When working with the list monad, I often find myself in need of one of the two following functions: -- | Produce a list of all ways of selecting an element from a list, each along with the remaining elements in the list. -- e.g. select [1,2,3,4] == [(1,[2,3,4]),(2,[1,3,4]),(3,[1,2,4]),(4,[1,2,3])] -- This is useful for selection without replacement in the list monad or list comprehensions. select :: [a] -> [(a,[a])] select [] = [] select (x:xs) = (x,xs) : [(y,x:ys) | (y,ys) <- select xs] -- | Produce a list of all ways of separating a list into an initial segment, a single element, and a final segment. -- e.g. separate [1,2,3,4] == [([],1,[2,3,4]),([1],2,[3,4]),([1,2],3,[4]),([1,2,3],4,[])] separate :: [a] -> [([a],a,[a])] separate [] = [] separate (x:xs) = ([],x,xs) : [(x:us,v,vs) | (us,v,vs) <- separate xs] It would be really nice if they were in Data.List. The first I find occurring in my code moreso than the second, though just a moment ago, the second of these was quite useful to a beginner on #haskell, and it has come up quite a number of times before for me. Twan van Laarhoven suggested that the following generalisation of select might also be useful: select' :: [t] -> [(t, ([t] -> [t]) -> [t])] select' [] = [] select' (x:xs) = (x,\f -> f xs) : [(y,\f -> x:ys f) | (y,ys) <- select' xs] This satisfies the equation select = map (second ($ id)) . select' and allows for simple replacement after modification of the selected element, for instance: [xs (toUpper x :) | (x,xs) <- select' "abcd"] == ["Abcd","aBcd","abCd","abcD"] but we're unsure if this might be too subtle to be as useful on a regular basis. - Cale Gibbard