This document summarizes applicative functors and Haskell 2014 features. It explains Maybe type, Functor instance for Maybe, Applicative instance for Maybe, and Monad instance for Maybe. It then compares Haskell's classes (Functor, Applicative, Monad) to category theory. Finally, it outlines the changes in Haskell 2014, including defining Monad in terms of Applicative and providing default implementations for (>>) and return.

1. アプリカティブファンクター
と
Haskell 2014版
株式会社インフィニットループ
Yanez Sanchez Luis David
2014/06/20 OpenIL vol.2

2. 「Haskell書く？」 「Maybe( ͡° ͜ʖ ͡°)」
● Maybeタイプ
● Just x (Just 1, Just “Haskell”...)
● Nothing (Nothing, Nothing, Nothing....)
● 3 + 2 = 5
● 3 + Just 2 = ＼(^o^)／ｵﾜﾀ

3. Functorの説明
● class Functor f where
fmap :: (a -> b) -> f a -> f b
● instance Functor Maybe where
fmap f (Just x) = Just (f x)
fmap f Nothing = Nothing
● Just (3+2)
● fmap (+3) (Just 2)

4. Applicativeの説明
● class (Functor f) => Applicative f where
pure :: a -> f a
(<*>) :: f (a -> b) -> f a -> f b
(*>) :: f a -> f b -> f b
● instance Applicative Maybe where
pure = Just
Nothing <*> _ = Nothing
(Just f) <*> something = fmap f something
● Just (+3) <*> Just 2

5. Monadの説明
● class Monad m where
(>>=) :: m a -> (a -> m b) -> m b
(>>) :: m a -> m b -> m b
return :: a -> m a
● instance Monad Maybe where
return x = Just x
(>>=) Nothing f = Nothing
(>>=) (Just x) f = f x
● Just 1000 >>= half >>= half >>= half >>= half....
half x = if even x
then Just (x `div` 2)
else Nothing

6. あれ？
class (Functor f) => Applicative f where
pure :: a -> f a
(<*>) :: f (a -> b) -> f a -> f b
(*>) :: f a -> f b -> f b
class Monad m where
(>>=) :: m a -> (a -> m b) -> m b
(>>) :: m a -> m b -> m b
return :: a -> m a
※画像引用元
http://adit.io/posts/2013-04-17-functors,_applicatives,_and_monads_in_pictures.html

7. 圏論とHaskellの違い
現在のHaskell
Functor
Applicative
Monad
圏論

8. Haskell 2014版
class Applicative m => Monad m where
-- Minimal complete definition: (>>=) or join
(>>=) :: m a -> (a -> m b) -> m b
m >>= f = join (fmap f m)
(>>) :: m a -> m b -> m b
(>>) = (*>)
join :: m (m a) -> m a
join m = m >>= id
return :: a -> m a
return = pure
fail :: String -> m a
fail s = error s

9. ご清聴ありがとうございました