Data.Sequence

General-purpose finite sequences.

A bidirectional pattern synonym matching an empty sequence.

A bidirectional pattern synonym viewing the front of a non-empty sequence.

A bidirectional pattern synonym viewing the rear of a non-empty sequence.

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(n_1,n_2))) . 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(n) . Convert a given sequence length and a function representing that sequence into a sequence.

O(n) . Create a sequence consisting of the elements of an Array. Note that the resulting sequence elements may be evaluated lazily (as on GHC), so you must force the entire structure to be sure that the original array can be garbage-collected.

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

O \Bigl(\bigl(\frac{n}{c}\bigr) \log c\Bigr). chunksOf c xs splits xs into chunks of size c>0. If c does not divide the length of xs evenly, then the last element of the result will be short.

Side note: the given performance bound is missing some messy terms that only really affect edge cases. Performance degrades smoothly from O(1) (for c = n ) to O(n) (for c = 1 ). The true bound is more like O \Bigl( \bigl(\frac{n}{c} - 1\bigr) (\log (c + 1)) + 1 \Bigr)

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 slightly faster.

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 slightly faster.

O(n \log n) . sortOn sorts the specified Seq by comparing the results of a key function applied to each element. sortOn f is equivalent to sortBy (compare `Data.Function.on` f), but has the performance advantage of only evaluating f once for each element in the input list. This is called the decorate-sort-undecorate paradigm, or Schwartzian transform.

An example of using sortOn might be to sort a Seq of strings according to their length:

sortOn length (fromList ["alligator", "monkey", "zebra"]) == fromList ["zebra", "monkey", "alligator"]

If, instead, sortBy had been used, length would be evaluated on every comparison, giving O(n \log n) evaluations, rather than O(n) .

If f is very cheap (for example a record selector, or fst), sortBy (compare `Data.Function.on` f) will be faster than sortOn f.

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.

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.

O(n \log n) . unstableSortOn sorts the specified Seq by comparing the results of a key function applied to each element. unstableSortOn f is equivalent to unstableSortBy (compare `Data.Function.on` f), but has the performance advantage of only evaluating f once for each element in the input list. This is called the decorate-sort-undecorate paradigm, or Schwartzian transform.

An example of using unstableSortOn might be to sort a Seq of strings according to their length:

unstableSortOn length (fromList ["alligator", "monkey", "zebra"]) == fromList ["zebra", "monkey", "alligator"]

If, instead, unstableSortBy had been used, length would be evaluated on every comparison, giving O(n \log n) evaluations, rather than O(n) .

If f is very cheap (for example a record selector, or fst), unstableSortBy (compare `Data.Function.on` f) will be faster than unstableSortOn f.

O(\log(\min(i,n-i))) . The element at the specified position, counting from 0. If the specified position is negative or at least the length of the sequence, lookup returns Nothing.

prop> 0 <= i < length xs ==> lookup i xs == Just (toList xs !! i)

prop> i < 0 || i >= length xs ==> lookup i xs = Nothing

Unlike index, this can be used to retrieve an element without forcing it. For example, to insert the fifth element of a sequence xs into a Data.Map.Lazy.Map m at key k, you could use

case lookup 5 xs of
  Nothing -> m
  Just x -> insert k x m

O(\log(\min(i,n-i))) . A flipped, infix version of lookup.

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.

prop> xs `index` i = toList xs !! i

Caution: index necessarily delays retrieving the requested element until the result is forced. It can therefore lead to a space leak if the result is stored, unforced, in another structure. To retrieve an element immediately without forcing it, use lookup or (!?).

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. adjust can lead to poor performance and even memory leaks, because it does not force the new value before installing it in the sequence. adjust' should usually be preferred.

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. The new value is forced before it is installed in the sequence.

adjust' f i xs =
 case xs !? i of
   Nothing -> xs
   Just x -> let !x' = f x
             in update i x' xs

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))) . insertAt i x xs inserts x into xs at the index i, shifting the rest of the sequence over.

insertAt 2 x (fromList [a,b,c,d]) = fromList [a,b,x,c,d]
insertAt 4 x (fromList [a,b,c,d]) = insertAt 10 x (fromList [a,b,c,d])
                                  = fromList [a,b,c,d,x]

prop> insertAt i x xs = take i xs >< singleton x >< drop i xs

O(\log(\min(i,n-i))) . Delete the element of a sequence at a given index. Return the original sequence if the index is out of range.

deleteAt 2 [a,b,c,d] = [a,b,d]
deleteAt 4 [a,b,c,d] = deleteAt (-1) [a,b,c,d] = [a,b,c,d]

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

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.

traverseWithIndex is a version of traverse that also offers access to the index of each element.

O(n) . The reverse of a sequence.

O(n) . Intersperse an element between the elements of a sequence.

intersperse a empty = empty
intersperse a (singleton x) = singleton x
intersperse a (fromList [x,y]) = fromList [x,a,y]
intersperse a (fromList [x,y,z]) = fromList [x,a,y,a,z]