:: Eq a => [a] -> [[a]] package:universum

The inits function returns all initial segments of the argument, shortest first. For example,

>>> inits "abc"
["","a","ab","abc"]

Note that inits has the following strictness property: inits (xs ++ _|_) = inits xs ++ _|_ In particular, inits _|_ = [] : _|_ inits is semantically equivalent to map reverse . scanl (flip (:)) [], but under the hood uses a queue to amortize costs of reverse.

The tails function returns all final segments of the argument, longest first. For example,

>>> tails "abc"
["abc","bc","c",""]

Note that tails has the following strictness property: tails _|_ = _|_ : _|_

The subsequences function returns the list of all subsequences of the argument.

>>> subsequences "abc"
["","a","b","ab","c","ac","bc","abc"]

This function is productive on infinite inputs:

>>> take 8 $ subsequences ['a'..]
["","a","b","ab","c","ac","bc","abc"]

The permutations function returns the list of all permutations of the argument.

>>> permutations "abc"
["abc","bac","cba","bca","cab","acb"]

The permutations function is maximally lazy: for each n, the value of permutations xs starts with those permutations that permute take n xs and keep drop n xs. This function is productive on infinite inputs:

>>> take 6 $ map (take 3) $ permutations ['a'..]
["abc","bac","cba","bca","cab","acb"]

Note that the order of permutations is not lexicographic. It satisfies the following property:

map (take n) (take (product [1..n]) (permutations ([1..n] ++ undefined))) == permutations [1..n]