[Haskell-beginners] my ugly code and the Maybe monad

[Jan Jakubuv]

On Wed, Aug 19, 2009 at 11:57:47PM +0100, Simon Parry wrote:
> Thanks Jan, very helpful and you're right I am just trying to combine 2
> lists; one with 'wrapped' values, one without.
> 
> > You can write your own version of `liftM2` (from
> > `Control.Monad`) like this:
> > 
> >     liftM2snd f a mb = do { b <- mb; return (f a b) }
> > 
> 
> so the b <- mb bit is 'unwrapping' the Maybe b to use it with the pure
> function f?  

That's correct. In fact it is just a syntactic abbreviation (sugar) for

    liftM2snd f a mb = mb >>= \b -> return (f a b) 

You can always rewrite expressions with `do` using just `>>=`, `>>`, and
`->`. (Note that `<-` becomes the “dot” `->`.)

> I guess I didn't realise this as I've only seen it in the IO monad, but
> naturally it would work with all monads.
> 
> > You can verify that
> > 
> >     liftM2snd == (fmap .)
> 
> if I look at this in GHCi the liftM2snd acts over monads and the (fmap .) acts over functors.  
> Now I'm still trying to get comfortable with simple monad manipulations so maybe I should just 
> read this as functors are equivalent to monads and not worry too much about it yet?  
> With that in mind fmap acts to map some pure function over a 'wrapped' value? 
> 

Every Monad is automatically a Functor as well. You can define `fmap` using
monadic operations:

    fmap f ma = ma >>= return . f

Anyway, for some reasons this is not done automatically. You can do it
automatically with some GHC extensions. Load this into GHCi (don't forget
the first line):

    {-# OPTIONS -XFlexibleInstances -XUndecidableInstances #-}

    instance Monad m => Functor m where
        fmap f ma = ma >>= return . f

And here we go (in my GHCi 6.10.4):

    *Main> :t fmap
    fmap :: (Monad f) => (a -> b) -> f a -> f b

Usually, however, you don't need to do this because all instances of Monad
are already instances of Functor.

Also note that 

    fmap :: (Functor f) => (a -> b) -> f a -> f b

holds as well, that is, the type of `fmap` is ambiguous (because of the
GHC extensions above).

Sincerely,
    Jan.
    


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