# (a -> b -> c) -> f a -> f b -> f c

Promote a function to a monad, scanning the monadic arguments from left to right. For example, > liftM2 (+) [0,1] [0,2] = [0,2,1,3] > liftM2 (+) (Just 1) Nothing = Nothing
Lift a binary function to actions.
O(n+m). The intersection with a combining function. > intersectionWith (++) (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (7, "C")]) == singleton 5 "aA"
O(min(n1,n2)). zipWith generalizes zip by zipping with the function given as the first argument, instead of a tupling function. For example, zipWith (+) is applied to two sequences to take the sequence of corresponding sums.
zipWith generalises zip by zipping with the function given as the first argument, instead of a tupling function. For example, zipWith (+) is applied to two lists to produce the list of corresponding sums.
O(n+m). The union with a combining function. > unionWith (++) (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (7, "C")]) == fromList [(3, "b"), (5, "aA"), (7, "C")]
scanl is similar to foldl, but returns a sequence of reduced values from the left: > scanl f z (fromList [x1, x2, ...]) = fromList [z, z `f` x1, (z `f` x1) `f` x2, ...]
scanl is similar to foldl, but returns a list of successive reduced values from the left: > scanl f z [x1, x2, ...] == [z, z `f` x1, (z `f` x1) `f` x2, ...] Note that > last (scanl f z xs) == foldl f z xs.
scanr is the right-to-left dual of scanl. Note that > head (scanr f z xs) == foldr f z xs.
scanr is the right-to-left dual of scanl.
O(n+m). Is this a proper submap? (ie. a submap but not equal). The expression (isProperSubmapOfBy f m1 m2) returns True when m1 and m2 are not equal, all keys in m1 are in m2, and when f returns True when applied to their respective values. For example, the following expressions are all True: > isProperSubmapOfBy (==) (fromList [(1,1)]) (fromList [(1,1),(2,2)]) > isProperSubmapOfBy (<=) (fromList [(1,1)]) (fromList [(1,1),(2,2)]) But the following are all False: > isProperSubmapOfBy (==) (fromList [(1,1),(2,2)]) (fromList [(1,1),(2,2)]) > isProperSubmapOfBy (==) (fromList [(1,1),(2,2)]) (fromList [(1,1)]) > isProperSubmapOfBy (<) (fromList [(1,1)]) (fromList [(1,1),(2,2)])
O(n+m). The expression (isSubmapOfBy f m1 m2) returns True if all keys in m1 are in m2, and when f returns True when applied to their respective values. For example, the following expressions are all True: > isSubmapOfBy (==) (fromList [(1,1)]) (fromList [(1,1),(2,2)]) > isSubmapOfBy (<=) (fromList [(1,1)]) (fromList [(1,1),(2,2)]) > isSubmapOfBy (==) (fromList [(1,1),(2,2)]) (fromList [(1,1),(2,2)]) But the following are all False: > isSubmapOfBy (==) (fromList [(1,2)]) (fromList [(1,1),(2,2)]) > isSubmapOfBy (<) (fromList [(1,1)]) (fromList [(1,1),(2,2)]) > isSubmapOfBy (==) (fromList [(1,1),(2,2)]) (fromList [(1,1)])
flip f takes its (first) two arguments in the reverse order of f.
Fold over the elements of a structure, associating to the left, but strictly.
The deleteFirstsBy function takes a predicate and two lists and returns the first list with the first occurrence of each element of the second list removed.
The intersectBy function is the non-overloaded version of intersect.
The unionBy function is the non-overloaded version of union.
O(n). Fold the values in the map using the given left-associative binary operator, such that foldl f z == foldl f z . elems. For example, > elems = reverse . foldl (flip (:)) [] > let f len a = len + (length a) > foldl f 0 (fromList [(5,"a"), (3,"bbb")]) == 4
O(n). A strict version of foldl. Each application of the operator is evaluated before using the result in the next application. This function is strict in the starting value.
O(n). Fold the elements in the set using the given left-associative binary operator, such that foldl f z == foldl f z . toAscList. For example, > toDescList set = foldl (flip (:)) [] set
O(n). A strict version of foldl. Each application of the operator is evaluated before using the result in the next application. This function is strict in the starting value.
foldl, applied to a binary operator, a starting value (typically the left-identity of the operator), and a list, reduces the list using the binary operator, from left to right: > foldl f z [x1, x2, ..., xn] == (...((z `f` x1) `f` x2) `f`...) `f` xn The list must be finite.
A strict version of foldl.
Fold over the elements of a structure, associating to the right, but strictly.
foldr, applied to a binary operator, a starting value (typically the right-identity of the operator), and a list, reduces the list using the binary operator, from right to left: > foldr f z [x1, x2, ..., xn] == x1 `f` (x2 `f` ... (xn `f` z)...)
O(n). Fold the elements in the set using the given right-associative binary operator. This function is an equivalent of foldr and is present for compatibility only. Please note that fold will be deprecated in the future and removed.
O(n). Fold the elements in the set using the given right-associative binary operator, such that foldr f z == foldr f z . toAscList. For example, > toAscList set = foldr (:) [] set
O(n). A strict version of foldr. Each application of the operator is evaluated before using the result in the next application. This function is strict in the starting value.
Deprecated. As of version 0.5, replaced by foldr. O(n). Fold the values in the map using the given right-associative binary operator. This function is an equivalent of foldr and is present for compatibility only.
O(n). Fold the values in the map using the given right-associative binary operator, such that foldr f z == foldr f z . elems. For example, > elems map = foldr (:) [] map > let f a len = len + (length a) > foldr f 0 (fromList [(5,"a"), (3,"bbb")]) == 4
O(n). A strict version of foldr. Each application of the operator is evaluated before using the result in the next application. This function is strict in the starting value.
O(min(n,W)). Adjust a value at a specific key. When the key is not a member of the map, the original map is returned. > let f key x = (show key) ++ ":new " ++ x > adjustWithKey f 5 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "5:new a")] > adjustWithKey f 7 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "a")] > adjustWithKey f 7 empty == empty
O(min(n,W)). Insert with a combining function. insertWith f key value mp will insert the pair (key, value) into mp if key does not exist in the map. If the key does exist, the function will insert f new_value old_value. > insertWith (++) 5 "xxx" (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "xxxa")] > insertWith (++) 7 "xxx" (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "a"), (7, "xxx")] > insertWith (++) 5 "xxx" empty == singleton 5 "xxx"
Deprecated. As of version 0.5, replaced by insertWith. O(log n). Same as insertWith, but the result of the combining function is evaluated to WHNF before inserted to the map.
The deleteBy function behaves like delete, but takes a user-supplied equality predicate.