࡞΁ड͚౉͢͜ͱ͕Ͱ͖ͨ • ௚લͷঢ়ଶ͸௚ޙͷঢ়ଶͷߋ৽ʹඞͣଋറ͞ ΕΔͱ͍͏҉໧ͷจ຺͕Ͱ͖ͨ
20. ͳʹ΋͠ͳ͍ૢ࡞ unit :: Integer -> Stack -> (Integer, Stack) unit i cs = (i, cs) ͦͷ··ฦ͢ ͳʹ͔Λड͚औͬͯ ”ͳʹ΋͠ͳ͍ૢ࡞”ͷ݁Ռͱͯ͠٧ΊࠐΉ Stackͷૢ࡞
21. 2ͭpopͯ͠଍͠ࢉ͢Δ͚ͩ calc op = pop `bind` \i1 -> pop `bind` \i2 -> unit (op i1 i2) calc :: (Integer -> Integer -> Integer) -> Stack -> (Integer, Stack) push͠ͳ͍Α calc op = pop `bind` \i1 -> pop `bind` \i2 -> push (op i1 i2) ݁ՌΛpushͯ͠Δ ଍͠ࢉͷ݁ՌΛฦ͢ ൺֱ
22. ✨ ੔ཧ ✨
23. Stackͷૢ࡞ͷܕΛ੔ཧ type StackOp = Stack -> (Integer, Stack) Stackͷૢ࡞ push :: Integer -> StackOp push :: StackOp calc :: (Integer -> Integer -> Integer) -> StackOp
24. Stackͷૢ࡞ͷܕΛ੔ཧ unit :: Integer -> StackOp bind :: StackOp -> (Integer -> StackOp) -> StackOp bind_ :: StackOp -> StackOp -> StackOp ɾલͷ݁ՌΛࣺͯͯ࣍ͷૢ࡞ͱܨ͙ ɾલͷ݁ՌΛݩʹ࣍ͷૢ࡞ͱܨ͙ ɾ͋Δ݁ՌΛฦ͢Կ΋͠ͳ͍ૢ࡞Λ࡞Δ
25. ॏཁͳͷ͸ίί main = do let stack = [1, 2, 3, 4, 5] print $ (pop `bind` \i1 -> pop `bind` \i2 -> unit $ i1 + i2) $ stack ෳ਺ͷૢ࡞(pop, push)ΛॱংΛ࣮࣋ͬͯߦ͢Δ Α͏ʹͭͳ͗߹Θ͍ͤͯΔ
26. ࣍ͷҰา newtype Stack a = Stack [a] deriving Show newtype StackOp a b = StackOp { run :: Stack a -> (b, Stack a) } ܕͷҰൠԽ https://github.com/pnlybubbles-gomibako/counter-haskell/blob/master/stack7.hs class MyMonad m where bind :: m b -> (b -> m c) -> m c bind_ :: m b -> m c -> m c unit :: b -> m b Ϟφυ(ͷΑ͏ͳ΋ͷ)
27. StateϞφυΛ࢖ͬͯΈΔ import Control.Monad.State newtype Stack a = Stack [a] deriving Show type StackOp a b = State (Stack a) b https://github.com/pnlybubbles-gomibako/counter-haskell/blob/master/stack8.hs push :: a -> StackOp a a push c = get >>= \(Stack cs) -> put (Stack (c:cs)) >> return c
28. doه๏Λ࢖ͬͯΈΔ https://github.com/pnlybubbles-gomibako/counter-haskell/blob/master/stack9.hs push :: a -> StackOp a a push c = get >>= \(Stack cs) -> put (Stack (c:cs)) >> return c push :: a -> StackOp a a push c = do (Stack cs) <- get put (Stack (c:cs)) return c
29. END https://github.com/pnlybubbles-gomibako/counter-haskell