Question

Is there some function in haskell that evaluates to (filter p xs, filter (not.p) xs) in one list traversal (here are two) or is there some common name in functional programming for this kind of function?

Answer 1

First look at the type that you need:

Prelude> :t \p xs -> (filter p xs, filter (not . p) xs)
\p xs -> (filter p xs, filter (not . p) xs)
  :: (a -> Bool) -> [a] -> ([a], [a])

Hoogle is your friend:

Prelude> :hoogle (a -> Bool) -> [a] -> ([a], [a])
Prelude break :: (a -> Bool) -> [a] -> ([a], [a])
Prelude span :: (a -> Bool) -> [a] -> ([a], [a])
Data.List break :: (a -> Bool) -> [a] -> ([a], [a])
Data.List partition :: (a -> Bool) -> [a] -> ([a], [a])
Data.List span :: (a -> Bool) -> [a] -> ([a], [a])

Now try out the functions:

Prelude> break odd [1..10]
([],[1,2,3,4,5,6,7,8,9,10])
Prelude> span odd [1..10]
([1],[2,3,4,5,6,7,8,9,10])
Prelude> import Data.List
Prelude Data.List> partition odd [1..10]
([1,3,5,7,9],[2,4,6,8,10])