Use Data.Set.intersection
:
import qualified Data.Set as S
sharedLetters str1 str2 = S.toList $ S.intersection (S.fromList str1) (S.fromList str2)
EDIT: As @jozefg pointed out, there is a function in Data.List
which does the same for lists:
> import Data.List (intersect)
> intersect "liked" "iced"
"ied"