[Haskell-beginners] Monads

[Brent Yorgey]

On Wed, Mar 02, 2011 at 10:04:38AM -0500, Patrick Lynch wrote:
> Daniel,
> Thank you...I understand now...
> Good day
> 
> Ps
> I think my problem that I'm facing is that I don't see how the
> instance Functor Maybe is derived from the class Functor...
> 
> for example,
>  the author Miran Lipovaca gives the following:
>     class Functor f where
>     fmap::(a->b)->f a->f b
> 
>  if Maybe replaces f:
>     fmap::(a->b)->Maybe a->Maybe b

Right.

> 
>  I don't see how the instance Functor Maybe is derived [presumably:
> 'f' is function (a->b) and not functor 'f' as shown in the class
> description):

Yes, here 'f' is a function (a -> b).  It is confusing that often the
letter f is used both to represent an arbitrary Functor or to
represent an arbitrary function.  But you can tell the difference by
seeing whether the f occurs in a type or in some code.

>     instance Functor Maybe where
>       fmap f (Just x) = Just (f x)
>       fmap f Nothing = Nothing

So you are confused about this code?  Can you be more specific what
you are confused about?  Try thinking carefully about all the types
involved.  What is the type of f? (You already answered this: a -> b.)
What is the type of (Just x)? The type of x?  What type is required on
the right hand side of the = ?  And so on.

-Brent