On Tue, Apr 19, 2011 at 11:48 PM, Tyson Whitehead
On April 19, 2011 23:22:12 Tyson Whitehead wrote:
ArrowLoop from MonadFix
loop' f = fst' .' loop'' (f .' arr' (second snd)) where loop'' f = mfix (\y -> f .' arr' (,y))
BTW haskellers, I've been wondering if mfix would better be defined as
mfix' :: (m a -> m a) -> m a
where "mfix' f = mfix (f . pure)" for the computational monads. The advantage being you can give a useful definition for structural monads as well.
Note: This does not generalize the signature of mfix, it only overlaps slightly, as not every monad m permits the extraction of the value a injected (consider Cont r), so you necessarily change the meaning or obliterate a number of instances. Recall the main motivation for mfix was to support Erkoek and Launchbury's recursive do: http://www.google.com/search?sourceid=chrome&ie=UTF-8&q=mfix+recursive+do http://www.haskell.org/haskellwiki/MonadFix This necessitates 4 laws for mfix, which don't translate nicely. - mfix (return . h) = return (fix h) - mfix (\x -> a >>= \y -> f x y) = a >>= \y -> mfix (\x -> f x y) - if h is strict, mfix (liftM h . f) = liftM h (mfix (f . h)) - mfix (\x -> mfix (\y -> f x y)) = mfix (\x -> f x x) The other commonly proposed mfix replacement is to define it once, as guided by the types, but while this works for fix and the the comonadic equivalent, it doesn't generate a useful mfix for recursive do either. -Edward