Henning Thielemann wrote:
On Sun, 9 Oct 2011, Heinrich Apfelmus wrote:
I recently noticed that the instance
MonadFix m => ArrowLoop (Kleisli m)
does not fulfill the ArrowLoop laws for most monads, rendering it either useless or dangerous for the unwary. Removing it would be the correct thing to do, but I think that the sensible thing to do is to merely document said fact at the instance declaration in the haddocks. This way, the few monads that do support an ArrowLoop instance (most notably the lazy state monad) can keep their instance while everyone else is warned.
.... and since the lazy state monad does not fulfill the Functor laws, there is no monad at all, where the ArrowLoop instance is correct?
Ah, I don't intend to haggle over seq and _|_. In my view, the ArrowLoop instance for the lazy state monad fulfills the right-tightening law just fine. The trouble is with monads where you cannot a write a function first :: (a -> M b) -> ((a,d) -> M (b,d)) that allows you to "lazily observe" the second parameter d without forcing a to some extend. The lazy state monad allows you to write first m = \p -> m (fst p) >>= \b -> return (b,snd p) = \p s -> let (b,s') = m (fst p) s in ((b,snd p),s') and you can extract the d component from the result just fine. But, according to the literature, you can't something similar for monads where >>= is strict in the first argument, like Maybe or [] or IO or various monad transformer stacks. Best regards, Heinrich Apfelmus -- http://apfelmus.nfshost.com