Ashley Yakeley writes:
Are there any useful monads that are instances of both MonadCont and MonadFix? I can't make the two meet. Perhaps this is because continuations have no fixed point, or something. Very annoying.
If you have a recursive monad with first-class references (such as IO or ST s), you can define a continuation monad on top of it with an instance of MonadFix I enclose below. The instance seems to make sense operationally, but as Levent Erkök has pointed out, it doesn't satisfy the left-shrinking axiom for recursive monads: fixM (\x -> a >>= f x) == a >>= \y -> fixM (\x -> f x y) This axiom comes from Levent's and John Launchbury's ICFP'00 paper, see http://www.cse.ogi.edu/PacSoft/projects/rmb/ Moreover, I suspect that the instance breaks the axiom for callcc, which shows how any evaluation context E can be pushed inside a callcc: E[callcc e] = callcc (\k' -> E[e (\z -> k' (E[z]))] This is for callcc without monadic types, see Sabry's and Friedman's paper on "Recursion is a Computational Effect", at http://www.cs.indiana.edu/hyplan/sabry/papers/ /M -- class Monad m => FixMonad m where fixM :: (a -> m a) -> m a class Monad m => Ref m r | m -> r where newRef :: a -> m (r a) readRef :: r a -> m a writeRef :: r a -> a -> m () newtype C m a = C ((a -> m ()) -> m ()) deC (C m) = m instance (FixMonad m, Ref m r) => FixMonad (C m) where fixM m = C $ \k -> do x <- newRef Nothing a <- fixM $ \a -> do deC (m a) $ \a -> do ma <- readRef x case ma of Nothing -> do writeRef x (Just a) Just _ -> k a ma <- readRef x case ma of Just a -> return a Nothing -> error "fixM" k a