I'm trying to learn Haskell and I'm through all the basics. But now I'm stuck, trying to get my head around functors.
I've read that "A functor transforms one category into another category". What does this mean?
I know it's a lot to ask, but could anyone give me a plain english explanation of functors or maybe a simple use case?
A fuzzy explanation would be that a Functor is some sort of container and an associated function fmap that allows you to alter whatever is contained, given a function that transforms the contained.
For instance, lists are this kind of container, such that fmap (+1) [1,2,3,4] yields [2,3,4,5].
Maybe can also be made a functor, such that fmap toUpper (Just 'a') yields Just 'A'.
The general type of fmap shows quite neatly what is going on:
fmap :: Functor f => (a -> b) -> f a -> f b
And the specialized versions may make it clearer. Here's the list version:
fmap :: (a -> b) -> [a] -> [b]
And the Maybe version:
fmap :: (a -> b) -> Maybe a -> Maybe b
You can gain information on the standard Functor instances by querying GHCI with :i Functor and many modules define more instances of Functors (and other type classes.)
Please don't take the word "container" too seriously, though. Functors are a well-defined concept, but you can often reason about it with this fuzzy analogy.
Your best bet in understanding what is going on is simply reading the definition of each of the instances, which should give you an intuition on what is going on. From there it's only a small step to really formalize your understanding of the concept. What needs to be added is a clarification of what our "container" really is, and that each instance much satisfy a pair of simple laws.