insertLookupWithKey package:containers

The expression (insertLookupWithKey f k x map) is a pair where the first element is equal to (lookup k map) and the second element equal to (insertWithKey f k x map).
let f key new_value old_value = (show key) ++ ":" ++ new_value ++ "|" ++ old_value
insertLookupWithKey f 5 "xxx" (fromList [(5,"a"), (3,"b")]) == (Just "a", fromList [(3, "b"), (5, "5:xxx|a")])
insertLookupWithKey f 7 "xxx" (fromList [(5,"a"), (3,"b")]) == (Nothing,  fromList [(3, "b"), (5, "a"), (7, "xxx")])
insertLookupWithKey f 5 "xxx" empty                         == (Nothing,  singleton 5 "xxx")
This is how to define insertLookup using insertLookupWithKey:
let insertLookup kx x t = insertLookupWithKey (\_ a _ -> a) kx x t
insertLookup 5 "x" (fromList [(5,"a"), (3,"b")]) == (Just "a", fromList [(3, "b"), (5, "x")])
insertLookup 7 "x" (fromList [(5,"a"), (3,"b")]) == (Nothing,  fromList [(3, "b"), (5, "a"), (7, "x")])
Also see the performance note on fromListWith.
Combines insert operation with old value retrieval. The expression (insertLookupWithKey f k x map) is a pair where the first element is equal to (lookup k map) and the second element equal to (insertWithKey f k x map).
let f key new_value old_value = (show key) ++ ":" ++ new_value ++ "|" ++ old_value
insertLookupWithKey f 5 "xxx" (fromList [(5,"a"), (3,"b")]) == (Just "a", fromList [(3, "b"), (5, "5:xxx|a")])
insertLookupWithKey f 7 "xxx" (fromList [(5,"a"), (3,"b")]) == (Nothing,  fromList [(3, "b"), (5, "a"), (7, "xxx")])
insertLookupWithKey f 5 "xxx" empty                         == (Nothing,  singleton 5 "xxx")
This is how to define insertLookup using insertLookupWithKey:
let insertLookup kx x t = insertLookupWithKey (\_ a _ -> a) kx x t
insertLookup 5 "x" (fromList [(5,"a"), (3,"b")]) == (Just "a", fromList [(3, "b"), (5, "x")])
insertLookup 7 "x" (fromList [(5,"a"), (3,"b")]) == (Nothing,  fromList [(3, "b"), (5, "a"), (7, "x")])
Also see the performance note on fromListWith.