General-purpose finite sequences.

O(1). The empty sequence.

O(1). A singleton sequence.

O(1). Add an element to the left end of a sequence. Mnemonic: a triangle with the single element at the pointy end.

O(1). Add an element to the right end of a sequence. Mnemonic: a triangle with the single element at the pointy end.

O(log(min(n1,n2))). Concatenate two sequences.

O(n). Create a sequence from a finite list of elements. There is a function toList in the opposite direction for all instances of the Foldable class, including Seq.

O(log n). replicate n x is a sequence consisting of n copies of x.

replicateA is an Applicative version of replicate, and makes O(log n) calls to <*> and pure.

 replicateA n x = sequenceA (replicate n x)

replicateM is a sequence counterpart of Control.Monad.replicateM.

 replicateM n x = sequence (replicate n x)

O(n). Constructs a sequence by repeated application of a function to a seed value.

 iterateN n f x = fromList (Prelude.take n (Prelude.iterate f x))

Builds a sequence from a seed value. Takes time linear in the number of generated elements. WARNING: If the number of generated elements is infinite, this method will not terminate.

unfoldl f x is equivalent to reverse (unfoldr (fmap swap . f) x).

O(1). Is this the empty sequence?

O(1). The number of elements in the sequence.

View of the left end of a sequence.

O(1). Analyse the left end of a sequence.

View of the right end of a sequence.

O(1). Analyse the right end of a sequence.

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, ...]

scanl1 is a variant of scanl that has no starting value argument:

 scanl1 f (fromList [x1, x2, ...]) = fromList [x1, x1 `f` x2, ...]

scanr is the right-to-left dual of scanl.

scanr1 is a variant of scanr that has no starting value argument.

O(n). Returns a sequence of all suffixes of this sequence, longest first. For example,

 tails (fromList "abc") = fromList [fromList "abc", fromList "bc", fromList "c", fromList ""]

Evaluating the ith suffix takes O(log(min(i, n-i))), but evaluating every suffix in the sequence takes O(n) due to sharing.

O(n). Returns a sequence of all prefixes of this sequence, shortest first. For example,

 inits (fromList "abc") = fromList [fromList "", fromList "a", fromList "ab", fromList "abc"]

Evaluating the ith prefix takes O(log(min(i, n-i))), but evaluating every prefix in the sequence takes O(n) due to sharing.

O(i) where i is the prefix length. takeWhileL, applied to a predicate p and a sequence xs, returns the longest prefix (possibly empty) of xs of elements that satisfy p.

O(i) where i is the suffix length. takeWhileR, applied to a predicate p and a sequence xs, returns the longest suffix (possibly empty) of xs of elements that satisfy p.

takeWhileR p xs is equivalent to reverse (takeWhileL p (reverse xs)).

O(i) where i is the prefix length. dropWhileL p xs returns the suffix remaining after takeWhileL p xs.

O(i) where i is the suffix length. dropWhileR p xs returns the prefix remaining after takeWhileR p xs.

dropWhileR p xs is equivalent to reverse (dropWhileL p (reverse xs)).

O(i) where i is the prefix length. spanl, applied to a predicate p and a sequence xs, returns a pair whose first element is the longest prefix (possibly empty) of xs of elements that satisfy p and the second element is the remainder of the sequence.

O(i) where i is the suffix length. spanr, applied to a predicate p and a sequence xs, returns a pair whose first element is the longest suffix (possibly empty) of xs of elements that satisfy p and the second element is the remainder of the sequence.

O(i) where i is the breakpoint index. breakl, applied to a predicate p and a sequence xs, returns a pair whose first element is the longest prefix (possibly empty) of xs of elements that do not satisfy p and the second element is the remainder of the sequence.

breakl p is equivalent to spanl (not . p).

breakr p is equivalent to spanr (not . p).

O(n). The partition function takes a predicate p and a sequence xs and returns sequences of those elements which do and do not satisfy the predicate.

O(n). The filter function takes a predicate p and a sequence xs and returns a sequence of those elements which satisfy the predicate.

O(n log n). sort sorts the specified Seq by the natural ordering of its elements. The sort is stable. If stability is not required, unstableSort can be considerably faster, and in particular uses less memory.

O(n log n). sortBy sorts the specified Seq according to the specified comparator. The sort is stable. If stability is not required, unstableSortBy can be considerably faster, and in particular uses less memory.

O(n log n). unstableSort sorts the specified Seq by the natural ordering of its elements, but the sort is not stable. This algorithm is frequently faster and uses less memory than sort, and performs extremely well -- frequently twice as fast as sort -- when the sequence is already nearly sorted.

O(n log n). A generalization of unstableSort, unstableSortBy takes an arbitrary comparator and sorts the specified sequence. The sort is not stable. This algorithm is frequently faster and uses less memory than sortBy, and performs extremely well -- frequently twice as fast as sortBy -- when the sequence is already nearly sorted.

O(log(min(i,n-i))). The element at the specified position, counting from 0. The argument should thus be a non-negative integer less than the size of the sequence. If the position is out of range, index fails with an error.

O(log(min(i,n-i))). Update the element at the specified position. If the position is out of range, the original sequence is returned.

O(log(min(i,n-i))). Replace the element at the specified position. If the position is out of range, the original sequence is returned.

O(log(min(i,n-i))). The first i elements of a sequence. If i is negative, take i s yields the empty sequence. If the sequence contains fewer than i elements, the whole sequence is returned.

O(log(min(i,n-i))). Elements of a sequence after the first i. If i is negative, drop i s yields the whole sequence. If the sequence contains fewer than i elements, the empty sequence is returned.

O(log(min(i,n-i))). Split a sequence at a given position. splitAt i s = (take i s, drop i s).

elemIndexL finds the leftmost index of the specified element, if it is present, and otherwise Nothing.

elemIndicesL finds the indices of the specified element, from left to right (i.e. in ascending order).

elemIndexR finds the rightmost index of the specified element, if it is present, and otherwise Nothing.

elemIndicesR finds the indices of the specified element, from right to left (i.e. in descending order).

findIndexL p xs finds the index of the leftmost element that satisfies p, if any exist.

findIndicesL p finds all indices of elements that satisfy p, in ascending order.

findIndexR p xs finds the index of the rightmost element that satisfies p, if any exist.

findIndicesR p finds all indices of elements that satisfy p, in descending order.

foldlWithIndex is a version of foldl that also provides access to the index of each element.

foldrWithIndex is a version of foldr that also provides access to the index of each element.

A generalization of fmap, mapWithIndex takes a mapping function that also depends on the element's index, and applies it to every element in the sequence.

O(n). The reverse of a sequence.

O(min(n1,n2)). zip takes two sequences and returns a sequence of corresponding pairs. If one input is short, excess elements are discarded from the right end of the longer sequence.

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.

O(min(n1,n2,n3)). zip3 takes three sequences and returns a sequence of triples, analogous to zip.

O(min(n1,n2,n3)). zipWith3 takes a function which combines three elements, as well as three sequences and returns a sequence of their point-wise combinations, analogous to zipWith.

O(min(n1,n2,n3,n4)). zip4 takes four sequences and returns a sequence of quadruples, analogous to zip.

O(min(n1,n2,n3,n4)). zipWith4 takes a function which combines four elements, as well as four sequences and returns a sequence of their point-wise combinations, analogous to zipWith.