Haskell学习笔记The state monad 状态变换器

Haskell学习笔记--The state monad 状态变换器  

快快快在回宿舍前搞完

失败了

状态变换器

type ST a = State -> ( a , State )

返回变换后的状态和一个参数a

type定义的类型不能被弄成monad，所以改成用newtype

newtype ST a = S (State -> (a,State))

app :: ST a -> State -> (a,State)
app (S f) x = f x

instance Functor ST where 
　　--fmap :: (a->b) -> f a -> f b
　　fmap f st = S(\s -> let (x,s') = app st s in (f x,s'))
　　--fmap f st = S(\inp -> (f x,s') where (x,s') = app st inp) 

 还可以变成applicative

instance Applicative ST where
    pure :: a  -> ST a
    pure x = S (\s -> (x,s))

    (<*>) :: ST (a->b) -> ST a -> ST b
    stf <*> stx = S(\s -> 
            let (f,s') = app stf s 
                (x,s'') = app stx s' in (f x ,s'')

还可以弄成Monad

instance Monad ST where
    --(>>=) ::  ST a -> (a -> ST b) -> ST b
    stx >>= f = S (\s -> 
                    let (x,s') = app stx s in app (f x) s' )