On 26.09 01:01, David Menendez wrote:
We'll also define the injection combinator from Kieburtz's paper[1]:
(.>>) :: Functor d => d a -> b -> d b d .>> a = fmap (const a) d
We add some nice combinators: (>>-) :: Comonad co => (co a -> co b) -> (co b -> co c) -> co a -> co c a >>- b = b . a infixr >>- (>>--) :: Comonad co => (co a -> co b) -> (b -> co b -> co c) -> co a -> co c a >>-- b = \co -> let x = a co in b (counit x) x infixr >>-- coreturn v = cobind (const v) And define the simple state comonad: data StateC st a = StateC (st -> a) st instance Comonad (StateC st) where counit (StateC f v) = f v cobind fun (StateC f v) = StateC (\v -> fun (StateC f v)) v get :: StateC st a -> StateC st st get (StateC _ st) = StateC id st set :: st -> StateC st a -> StateC st a set new (StateC fun _) = StateC fun new modify :: (c -> c) -> StateC c a -> StateC c a modify mutator (StateC fun st) = StateC fun $ mutator st runStateC fun v0 = let StateC a b = fun (StateC id v0) in (a b,b) Now we can write comonadic code like monadic code: foobar = get >>-- \x -> coreturn (3*x) test3 = get >>-- \x -> set 15 >>- foobar >>-- \y -> set x >>- coreturn (show y) This looks very much like monadic code written with >> and >>=. A general Functor instance is easy (but non-haskell98): instance Comonad w => Functor w where fmap f = cobind (f . counit) - Einar Karttunen