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| Data.Sequence | | Portability | portable | | Stability | experimental | | Maintainer | libraries@haskell.org |
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| Description |
General purpose finite sequences.
Apart from being finite and having strict operations, sequences
also differ from lists in supporting a wider variety of operations
efficiently.
An amortized running time is given for each operation, with n referring
to the length of the sequence and i being the integral index used by
some operations. These bounds hold even in a persistent (shared) setting.
The implementation uses 2-3 finger trees annotated with sizes,
as described in section 4.2 of
Note: Many of these operations have the same names as similar
operations on lists in the Prelude. The ambiguity may be resolved
using either qualification or the hiding clause.
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| Synopsis |
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| data Seq a | | | empty :: Seq a | | | singleton :: a -> Seq a | | | (<|) :: a -> Seq a -> Seq a | | | (|>) :: Seq a -> a -> Seq a | | | (><) :: Seq a -> Seq a -> Seq a | | | fromList :: [a] -> Seq a | | | replicate :: Int -> a -> Seq a | | | replicateA :: Applicative f => Int -> f a -> f (Seq a) | | | replicateM :: Monad m => Int -> m a -> m (Seq a) | | | iterateN :: Int -> (a -> a) -> a -> Seq a | | | unfoldr :: (b -> Maybe (a, b)) -> b -> Seq a | | | unfoldl :: (b -> Maybe (b, a)) -> b -> Seq a | | | null :: Seq a -> Bool | | | length :: Seq a -> Int | | | | | viewl :: Seq a -> ViewL a | | | | | viewr :: Seq a -> ViewR a | | | scanl :: (a -> b -> a) -> a -> Seq b -> Seq a | | | scanl1 :: (a -> a -> a) -> Seq a -> Seq a | | | scanr :: (a -> b -> b) -> b -> Seq a -> Seq b | | | scanr1 :: (a -> a -> a) -> Seq a -> Seq a | | | tails :: Seq a -> Seq (Seq a) | | | inits :: Seq a -> Seq (Seq a) | | | takeWhileL :: (a -> Bool) -> Seq a -> Seq a | | | takeWhileR :: (a -> Bool) -> Seq a -> Seq a | | | dropWhileL :: (a -> Bool) -> Seq a -> Seq a | | | dropWhileR :: (a -> Bool) -> Seq a -> Seq a | | | spanl :: (a -> Bool) -> Seq a -> (Seq a, Seq a) | | | spanr :: (a -> Bool) -> Seq a -> (Seq a, Seq a) | | | breakl :: (a -> Bool) -> Seq a -> (Seq a, Seq a) | | | breakr :: (a -> Bool) -> Seq a -> (Seq a, Seq a) | | | partition :: (a -> Bool) -> Seq a -> (Seq a, Seq a) | | | filter :: (a -> Bool) -> Seq a -> Seq a | | | sort :: Ord a => Seq a -> Seq a | | | sortBy :: (a -> a -> Ordering) -> Seq a -> Seq a | | | unstableSort :: Ord a => Seq a -> Seq a | | | unstableSortBy :: (a -> a -> Ordering) -> Seq a -> Seq a | | | index :: Seq a -> Int -> a | | | adjust :: (a -> a) -> Int -> Seq a -> Seq a | | | update :: Int -> a -> Seq a -> Seq a | | | take :: Int -> Seq a -> Seq a | | | drop :: Int -> Seq a -> Seq a | | | splitAt :: Int -> Seq a -> (Seq a, Seq a) | | | elemIndexL :: Eq a => a -> Seq a -> Maybe Int | | | elemIndicesL :: Eq a => a -> Seq a -> [Int] | | | elemIndexR :: Eq a => a -> Seq a -> Maybe Int | | | elemIndicesR :: Eq a => a -> Seq a -> [Int] | | | findIndexL :: (a -> Bool) -> Seq a -> Maybe Int | | | findIndicesL :: (a -> Bool) -> Seq a -> [Int] | | | findIndexR :: (a -> Bool) -> Seq a -> Maybe Int | | | findIndicesR :: (a -> Bool) -> Seq a -> [Int] | | | foldlWithIndex :: (b -> Int -> a -> b) -> b -> Seq a -> b | | | foldrWithIndex :: (Int -> a -> b -> b) -> b -> Seq a -> b | | | mapWithIndex :: (Int -> a -> b) -> Seq a -> Seq b | | | reverse :: Seq a -> Seq a | | | zip :: Seq a -> Seq b -> Seq (a, b) | | | zipWith :: (a -> b -> c) -> Seq a -> Seq b -> Seq c | | | zip3 :: Seq a -> Seq b -> Seq c -> Seq (a, b, c) | | | zipWith3 :: (a -> b -> c -> d) -> Seq a -> Seq b -> Seq c -> Seq d | | | zip4 :: Seq a -> Seq b -> Seq c -> Seq d -> Seq (a, b, c, d) | | | zipWith4 :: (a -> b -> c -> d -> e) -> Seq a -> Seq b -> Seq c -> Seq d -> Seq e |
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| Documentation |
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| General-purpose finite sequences.
|  Instances | |
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| Construction
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| O(1). The empty sequence.
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| O(1). A singleton sequence.
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| O(1). Add an element to the left end of a sequence.
Mnemonic: a triangle with the single element at the pointy end.
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| O(1). Add an element to the right end of a sequence.
Mnemonic: a triangle with the single element at the pointy end.
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| O(log(min(n1,n2))). Concatenate two sequences.
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| 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.
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| Repetition
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| O(log n). replicate n x is a sequence consisting of n copies of x.
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replicateA is an Applicative version of replicate, and makes
O(log n) calls to <*> and pure.
replicateA n x = sequenceA (replicate n x)
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replicateM is a sequence counterpart of Control.Monad.replicateM.
replicateM n x = sequence (replicate n x)
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| Iterative construction
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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))
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| 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.
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| unfoldl f x is equivalent to reverse (unfoldr (swap . f) x).
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| Deconstruction
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| Additional functions for deconstructing sequences are available
via the Foldable instance of Seq.
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| Queries
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| O(1). Is this the empty sequence?
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| O(1). The number of elements in the sequence.
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| Views
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| View of the left end of a sequence.
| | Constructors | | EmptyL | empty sequence
| | a :< (Seq a) | leftmost element and the rest of the sequence
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| O(1). Analyse the left end of a sequence.
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| View of the right end of a sequence.
| | Constructors | | EmptyR | empty sequence
| | (Seq a) :> a | the sequence minus the rightmost element,
and the rightmost element
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| O(1). Analyse the right end of a sequence.
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| Scans
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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, ...]
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scanl1 is a variant of scanl that has no starting value argument:
scanl1 f (fromList [x1, x2, ...]) = fromList [x1, x1 `f` x2, ...]
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| scanr is the right-to-left dual of scanl.
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| scanr1 is a variant of scanr that has no starting value argument.
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| Sublists
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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.
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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.
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| Sequential searches
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| 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.
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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)).
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| O(i) where i is the prefix length. dropWhileL p xs returns
the suffix remaining after takeWhileL p xs.
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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)).
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| 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.
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| 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.
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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).
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| breakr p is equivalent to spanr (not . p).
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| 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.
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| O(n). The filter function takes a predicate p and a sequence
xs and returns a sequence of those elements which satisfy the
predicate.
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| Sorting
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| 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.
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| 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.
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| 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.
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| 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.
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| Indexing
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| 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.
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| 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.
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| 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.
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| 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.
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| 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.
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| O(log(min(i,n-i))). Split a sequence at a given position.
splitAt i s = (take i s, drop i s).
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| Indexing with predicates
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| These functions perform sequential searches from the left
or right ends of the sequence, returning indices of matching
elements.
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| elemIndexL finds the leftmost index of the specified element,
if it is present, and otherwise Nothing.
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| elemIndicesL finds the indices of the specified element, from
left to right (i.e. in ascending order).
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| elemIndexR finds the rightmost index of the specified element,
if it is present, and otherwise Nothing.
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| elemIndicesR finds the indices of the specified element, from
right to left (i.e. in descending order).
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| findIndexL p xs finds the index of the leftmost element that
satisfies p, if any exist.
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| findIndicesL p finds all indices of elements that satisfy p,
in ascending order.
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| findIndexR p xs finds the index of the rightmost element that
satisfies p, if any exist.
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| findIndicesR p finds all indices of elements that satisfy p,
in descending order.
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| Folds
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| General folds are available via the Foldable instance of Seq.
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| foldlWithIndex :: (b -> Int -> a -> b) -> b -> Seq a -> b | Source |
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| foldlWithIndex is a version of foldl that also provides access
to the index of each element.
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| foldrWithIndex :: (Int -> a -> b -> b) -> b -> Seq a -> b | Source |
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| foldrWithIndex is a version of foldr that also provides access
to the index of each element.
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| Transformations
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| 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.
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| O(n). The reverse of a sequence.
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| Zips
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| 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.
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| 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.
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| O(min(n1,n2,n3)). zip3 takes three sequences and returns a
sequence of triples, analogous to zip.
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| 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.
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| O(min(n1,n2,n3,n4)). zip4 takes four sequences and returns a
sequence of quadruples, analogous to zip.
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| 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.
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| Produced by Haddock version 2.6.0 |
