[Haskell-beginners] Monads

[Daniel Fischer]

On Wednesday 02 March 2011 15:03:00, Patrick Lynch wrote:
> In Learn You a Haskell for Great Good!, the author Miran Lipovaca
> indicates that to understand Monads you need to know Functors... So, I
> noticed the following:
> 
> class Functor f where
>   fmap::(a->b)->f a->f b
> 
> instance Functor [] where
>   fmap = map
> 
> map::(a->b)->[a]->[b]
> 
> if [] is substituted for f in the class definition of Functor the
> following is obtained class Functor [] where
>   fmap::(a->b)->[]a->[]b
> 
> my questions are:
>   1. is this substitution ok?
>   2. is []a = [a]?
>   3. is []b = [b]?
> 
> if 2. and 3. are valid then the following is obtained:
>   fmap::(a->b)->[a]->[b]
> which is the same as map type and therefore: fmap = map. QED.
> 
> Can you please answer questions 2 and 3 above?
> 
> Thank you

Yes, that's correct. The list constructor is special ([] isn't valid 
Haskell for a type constructor, so it's wired in), it can be used prefix 
([] a) or `roundfix' ([a]). Ordinarily, you can use type constructors 
prefix or infix (if they take two type arguments), e.g. a -> b = (->) a b; 
Either a b = a `Either` b.