Functors and lifting
Functors are like cranes lifting a function into a context
class Functor f where
fmap :: (a -> b) -> f a -> f b
It's like function application in the context of f:
($)
::
(a -> b)
->
a
->
b
(<$>)
:: Functor f =>
(a -> b)
->
f a
->
f b
Let's work through an example
let replace = const "a" <- function to apply
let value = [ Just [ "this", "that" ] ] <- variable to change
replace value <- apply to []
"a"
fmap replace value <- lift once - apply to Just
[ "a" ]
(fmap . fmap) replace value <- lift twice - apply to the internal list
[ Just "a" ]
(fmap . fmap . fmap) replace value <- lift thrice - apply to the elements of the internal list
[ Just [ "a", "a" ] ]
(fmap . fmap . fmap . fmap) replace value <- lift one last time - apply to each letter of each string
[ Just [ [ "a", "a", "a", "a" ], [ "a", "a", "a", "a" ] ] ]