I'm in Bird's
Thinking Functionally with Haskell and the topic is natural transformations. He says
filter p . map f = map f . filter (p . f)
and he has a proof, but one step of the proof he goes from
filter p . map f = concat . map (map f) . map (test (p . f))
to
filter p . map f = map f . concat . map (test (p . f))
which means
concat . map (map f) => map f . concat
which means
map (map f) = map f
... or I'm getting this step wrong somehow. To begin with, I'm having a hard time comprehending map(map f), Any ideas on how this is possible?
LB