| Copyright | (c) Ross Paterson 2005 (c) Louis Wasserman 2009 (c) Bertram Felgenhauer, David Feuer, Ross Paterson, and Milan Straka 2014 |
|---|---|
| License | BSD-style |
| Maintainer | libraries@haskell.org |
| Stability | experimental |
| Portability | portable |
| Safe Haskell | Trustworthy |
| Language | Haskell98 |
Data.Sequence
Contents
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
- Ralf Hinze and Ross Paterson, "Finger trees: a simple general-purpose data structure", Journal of Functional Programming 16:2 (2006) pp 197-217. http://staff.city.ac.uk/~ross/papers/FingerTree.html
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.
Warning: The size of a Seq must not exceed maxBound::Int. Violation
of this condition is not detected and if the size limit is exceeded, the
behaviour of the sequence is undefined. This is unlikely to occur in most
applications, but some care may be required when using ><, <*>, *>, or
>>, particularly repeatedly and particularly in combination with
replicate or fromFunction.
- 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
- fromFunction :: Int -> (Int -> a) -> Seq a
- fromArray :: Ix i => Array i 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
- data ViewL a
- viewl :: Seq a -> ViewL a
- data ViewR 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
Documentation
General-purpose finite sequences.
Instances
| Monad Seq Source | |
| Functor Seq Source | |
| Applicative Seq Source | |
| Foldable Seq Source | |
| Traversable Seq Source | |
| Alternative Seq Source | |
| MonadPlus Seq Source | |
| IsList (Seq a) Source | |
| Eq a => Eq (Seq a) Source | |
| Data a => Data (Seq a) Source | |
| Ord a => Ord (Seq a) Source | |
| Read a => Read (Seq a) Source | |
| Show a => Show (Seq a) Source | |
| IsString (Seq Char) Source | |
| Monoid (Seq a) Source | |
| NFData a => NFData (Seq a) Source | |
| type Item (Seq a) = a Source | |
Construction
(<|) :: a -> Seq a -> Seq a infixr 5 Source
O(1). Add an element to the left end of a sequence. Mnemonic: a triangle with the single element at the pointy end.
(|>) :: Seq a -> a -> Seq a infixl 5 Source
O(1). Add an element to the right end of a sequence. Mnemonic: a triangle with the single element at the pointy end.
fromFunction :: Int -> (Int -> a) -> Seq a Source
O(n). Convert a given sequence length and a function representing that sequence into a sequence.
fromArray :: Ix i => Array i a -> Seq a Source
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.
Repetition
replicate :: Int -> a -> Seq a Source
O(log n). replicate n x is a sequence consisting of n copies of x.
replicateA :: Applicative f => Int -> f a -> f (Seq a) Source
replicateA is an Applicative version of replicate, and makes
O(log n) calls to <*> and pure.
replicateA n x = sequenceA (replicate n x)
replicateM :: Monad m => Int -> m a -> m (Seq a) Source
replicateM is a sequence counterpart of replicateM.
replicateM n x = sequence (replicate n x)
Iterative construction
iterateN :: Int -> (a -> a) -> a -> Seq a Source
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))
unfoldr :: (b -> Maybe (a, b)) -> b -> Seq a Source
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.
Deconstruction
Queries
Views
View of the left end of a sequence.
View of the right end of a sequence.
Scans
Sublists
tails :: Seq a -> Seq (Seq a) Source
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.
inits :: Seq a -> Seq (Seq a) Source
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.
Sequential searches
takeWhileL :: (a -> Bool) -> Seq a -> Seq a Source
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.
takeWhileR :: (a -> Bool) -> Seq a -> Seq a Source
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 xsreverse (takeWhileL p (reverse xs))
dropWhileL :: (a -> Bool) -> Seq a -> Seq a Source
O(i) where i is the prefix length. dropWhileL p xstakeWhileL p xs
dropWhileR :: (a -> Bool) -> Seq a -> Seq a Source
O(i) where i is the suffix length. dropWhileR p xstakeWhileR p xs
dropWhileR p xsreverse (dropWhileL p (reverse xs))
spanl :: (a -> Bool) -> Seq a -> (Seq a, Seq a) Source
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.
spanr :: (a -> Bool) -> Seq a -> (Seq a, Seq a) Source
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.
breakl :: (a -> Bool) -> Seq a -> (Seq a, Seq a) Source
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.
partition :: (a -> Bool) -> Seq a -> (Seq a, Seq a) Source
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.
filter :: (a -> Bool) -> Seq a -> Seq a Source
O(n). The filter function takes a predicate p and a sequence
xs and returns a sequence of those elements which satisfy the
predicate.
Sorting
sort :: Ord a => Seq a -> Seq a Source
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.
sortBy :: (a -> a -> Ordering) -> Seq a -> Seq a Source
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.
unstableSort :: Ord a => Seq a -> Seq a Source
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.
unstableSortBy :: (a -> a -> Ordering) -> Seq a -> Seq a Source
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.
Indexing
index :: Seq a -> Int -> a Source
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.
adjust :: (a -> a) -> Int -> Seq a -> Seq a Source
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.
update :: Int -> a -> Seq a -> Seq a Source
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.
take :: Int -> Seq a -> Seq a Source
O(log(min(i,n-i))). The first i elements of a sequence.
If i is negative, take i si elements, the whole sequence
is returned.
drop :: Int -> Seq a -> Seq a Source
O(log(min(i,n-i))). Elements of a sequence after the first i.
If i is negative, drop i si elements, the empty sequence
is returned.
Indexing with predicates
These functions perform sequential searches from the left or right ends of the sequence, returning indices of matching elements.
elemIndexL :: Eq a => a -> Seq a -> Maybe Int Source
elemIndexL finds the leftmost index of the specified element,
if it is present, and otherwise Nothing.
elemIndicesL :: Eq a => a -> Seq a -> [Int] Source
elemIndicesL finds the indices of the specified element, from
left to right (i.e. in ascending order).
elemIndexR :: Eq a => a -> Seq a -> Maybe Int Source
elemIndexR finds the rightmost index of the specified element,
if it is present, and otherwise Nothing.
elemIndicesR :: Eq a => a -> Seq a -> [Int] Source
elemIndicesR finds the indices of the specified element, from
right to left (i.e. in descending order).
findIndexL :: (a -> Bool) -> Seq a -> Maybe Int Source
findIndexL p xsp, if any exist.
findIndicesL :: (a -> Bool) -> Seq a -> [Int] Source
findIndicesL pp,
in ascending order.
findIndexR :: (a -> Bool) -> Seq a -> Maybe Int Source
findIndexR p xsp, if any exist.
findIndicesR :: (a -> Bool) -> Seq a -> [Int] Source
findIndicesR pp,
in descending order.
Folds
foldlWithIndex :: (b -> Int -> a -> b) -> b -> Seq a -> b Source
foldlWithIndex is a version of foldl that also provides access
to the index of each element.
foldrWithIndex :: (Int -> a -> b -> b) -> b -> Seq a -> b Source
foldrWithIndex is a version of foldr that also provides access
to the index of each element.
Transformations
mapWithIndex :: (Int -> a -> b) -> Seq a -> Seq b Source
O(n). 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.
Zips
zip :: Seq a -> Seq b -> Seq (a, b) Source
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.