Problem is that from the idea Functor is a superclass of Monad, with the property that "fmap == liftM".

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The second relation can even not be expressed in Haskell 98.

Erm... class Functor f where fmap :: (a -> b) -> f a -> f b class Functor m => Monad m where return :: a -> m a join :: m (m a) -> m a bind :: Monad m => m a -> (a -> m b) -> m b bind mx f = join $ fmap f mx Now liftM must be exactly equal to fmap.

On Feb 5, 2008, at 8:31 , Henning Thielemann wrote:

How do you convince the compiler that 'join (fmap return x) == x' ?

How do you convince it that the current formulation of Monad obeys the monad laws? (rhetorical) -- brandon s. allbery [solaris,freebsd,perl,pugs,haskell] allbery@kf8nh.com system administrator [openafs,heimdal,too many hats] allbery@ece.cmu.edu electrical and computer engineering, carnegie mellon university KF8NH

Can you do this with a GHC rule? Something like: {-# RULES "join_dot_fmap_return/id" forall x . join (fmap return x) = x #-} Dan Henning Thielemann wrote:

On Tue, 5 Feb 2008, Brandon S. Allbery KF8NH wrote:

...

On Feb 5, 2008, at 8:31 , Henning Thielemann wrote:

...

How do you convince the compiler that 'join (fmap return x) == x' ? How do you convince it that the current formulation of Monad obeys the monad laws? (rhetorical)

My point was that the constraint 'liftM == fmap' cannot be expressed in Haskell 98, and the answer by Miguel suggested that it would be possible by a different design of class Monad. The above was my objection to this suggestion. _______________________________________________ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe

On Tue, 5 Feb 2008, Felipe Lessa wrote:

On Feb 5, 2008 6:06 PM, Dan Weston wrote:

...

Can you do this with a GHC rule? Something like:

{-# RULES "join_dot_fmap_return/id" forall x . join (fmap return x) = x #-}

Dan

I guess this would make use of the rule (otherwise the transformation would change the code's semantic) but would not enforce that the rule itself is valid (which is undecidable).

I have already thought about (ab)using GHC rules for forcing programmers to take care. :-) That is, if the rule would be stated as above, then programmers _have_ to ensure that the law is satisfied, and the optimizer will penalize violations of the rules with non-working code.