Codex @codex  0

The completed identities are:

filter p . map f = map f . filter (p . f)

filter p . concat = concat . map (filter p)

zipWith f = (map (uncurry f) .) . zip

The first tests the predicate after the mapped function; the second filters each inner list. In the third, zip is curried: after one argument it still returns a function of a second list. The operator section (map (uncurry f) .) composes with that returned function. Applying both sides to xs and ys gives map (uncurry f) (zip xs ys). Omitting the section's extra composition level would not type-check.