Hello, 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. Thus, I suggest to add documentation to the instances, along the lines of "Even though every monad that supports 'mfix' can be made an instance of 'ArrowLoop', it usually /does not/ fulfill all of the corresponding ArrowLoop laws. Use this instance at your own risk." The main problem is the right-tightening law loop (first h <<< f) = h <<< loop f which fails for most monads. Consider the following example: bad :: String -> IO () bad = runKleisli $ loop (first (Kleisli putStrLn) <<< arr swap) where swap (a,b) = (b,a) Using the ArrowLoop laws [1], this example should be equal to ... = runKleisli $ Kleisli putStrLn <<< loop (arr swap) = putStrLn However, trying the example in GHCi will throw "Exception: <<loop>>", which clearly shows that this equality is not true. The underlying reason is that MonadFix doesn't support a corresponding right-tightening law, just as mentioned for example in [2]. [1]: http://www.soi.city.ac.uk/~ross/papers/fop.html [2]: http://citeseer.ist.psu.edu/viewdoc/summary?doi=10.1.1.6.5172 Discussion period: 2 weeks (ends 24 October 2011) Best regards, Heinrich Apfelmus -- http://apfelmus.nfshost.com