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
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):
instance Functor Maybe where
fmap f (Just x) = Just (f x)
fmap f Nothing = Nothing
the author's examples [presumably: 'f'' = (++ " HEY GUYS IM INSIDE THE JUST
") and 'x' = " Something serious ." and it associates from the right...]:
ghci > fmap (++ " HEY GUYS IM INSIDE THE JUST ") ( Just " Something
serious .")
Just " Something serious . HEY GUYS IM INSIDE THE JUST "
ghci > fmap (++ " HEY GUYS IM INSIDE THE JUST ") Nothing
Nothing
I can continue on my Monad journey, just using the instance defintion for
Functor Maybe - but it bothers me that I can't see its derivation...
I'd appreciate any advice.
Thank you
----- Original Message -----
From: "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.