haskell - How to make this alternative definition of Maybe work? -

i hvae invended following alternative definition of maybe:

type maybe' = forall b. (b -> (a -> b) -> b)  :: -> maybe' = \d f -> f  nothing :: maybe' nothing = const  bind :: maybe' -> (a -> maybe' b) -> maybe' b bind ma f = ma nothing (\a -> f a) 

the problem can't add following instance declaration

instance monad (maybe')     return =     >>= f = bind f 

the error message :

type synonym maybe' should have 1 argument, has been given none 

are there way fix?

you can make instance of monad if wrap in newtype. have use polymorphiccomponents extension (a weaker form of rankntypes) universally quantify b:

{-# language polymorphiccomponents #-}  newtype maybe' = maybe' { unmaybe' :: forall b. (b -> (a -> b) -> b) }  :: -> maybe' = maybe' (\d f -> f a)  nothing :: maybe' nothing = maybe' const  bind :: maybe' -> (a -> maybe' b) -> maybe' b bind ma f = maybe' (unmaybe' ma const (\a -> unmaybe' (f a)))  instance monad maybe'     return =     (>>=)  = bind 

the reason need newtype haskell type synonyms not "stick". when haskell tries match type signature of maybe' without newtype against monad type class, not see maybe' @ , instead sees raw underlying function type.

haskell uses "principal types" ensure every type has normal form. normal form of underlying function is:

(->) b ((->) ((->) b) b) 

type synonyms not change normal form of type, newtypes do. specifically, newtype in case rearranging type normal form has a last type parameter monad instance requires.