map -package:Cabal -package:base package:pipes

Apply a function to all values flowing downstream
map id = cat

map (g . f) = map f >-> map g
Apply a function to all values flowing downstream, and forward each element of the result.
Apply a monadic function to all values flowing downstream
mapM return = cat

mapM (f >=> g) = mapM f >-> mapM g
Consume all values using a monadic function
(mapMaybe f) yields Just results of f. Basic laws:
mapMaybe (f >=> g) = mapMaybe f >-> mapMaybe g

mapMaybe (pure @Maybe . f) = mapMaybe (Just . f) = map f

mapMaybe (const Nothing) = drain
As a result of the second law,
mapMaybe return = mapMaybe Just = cat