zipLazy is a kind of zip that is lazy in the second list (observe the ~)

stretchZipWith p z f xs ys stretches ys by inserting z in the places where p returns True

zipWithLazy is like zipWith but is lazy in the second list. The length of the output is always the same as the length of the first list.

zipWith3Lazy is like zipWith3 but is lazy in the second and third lists. The length of the output is always the same as the length of the first list.

filterByList takes a list of Bools and a list of some elements and filters out these elements for which the corresponding value in the list of Bools is False. This function does not check whether the lists have equal length.

filterByLists takes a list of Bools and two lists as input, and outputs a new list consisting of elements from the last two input lists. For each Bool in the list, if it is True, then it takes an element from the former list. If it is False, it takes an element from the latter list. The elements taken correspond to the index of the Bool in its list. For example:

filterByLists [True, False, True, False] "abcd" "wxyz" = "axcz"

This function does not check whether the lists have equal length.

partitionByList takes a list of Bools and a list of some elements and partitions the list according to the list of Bools. Elements corresponding to True go to the left; elements corresponding to False go to the right. For example, partitionByList [True, False, True] [1,2,3] == ([1,3], [2]) This function does not check whether the lists have equal length.

Like filter, only it reverses the sense of the test

Uses a function to determine which of two output lists an input element should join

Teases a list of Eithers apart into two lists

spanEnd p l == reverse (span p (reverse l)). The first list returns actually comes after the second list (when you look at the input list).

A strict version of foldl1

(lengthExceeds xs n) = (length xs > n)

atLength atLen atEnd ls n unravels list ls to position n. Precisely:

 atLength atLenPred atEndPred ls n
  | n < 0         = atLenPred ls
  | length ls < n = atEndPred (n - length ls)
  | otherwise     = atLenPred (drop n ls)

True if length xs <= length ys

Split a list into chunks of n elements

Compose a function with itself n times. (nth rather than twice)

The sortWith function sorts a list of elements using the user supplied function to project something out of each element

Search for possible matches to the users input in the given list, returning a small number of ranked results

Constructs a non-representation for a non-representable type

A sample hash function for Strings. We keep multiplying by the golden ratio and adding. The implementation is:

hashString = foldl' f golden
  where f m c = fromIntegral (ord c) * magic + hashInt32 m
        magic = 0xdeadbeef

Where hashInt32 works just as hashInt shown above.

Knuth argues that repeated multiplication by the golden ratio will minimize gaps in the hash space, and thus it's a good choice for combining together multiple keys to form one.

Here we know that individual characters c are often small, and this produces frequent collisions if we use ord c alone. A particular problem are the shorter low ASCII and ISO-8859-1 character strings. We pre-multiply by a magic twiddle factor to obtain a good distribution. In fact, given the following test:

testp :: Int32 -> Int
testp k = (n - ) . length . group . sort . map hs . take n $ ls
  where ls = [] : [c : l | l <- ls, c <- ['\0'..'\xff']]
        hs = foldl' f golden
        f m c = fromIntegral (ord c) * k + hashInt32 m
        n = 100000

We discover that testp magic = 0.