module TypeClass

data Monad : (U -> U) -> U where
  MkMonad : { M : U -> U } ->
            (bind : {A B : U} -> (M A) -> (A -> M B) -> M B) ->
            Monad M

data Maybe : U -> U where
  Just    : {A : U} -> A -> Maybe A
  Nothing : {A : U} -> Maybe A

data Either : U -> U -> U where
  Left : {A B : U} -> A -> Either A B
  Right : {A B : U} -> B -> Either A B

bindEither : {A B C : U} -> (Either A B) -> (B -> Either A C) -> Either A C
bindEither (Left a) amb = Left a
bindEither (Right b) amb = amb b

EitherMonad : {A : U} -> Monad (Either A)
EitherMonad = MkMonad {Either A} bindEither

bindMaybe : {A B : U} -> Maybe A -> (A -> Maybe B) -> Maybe B
bindMaybe Nothing amb = Nothing
bindMaybe (Just a) amb = amb a

MaybeMonad : Monad Maybe
MaybeMonad = MkMonad bindMaybe

_>>=_ : {a b : U} -> {m : U -> U} -> {{x : Monad m}} -> (m a) -> (a -> m b) -> m b
_>>=_ {a} {b} {m} {{MkMonad bind'}}  ma amb = bind' {a} {b} ma amb

infixl 1 _>>=_

ptype Int

foo : Int -> Maybe Int
foo x = (Just x) >>= (\ x => Just 10)