| containers-0.3.0.0: Assorted concrete container types | Contents | Index

Data.Sequence

Portability | portable
Stability | experimental
Maintainer | libraries@haskell.org

Contents

Construction
  Repetition
  Iterative construction
Deconstruction
  Queries
  Views
Scans
Sublists
  Sequential searches
Sorting
Indexing
  Indexing with predicates
Folds
Transformations
  Zips

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://www.soi.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.

Synopsis

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

data ViewL a

= EmptyL
| a :< (Seq a)

viewl :: Seq a -> ViewL a

data ViewR a

= EmptyR
| (Seq a) :> 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
data Seq a

General-purpose finite sequences.
Instances

Monad Seq
Functor Seq
Typeable1 Seq
MonadPlus Seq
Foldable Seq
Traversable Seq
Eq a => Eq (Seq a)
Data a => Data (Seq a)
Ord a => Ord (Seq a)
Read a => Read (Seq a)
Show a => Show (Seq a)
Monoid (Seq a)

Construction
empty :: Seq a
O(1). The empty sequence.
singleton :: a -> Seq a
O(1). A singleton sequence.
(<|) :: a -> Seq a -> Seq a
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
O(1). Add an element to the right end of a sequence. Mnemonic: a triangle with the single element at the pointy end.
(><) :: Seq a -> Seq a -> Seq a
O(log(min(n1,n2))). Concatenate two sequences.
fromList :: [a] -> Seq a
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`.
Repetition
replicate :: Int -> a -> Seq a
O(log n). `replicate n x` is a sequence consisting of `n` copies of `x`.
replicateA :: Applicative f => Int -> f a -> f (Seq a)

`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)

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

     replicateM n x = sequence (replicate n x)

Iterative construction
iterateN :: Int -> (a -> a) -> a -> Seq a

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
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 :: (b -> Maybe (b, a)) -> b -> Seq a
``unfoldl` f x` is equivalent to ``reverse` (`unfoldr` (swap . f) x)`.
Deconstruction
Additional functions for deconstructing sequences are available via the `Foldable` instance of `Seq`.
Queries
null :: Seq a -> Bool
O(1). Is this the empty sequence?
length :: Seq a -> Int
O(1). The number of elements in the sequence.
Views
data ViewL a

View of the left end of a sequence.
Constructors

EmptyL | empty sequence
a :< (Seq a) | leftmost element and the rest of the sequence

Instances

Functor ViewL
Typeable1 ViewL
Foldable ViewL
Traversable ViewL
Eq a => Eq (ViewL a)
Data a => Data (ViewL a)
Ord a => Ord (ViewL a)
Read a => Read (ViewL a)
Show a => Show (ViewL a)

viewl :: Seq a -> ViewL a
O(1). Analyse the left end of a sequence.
data ViewR a

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

Instances

Functor ViewR
Typeable1 ViewR
Foldable ViewR
Traversable ViewR
Eq a => Eq (ViewR a)
Data a => Data (ViewR a)
Ord a => Ord (ViewR a)
Read a => Read (ViewR a)
Show a => Show (ViewR a)

viewr :: Seq a -> ViewR a
O(1). Analyse the right end of a sequence.
Scans
scanl :: (a -> b -> a) -> a -> Seq b -> Seq a

`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 :: (a -> a -> a) -> Seq a -> Seq a

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

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

scanr :: (a -> b -> b) -> b -> Seq a -> Seq b
`scanr` is the right-to-left dual of `scanl`.
scanr1 :: (a -> a -> a) -> Seq a -> Seq a
`scanr1` is a variant of `scanr` that has no starting value argument.
Sublists
tails :: Seq a -> Seq (Seq a)

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)

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
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
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))`.
dropWhileL :: (a -> Bool) -> Seq a -> Seq a
O(i) where i is the prefix length. ``dropWhileL` p xs` returns the suffix remaining after ``takeWhileL` p xs`.
dropWhileR :: (a -> Bool) -> Seq a -> Seq a
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))`.
spanl :: (a -> Bool) -> Seq a -> (Seq a, Seq a)
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)
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)
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 :: (a -> Bool) -> Seq a -> (Seq a, Seq a)
``breakr` p` is equivalent to ``spanr` (not . p)`.
partition :: (a -> Bool) -> Seq a -> (Seq a, Seq a)
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
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
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
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
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
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
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
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
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
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.
drop :: Int -> Seq a -> Seq a
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.
splitAt :: Int -> Seq a -> (Seq a, Seq a)
O(log(min(i,n-i))). Split a sequence at a given position. ``splitAt` i s = (`take` i s, `drop` i s)`.
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
`elemIndexL` finds the leftmost index of the specified element, if it is present, and otherwise `Nothing`.
elemIndicesL :: Eq a => a -> Seq a -> [Int]
`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
`elemIndexR` finds the rightmost index of the specified element, if it is present, and otherwise `Nothing`.
elemIndicesR :: Eq a => a -> Seq a -> [Int]
`elemIndicesR` finds the indices of the specified element, from right to left (i.e. in descending order).
findIndexL :: (a -> Bool) -> Seq a -> Maybe Int
``findIndexL` p xs` finds the index of the leftmost element that satisfies `p`, if any exist.
findIndicesL :: (a -> Bool) -> Seq a -> [Int]
``findIndicesL` p` finds all indices of elements that satisfy `p`, in ascending order.
findIndexR :: (a -> Bool) -> Seq a -> Maybe Int
``findIndexR` p xs` finds the index of the rightmost element that satisfies `p`, if any exist.
findIndicesR :: (a -> Bool) -> Seq a -> [Int]
``findIndicesR` p` finds all indices of elements that satisfy `p`, in descending order.
Folds
General folds are available via the `Foldable` instance of `Seq`.
foldlWithIndex :: (b -> Int -> a -> b) -> b -> Seq a -> b
`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
`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
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.
reverse :: Seq a -> Seq a
O(n). The reverse of a sequence.
Zips
zip :: Seq a -> Seq b -> Seq (a, b)
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.
zipWith :: (a -> b -> c) -> Seq a -> Seq b -> Seq c
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.
zip3 :: Seq a -> Seq b -> Seq c -> Seq (a, b, c)
O(min(n1,n2,n3)). `zip3` takes three sequences and returns a sequence of triples, analogous to `zip`.
zipWith3 :: (a -> b -> c -> d) -> Seq a -> Seq b -> Seq c -> Seq d
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`.
zip4 :: Seq a -> Seq b -> Seq c -> Seq d -> Seq (a, b, c, d)
O(min(n1,n2,n3,n4)). `zip4` takes four sequences and returns a sequence of quadruples, analogous to `zip`.
zipWith4 :: (a -> b -> c -> d -> e) -> Seq a -> Seq b -> Seq c -> Seq d -> Seq e
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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