"Iavor Diatchki"
class IxMonad m where (>>>=) :: m i j a -> (a -> m j k b) -> m i k b ret :: a -> m i i a
And just for fun we can define another indexed monad: state that supports "strong updates" (i.e., the type of the state can change as you compute):
newtype State i j a = S { unS :: i -> (a,j) }
This reminded me very much of the state monad (actually more general than a monad) used internally in the nhc98/yhc compiler. Attached below. Niklas Rojemo came up with this formulation in 1993. Regards, Malcolm ---- module State where -- Use >>> and >>>= instead of >> and >>= to avoid problems with 1.3 prelude infixl 5 >>>,>>>=,=>>> infixr 4 >=> type State0 d s s' = d -> s -> s' type State d s u s' = d -> s -> (u,s') -- 'unit' is what is now known as 'return' in monad-speak unitS :: u -> State d s u s unitS u = (\d s -> (u,s)) unitS0 :: State0 d s s unitS0 = (\d s -> s) -- There are four 'bind'-like operators, >>>, >>>=, =>>>, and >=> (>>>) :: State0 d a b -> State0 d b c -> State0 d a c f >>> g = \d s -> g d (f d s) (=>>>) :: State d s (a->b) s' -> State d s' a s'' -> State d s b s'' f =>>> g = \d s -> case f d s of (h,s) -> case g d s of (x,s) -> let hx = h x in seq hx (hx,s) -- f =>>> g = \d s -> case f d s of (h,s) -> case g d s of (x,s) -> (h x,s) (>>>=) :: State d s a s' -> (a -> State0 d s' s'') -> State0 d s s'' f >>>= g = \d s -> case f d s of (x,s) -> g x d s (>=>) :: State d s d' s' -> State0 d' s' s'' -> State0 d s s'' f >=> g = \d s -> case f d s of (d,s) -> (g d s) mapS :: (a->State d s b s) -> [a] -> State d s [b] s mapS f [] = unitS [] mapS f (x:xs) = unitS (:) =>>> f x =>>> mapS f xs mapS0 :: (a->State0 d s s) -> [a] -> State0 d s s mapS0 f [] = unitS0 mapS0 f (x:xs) = f x >>> mapS0 f xs zipWithS :: (a -> b -> State d s c s) -> [a] -> [b] -> State d s [c] s zipWithS f [] [] = unitS [] zipWithS f (x:xs) (y:ys) = unitS (:) =>>> f x y =>>> zipWithS f xs ys zipWithS _ _ _ = error "zipWithS: lists of different lengths" ----