Maybeとかリストの復習用日本語オレメモ

jmonad.hs

{- 学習用
   復習として、Maybeやリストを改めて実装してみる.
   
   本物と区別するために日本語を使う。
   数学や情報科学の用語とあっていないのは気にしない。
   大文字・小文字の区別がないと識別子として認識されないので
   識別子の先頭はラテン文字にした
-}

import Control.Monad

-- Maybe a = Nothing | Just a
data Tたぶん a = K空 | J実 a
  deriving Show

fromMaybe :: Maybe a -> Tたぶん a
fromMaybe Nothing   = K空
fromMaybe (Just x)  = J実 x

instance Monad Tたぶん where
  -- return :: a -> Maybe a
  return  = J実

  -- (>>=) :: Maybe a -> (a -> Maybe b) -> Maybe b
  x >>= f = case x of
               K空   -> K空
               J実 a -> f a

instance MonadPlus Tたぶん where
  mzero       = K空
  a `mplus` b = case a of
                  K空 -> b
                  _   -> a

-- MaybeT
newtype T多分変換 m a = T多分変換
  -- コンストラクタ引数兼アクセサ定義
  { runT多分変換 :: m (Tたぶん a) }

instance Monad m => Monad (T多分変換 m) where
  -- return :: a -> MaybeT m a
  return x =  T多分変換 $ return $ J実 x
  -- (>>=) :: MaybeT m a -> (a -> MaybeT m b) -> m b
  x >>= f  = T多分変換 $
                     -- t :: Maybe a
                     do t <- runT多分変換 x
                        case t of
                          K空   -> return K空
                          J実 a -> runT多分変換 $ f a

-- List a = Atom | Cons a (List a)
data R列 a = H端 | R連 a (R列 a)
x `s挿入` xs = R連 x xs

fromList [] = H端
fromList (x:xs) = s挿入 x $ fromList xs

instance Show a => Show (R列 a) where
  show x = "<" ++ (show' x) ++ ">"
    where 
      show' :: Show a => R列 a -> String
      show' H端         = ""
      show' (R連 x H端) = show x
      show' (R連 x xs ) = (show x) ++ "," ++ show' xs

--map :: (a->b)->[a]->[b]
s写像 :: (a -> b) -> R列 a -> R列 b
s写像 f H端 = H端
s写像 f (R連 x xs) = R連 (f x) (s写像 f xs)

-- (++) :: [a]->[a]->[a]
g合体 :: R列 a -> R列 a -> R列 a
g合体 H端 y = y
g合体 (R連 x xs) y = R連 x (g合体 xs y)

-- concat :: [[a]] -> [a]
r連結 :: R列 (R列 a) -> R列 a
r連結 H端 = H端
r連結 (R連 x xs) = g合体 x (r連結 xs)

instance Monad R列 where
  return x = R連 x H端
  x >>= f = r連結 $ s写像 f x

instance MonadPlus R列 where
  mzero = H端
  mplus = g合体