containers-0.5.7.0: Assorted concrete container types

Copyright (c) Ross Paterson 2005 (c) Louis Wasserman 2009 (c) Bertram Felgenhauer, David Feuer, Ross Paterson, and Milan Straka 2014 BSD-style libraries@haskell.org experimental portable Trustworthy Haskell98

Data.Sequence

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.

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`.

Synopsis

# Documentation

data Seq a Source

General-purpose finite sequences.

Instances

 Source Source Source Source Source Source 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 Source Monoid (Seq a) Source NFData a => NFData (Seq a) Source type Item (Seq a) = a Source

# Construction

O(1). The empty sequence.

singleton :: a -> Seq a Source

O(1). A singleton sequence.

(<|) :: 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.

(><) :: Seq a -> Seq a -> Seq a infixr 5 Source

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

fromList :: [a] -> Seq a Source

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`.

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.

unfoldl :: (b -> Maybe (b, a)) -> b -> Seq a Source

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

# Deconstruction

Additional functions for deconstructing sequences are available via the `Foldable` instance of `Seq`.

## Queries

null :: Seq a -> Bool Source

O(1). Is this the empty sequence?

length :: Seq a -> Int Source

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

## Views

data ViewL a Source

View of the left end of a sequence.

Constructors

 EmptyL empty sequence a :< (Seq a) infixr 5 leftmost element and the rest of the sequence

Instances

 Source Source Source Eq a => Eq (ViewL a) Source Data a => Data (ViewL a) Source Ord a => Ord (ViewL a) Source Read a => Read (ViewL a) Source Show a => Show (ViewL a) Source

viewl :: Seq a -> ViewL a Source

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

data ViewR a Source

View of the right end of a sequence.

Constructors

 EmptyR empty sequence (Seq a) :> a infixl 5 the sequence minus the rightmost element, and the rightmost element

Instances

 Source Source Source Eq a => Eq (ViewR a) Source Data a => Data (ViewR a) Source Ord a => Ord (ViewR a) Source Read a => Read (ViewR a) Source Show a => Show (ViewR a) Source

viewr :: Seq a -> ViewR a Source

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

# Scans

scanl :: (a -> b -> a) -> a -> Seq b -> Seq a Source

`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 Source

`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 Source

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

scanr1 :: (a -> a -> a) -> Seq a -> Seq a Source

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

# 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 xs` is equivalent to `reverse (takeWhileL p (reverse xs))`.

dropWhileL :: (a -> Bool) -> Seq a -> Seq a Source

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 Source

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) 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.

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

breakr :: (a -> Bool) -> Seq a -> (Seq a, Seq a) Source

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

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 s` yields the empty sequence. If the sequence contains fewer than `i` 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 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) Source

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

findIndicesL :: (a -> Bool) -> Seq a -> [Int] Source

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

findIndexR :: (a -> Bool) -> Seq a -> Maybe Int Source

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

findIndicesR :: (a -> Bool) -> Seq a -> [Int] Source

`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 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.

reverse :: Seq a -> Seq a Source

O(n). The reverse of a 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.

zipWith :: (a -> b -> c) -> Seq a -> Seq b -> Seq c Source

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) Source

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 Source

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) Source

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 Source

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`.