Data.Sequence

containers-0.6.4.1: Assorted concrete container types

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
Portability | portable
Safe Haskell | Safe-Inferred
Language | Haskell2010

Data.Sequence

Contents

- Finite sequences
- Construction
  - Repetition
  - Iterative construction
- Deconstruction
  - Queries
  - Views
- Scans
- Sublists
  - Sequential searches
- Sorting
- Indexing
  - Indexing with predicates
- Folds
- Transformations
  - Zips and unzip

Description

# Finite sequences

The ``Seq` a` type represents a finite sequence of values of type `a`.

Sequences generally behave very much like lists.

- The class instances for sequences are all based very closely on those for lists.
- Many functions in this module have the same names as functions in the Prelude or in Data.List. In almost all cases, these functions behave analogously. For example, `filter` filters a sequence in exactly the same way that `Prelude.`filter`` filters a list. The only major exception is the `lookup` function, which is based on the function by that name in Data.IntMap rather than the one in Prelude.

There are two major differences between sequences and lists:

- Sequences support a wider variety of efficient operations than do lists. Notably, they offer

  - Constant-time access to both the front and the rear with `<|`, `|>`, `viewl`, `viewr`. For recent GHC versions, this can be done more conveniently using the bidirectional patterns `Empty`, `:<|`, and `:|>`. See the detailed explanation in the "Pattern synonyms" section.
  - Logarithmic-time concatenation with `><`
  - Logarithmic-time splitting with `splitAt`, `take` and `drop`
  - Logarithmic-time access to any element with `lookup`, `!?`, `index`, `insertAt`, `deleteAt`, `adjust'`, and `update`

Note that sequences are typically slower than lists when using only operations for which they have the same big-(O) complexity: sequences make rather mediocre stacks!

- Whereas lists can be either finite or infinite, sequences are always finite. As a result, a sequence is strict in its length. Ignoring efficiency, you can imagine that `Seq` is defined

       data Seq a = Empty | a :<| !(Seq a)

  This means that many operations on sequences are stricter than those on lists. For example,

       (1 : undefined) !! 0 = 1

  but

       (1 :<| undefined) `index` 0 = undefined

Sequences may also be compared to immutable arrays or vectors. Like these structures, sequences support fast indexing, although not as fast. But editing an immutable array or vector, or combining it with another, generally requires copying the entire structure; sequences generally avoid that, copying only the portion that has changed.

## Detailed performance information

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.

Despite sequences being structurally strict from a semantic standpoint, they are in fact implemented using laziness internally. As a result, many operations can be performed incrementally, producing their results as they are demanded. This greatly improves performance in some cases. These functions include

- The `Functor` methods `fmap` and `<$`, along with `mapWithIndex`
- The `Applicative` methods `<*>`, `*>`, and `<*`
- The zips: `zipWith`, `zip`, etc.
- `inits`, `tails`
- `fromFunction`, `replicate`, `intersperse`, and `cycleTaking`
- `reverse`
- `chunksOf`

Note that the `Monad` method, `>>=`, is not particularly lazy. It will take time proportional to the sum of the logarithms of the individual result sequences to produce anything whatsoever.

Several functions take special advantage of sharing to produce results using much less time and memory than one might expect. These are documented individually for functions, but also include certain class methods:

`<$` and `*>` each take time and space proportional to the logarithm of the size of their result.

`<*` takes time and space proportional to the product of the length of its first argument and the logarithm of the length of its second argument.

## 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`.

## Implementation

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.

Synopsis

- data Seq a where
  - pattern Empty :: Seq a
  - pattern (:<|) :: a -> Seq a -> Seq a
  - pattern (:|>) :: Seq a -> a -> 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 :: Applicative m => Int -> m a -> m (Seq a)
- cycleTaking :: Int -> Seq a -> 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)
- chunksOf :: Int -> 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
- sortOn :: Ord b => (a -> b) -> Seq a -> Seq a
- unstableSort :: Ord a => Seq a -> Seq a
- unstableSortBy :: (a -> a -> Ordering) -> Seq a -> Seq a
- unstableSortOn :: Ord b => (a -> b) -> Seq a -> Seq a
- lookup :: Int -> Seq a -> Maybe a
- (!?) :: Seq a -> Int -> Maybe a
- index :: Seq a -> Int -> a
- adjust :: (a -> a) -> Int -> Seq a -> Seq a
- adjust' :: forall a. (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
- insertAt :: Int -> a -> Seq a -> Seq a
- deleteAt :: 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]
- foldMapWithIndex :: Monoid m => (Int -> a -> m) -> Seq a -> m
- 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
- traverseWithIndex :: Applicative f => (Int -> a -> f b) -> Seq a -> f (Seq b)
- reverse :: Seq a -> Seq a
- intersperse :: a -> 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
- unzip :: Seq (a, b) -> (Seq a, Seq b)
- unzipWith :: (a -> (b, c)) -> Seq a -> (Seq b, Seq c)

# Finite sequences

data Seq a where #

General-purpose finite sequences.

Bundled Patterns

pattern Empty :: Seq a | A bidirectional pattern synonym matching an empty sequence. Since: containers-0.5.8
pattern (:<|) :: a -> Seq a -> Seq a infixr 5 | A bidirectional pattern synonym viewing the front of a non-empty sequence. Since: containers-0.5.8
pattern (:|>) :: Seq a -> a -> Seq a infixl 5 | A bidirectional pattern synonym viewing the rear of a non-empty sequence. Since: containers-0.5.8

#### Instances

Instances details

MonadFix Seq # | Since: containers-0.5.11
Instance details Defined in Data.Sequence.Internal Methods mfix :: (a -> Seq a) -> Seq a Source #
MonadZip Seq # |
     mzipWith = zipWith
     munzip = unzip
Instance details Defined in Data.Sequence.Internal Methods mzip :: Seq a -> Seq b -> Seq (a, b) Source # mzipWith :: (a -> b -> c) -> Seq a -> Seq b -> Seq c Source # munzip :: Seq (a, b) -> (Seq a, Seq b) Source #
Foldable Seq # |
Instance details Defined in Data.Sequence.Internal Methods fold :: Monoid m => Seq m -> m Source # foldMap :: Monoid m => (a -> m) -> Seq a -> m Source # foldMap' :: Monoid m => (a -> m) -> Seq a -> m Source # foldr :: (a -> b -> b) -> b -> Seq a -> b Source # foldr' :: (a -> b -> b) -> b -> Seq a -> b Source # foldl :: (b -> a -> b) -> b -> Seq a -> b Source # foldl' :: (b -> a -> b) -> b -> Seq a -> b Source # foldr1 :: (a -> a -> a) -> Seq a -> a Source # foldl1 :: (a -> a -> a) -> Seq a -> a Source # toList :: Seq a -> [a] Source # null :: Seq a -> Bool Source # length :: Seq a -> Int Source # elem :: Eq a => a -> Seq a -> Bool Source # maximum :: Ord a => Seq a -> a Source # minimum :: Ord a => Seq a -> a Source # sum :: Num a => Seq a -> a Source # product :: Num a => Seq a -> a Source #
Eq1 Seq # | Since: containers-0.5.9
Instance details Defined in Data.Sequence.Internal Methods liftEq :: (a -> b -> Bool) -> Seq a -> Seq b -> Bool Source #
Ord1 Seq # | Since: containers-0.5.9
Instance details Defined in Data.Sequence.Internal Methods liftCompare :: (a -> b -> Ordering) -> Seq a -> Seq b -> Ordering Source #
Read1 Seq # | Since: containers-0.5.9
Instance details Defined in Data.Sequence.Internal Methods liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (Seq a) Source # liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [Seq a] Source # liftReadPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec (Seq a) Source # liftReadListPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec [Seq a] Source #
Show1 Seq # | Since: containers-0.5.9
Instance details Defined in Data.Sequence.Internal Methods liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> Seq a -> ShowS Source # liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [Seq a] -> ShowS Source #
Traversable Seq # |
Instance details Defined in Data.Sequence.Internal Methods traverse :: Applicative f => (a -> f b) -> Seq a -> f (Seq b) Source # sequenceA :: Applicative f => Seq (f a) -> f (Seq a) Source # mapM :: Monad m => (a -> m b) -> Seq a -> m (Seq b) Source # sequence :: Monad m => Seq (m a) -> m (Seq a) Source #
Alternative Seq # | Since: containers-0.5.4
Instance details Defined in Data.Sequence.Internal Methods empty :: Seq a Source # (<|>) :: Seq a -> Seq a -> Seq a Source # some :: Seq a -> Seq [a] Source # many :: Seq a -> Seq [a] Source #
Applicative Seq # | Since: containers-0.5.4
Instance details Defined in Data.Sequence.Internal Methods pure :: a -> Seq a Source # (<*>) :: Seq (a -> b) -> Seq a -> Seq b Source # liftA2 :: (a -> b -> c) -> Seq a -> Seq b -> Seq c Source # (*>) :: Seq a -> Seq b -> Seq b Source # (<*) :: Seq a -> Seq b -> Seq a Source #
Functor Seq # |
Instance details Defined in Data.Sequence.Internal Methods fmap :: (a -> b) -> Seq a -> Seq b Source # (<$) :: a -> Seq b -> Seq a Source #
Monad Seq # |
Instance details Defined in Data.Sequence.Internal Methods (>>=) :: Seq a -> (a -> Seq b) -> Seq b Source # (>>) :: Seq a -> Seq b -> Seq b Source # return :: a -> Seq a Source #
MonadPlus Seq # |
Instance details Defined in Data.Sequence.Internal Methods mzero :: Seq a Source # mplus :: Seq a -> Seq a -> Seq a Source #
Data a => Data (Seq a) # |
Instance details Defined in Data.Sequence.Internal Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Seq a -> c (Seq a) Source # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Seq a) Source # toConstr :: Seq a -> Constr Source # dataTypeOf :: Seq a -> DataType Source # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Seq a)) Source # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Seq a)) Source # gmapT :: (forall b. Data b => b -> b) -> Seq a -> Seq a Source # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Seq a -> r Source # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Seq a -> r Source # gmapQ :: (forall d. Data d => d -> u) -> Seq a -> [u] Source # gmapQi :: Int -> (forall d. Data d => d -> u) -> Seq a -> u Source # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Seq a -> m (Seq a) Source # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Seq a -> m (Seq a) Source # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Seq a -> m (Seq a) Source #
a ~ Char => IsString (Seq a) # | Since: containers-0.5.7
Instance details Defined in Data.Sequence.Internal Methods fromString :: String -> Seq a Source #
Monoid (Seq a) # |
Instance details Defined in Data.Sequence.Internal Methods mempty :: Seq a Source # mappend :: Seq a -> Seq a -> Seq a Source # mconcat :: [Seq a] -> Seq a Source #
Semigroup (Seq a) # | Since: containers-0.5.7
Instance details Defined in Data.Sequence.Internal Methods (<>) :: Seq a -> Seq a -> Seq a Source # sconcat :: NonEmpty (Seq a) -> Seq a Source # stimes :: Integral b => b -> Seq a -> Seq a Source #
IsList (Seq a) # |
Instance details Defined in Data.Sequence.Internal Associated Types type Item (Seq a) Source # Methods fromList :: [Item (Seq a)] -> Seq a Source # fromListN :: Int -> [Item (Seq a)] -> Seq a Source # toList :: Seq a -> [Item (Seq a)] Source #
Read a => Read (Seq a) # |
Instance details Defined in Data.Sequence.Internal Methods readsPrec :: Int -> ReadS (Seq a) Source # readList :: ReadS [Seq a] Source # readPrec :: ReadPrec (Seq a) Source # readListPrec :: ReadPrec [Seq a] Source #
Show a => Show (Seq a) # |
Instance details Defined in Data.Sequence.Internal Methods showsPrec :: Int -> Seq a -> ShowS Source # show :: Seq a -> String Source # showList :: [Seq a] -> ShowS Source #
NFData a => NFData (Seq a) # |
Instance details Defined in Data.Sequence.Internal Methods rnf :: Seq a -> () Source #
Eq a => Eq (Seq a) # |
Instance details Defined in Data.Sequence.Internal Methods (==) :: Seq a -> Seq a -> Bool # (/=) :: Seq a -> Seq a -> Bool #
Ord a => Ord (Seq a) # |
Instance details Defined in Data.Sequence.Internal Methods compare :: Seq a -> Seq a -> Ordering # (<) :: Seq a -> Seq a -> Bool # (<=) :: Seq a -> Seq a -> Bool # (>) :: Seq a -> Seq a -> Bool # (>=) :: Seq a -> Seq a -> Bool # max :: Seq a -> Seq a -> Seq a # min :: Seq a -> Seq a -> Seq a #
type Item (Seq a) # |
Instance details Defined in Data.Sequence.Internal type Item (Seq a) = a

## Pattern synonyms

Much like lists can be constructed and matched using the `:` and `[]` constructors, sequences can be constructed and matched using the `Empty`, `:<|`, and `:|>` pattern synonyms.

### Note

These patterns are only available with GHC version 8.0 or later, and version 8.2 works better with them. When writing for such recent versions of GHC, the patterns can be used in place of `empty`, `<|`, `|>`, `viewl`, and `viewr`.

### Pattern synonym examples

Expand

Import the patterns:

    import Data.Sequence (Seq (..))

Look at the first three elements of a sequence

    getFirst3 :: Seq a -> Maybe (a,a,a)
    getFirst3 (x1 :<| x2 :<| x3 :<| _xs) = Just (x1,x2,x3)
    getFirst3 _ = Nothing

    > getFirst3 (fromList [1,2,3,4]) = Just (1,2,3)
    > getFirst3 (fromList [1,2]) = Nothing

Move the last two elements from the end of the first list onto the beginning of the second one.

    shift2Right :: Seq a -> Seq a -> (Seq a, Seq a)
    shift2Right Empty ys = (Empty, ys)
    shift2Right (Empty :|> x) ys = (Empty, x :<| ys)
    shift2Right (xs :|> x1 :|> x2) = (xs, x1 :<| x2 :<| ys)

    > shift2Right (fromList []) (fromList [10]) = (fromList [], fromList [10])
    > shift2Right (fromList [9]) (fromList [10]) = (fromList [], fromList [9,10])
    > shift2Right (fromList [8,9]) (fromList [10]) = (fromList [], fromList [8,9,10])
    > shift2Right (fromList [7,8,9]) (fromList [10]) = (fromList [7], fromList [8,9,10])

# Construction

empty :: Seq a #

\( O(1) \). The empty sequence.

singleton :: a -> Seq a #

\( O(1) \). A singleton sequence.

(<|) :: a -> Seq a -> Seq a infixr 5 #

\( O(1) \). 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 #

\( O(1) \). 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 #

\( O(\log(\min(n_1,n_2))) \). 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`.

fromFunction :: Int -> (Int -> a) -> Seq a #

\( O(n) \). Convert a given sequence length and a function representing that sequence into a sequence.

Since: containers-0.5.6.2

fromArray :: Ix i => Array i a -> Seq a #

\( O(n) \). 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.

Since: containers-0.5.6.2

## 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 `liftA2` and `pure`.

    replicateA n x = sequenceA (replicate n x)

replicateM :: Applicative m => Int -> m a -> m (Seq a) #

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

    replicateM n x = sequence (replicate n x)

For `base >= 4.8.0` and `containers >= 0.5.11`, `replicateM` is a synonym for `replicateA`.

cycleTaking :: Int -> Seq a -> Seq a #

O(log k). ``cycleTaking` k xs` forms a sequence of length `k` by repeatedly concatenating `xs` with itself. `xs` may only be empty if `k` is 0.

    cycleTaking k = fromList . take k . cycle . toList

## 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` (`fmap` 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) infixr 5 | leftmost element and the rest of the sequence

#### Instances

Instances details

Foldable ViewL # |
Instance details Defined in Data.Sequence.Internal Methods fold :: Monoid m => ViewL m -> m Source # foldMap :: Monoid m => (a -> m) -> ViewL a -> m Source # foldMap' :: Monoid m => (a -> m) -> ViewL a -> m Source # foldr :: (a -> b -> b) -> b -> ViewL a -> b Source # foldr' :: (a -> b -> b) -> b -> ViewL a -> b Source # foldl :: (b -> a -> b) -> b -> ViewL a -> b Source # foldl' :: (b -> a -> b) -> b -> ViewL a -> b Source # foldr1 :: (a -> a -> a) -> ViewL a -> a Source # foldl1 :: (a -> a -> a) -> ViewL a -> a Source # toList :: ViewL a -> [a] Source # null :: ViewL a -> Bool Source # length :: ViewL a -> Int Source # elem :: Eq a => a -> ViewL a -> Bool Source # maximum :: Ord a => ViewL a -> a Source # minimum :: Ord a => ViewL a -> a Source # sum :: Num a => ViewL a -> a Source # product :: Num a => ViewL a -> a Source #
Traversable ViewL # |
Instance details Defined in Data.Sequence.Internal Methods traverse :: Applicative f => (a -> f b) -> ViewL a -> f (ViewL b) Source # sequenceA :: Applicative f => ViewL (f a) -> f (ViewL a) Source # mapM :: Monad m => (a -> m b) -> ViewL a -> m (ViewL b) Source # sequence :: Monad m => ViewL (m a) -> m (ViewL a) Source #
Functor ViewL # |
Instance details Defined in Data.Sequence.Internal Methods fmap :: (a -> b) -> ViewL a -> ViewL b Source # (<$) :: a -> ViewL b -> ViewL a Source #
Data a => Data (ViewL a) # |
Instance details Defined in Data.Sequence.Internal Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> ViewL a -> c (ViewL a) Source # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (ViewL a) Source # toConstr :: ViewL a -> Constr Source # dataTypeOf :: ViewL a -> DataType Source # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (ViewL a)) Source # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (ViewL a)) Source # gmapT :: (forall b. Data b => b -> b) -> ViewL a -> ViewL a Source # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> ViewL a -> r Source # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> ViewL a -> r Source # gmapQ :: (forall d. Data d => d -> u) -> ViewL a -> [u] Source # gmapQi :: Int -> (forall d. Data d => d -> u) -> ViewL a -> u Source # gmapM :: Monad m => (forall d. Data d => d -> m d) -> ViewL a -> m (ViewL a) Source # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> ViewL a -> m (ViewL a) Source # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> ViewL a -> m (ViewL a) Source #
Generic (ViewL a) # |
Instance details Defined in Data.Sequence.Internal Associated Types type Rep (ViewL a) :: Type -> Type Source # Methods from :: ViewL a -> Rep (ViewL a) x Source # to :: Rep (ViewL a) x -> ViewL a Source #
Read a => Read (ViewL a) # |
Instance details Defined in Data.Sequence.Internal Methods readsPrec :: Int -> ReadS (ViewL a) Source # readList :: ReadS [ViewL a] Source # readPrec :: ReadPrec (ViewL a) Source # readListPrec :: ReadPrec [ViewL a] Source #
Show a => Show (ViewL a) # |
Instance details Defined in Data.Sequence.Internal Methods showsPrec :: Int -> ViewL a -> ShowS Source # show :: ViewL a -> String Source # showList :: [ViewL a] -> ShowS Source #
Eq a => Eq (ViewL a) # |
Instance details Defined in Data.Sequence.Internal Methods (==) :: ViewL a -> ViewL a -> Bool # (/=) :: ViewL a -> ViewL a -> Bool #
Ord a => Ord (ViewL a) # |
Instance details Defined in Data.Sequence.Internal Methods compare :: ViewL a -> ViewL a -> Ordering # (<) :: ViewL a -> ViewL a -> Bool # (<=) :: ViewL a -> ViewL a -> Bool # (>) :: ViewL a -> ViewL a -> Bool # (>=) :: ViewL a -> ViewL a -> Bool # max :: ViewL a -> ViewL a -> ViewL a # min :: ViewL a -> ViewL a -> ViewL a #
Generic1 ViewL # |
Instance details Defined in Data.Sequence.Internal Associated Types type Rep1 ViewL :: k -> Type Source # Methods from1 :: forall (a :: k). ViewL a -> Rep1 ViewL a Source # to1 :: forall (a :: k). Rep1 ViewL a -> ViewL a Source #
type Rep (ViewL a) # | Since: containers-0.5.8
Instance details Defined in Data.Sequence.Internal type Rep (ViewL a) = D1 ('MetaData "ViewL" "Data.Sequence.Internal" "containers-0.6.4.1" 'False) (C1 ('MetaCons "EmptyL" 'PrefixI 'False) (U1 :: Type -> Type) :+: C1 ('MetaCons ":<" ('InfixI 'RightAssociative 5) 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (Seq a))))
type Rep1 ViewL # | Since: containers-0.5.8
Instance details Defined in Data.Sequence.Internal type Rep1 ViewL = D1 ('MetaData "ViewL" "Data.Sequence.Internal" "containers-0.6.4.1" 'False) (C1 ('MetaCons "EmptyL" 'PrefixI 'False) (U1 :: Type -> Type) :+: C1 ('MetaCons ":<" ('InfixI 'RightAssociative 5) 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1 :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec1 Seq)))

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 infixl 5 | the sequence minus the rightmost element, and the rightmost element

#### Instances

Instances details

Foldable ViewR # |
Instance details Defined in Data.Sequence.Internal Methods fold :: Monoid m => ViewR m -> m Source # foldMap :: Monoid m => (a -> m) -> ViewR a -> m Source # foldMap' :: Monoid m => (a -> m) -> ViewR a -> m Source # foldr :: (a -> b -> b) -> b -> ViewR a -> b Source # foldr' :: (a -> b -> b) -> b -> ViewR a -> b Source # foldl :: (b -> a -> b) -> b -> ViewR a -> b Source # foldl' :: (b -> a -> b) -> b -> ViewR a -> b Source # foldr1 :: (a -> a -> a) -> ViewR a -> a Source # foldl1 :: (a -> a -> a) -> ViewR a -> a Source # toList :: ViewR a -> [a] Source # null :: ViewR a -> Bool Source # length :: ViewR a -> Int Source # elem :: Eq a => a -> ViewR a -> Bool Source # maximum :: Ord a => ViewR a -> a Source # minimum :: Ord a => ViewR a -> a Source # sum :: Num a => ViewR a -> a Source # product :: Num a => ViewR a -> a Source #
Traversable ViewR # |
Instance details Defined in Data.Sequence.Internal Methods traverse :: Applicative f => (a -> f b) -> ViewR a -> f (ViewR b) Source # sequenceA :: Applicative f => ViewR (f a) -> f (ViewR a) Source # mapM :: Monad m => (a -> m b) -> ViewR a -> m (ViewR b) Source # sequence :: Monad m => ViewR (m a) -> m (ViewR a) Source #
Functor ViewR # |
Instance details Defined in Data.Sequence.Internal Methods fmap :: (a -> b) -> ViewR a -> ViewR b Source # (<$) :: a -> ViewR b -> ViewR a Source #
Data a => Data (ViewR a) # |
Instance details Defined in Data.Sequence.Internal Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> ViewR a -> c (ViewR a) Source # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (ViewR a) Source # toConstr :: ViewR a -> Constr Source # dataTypeOf :: ViewR a -> DataType Source # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (ViewR a)) Source # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (ViewR a)) Source # gmapT :: (forall b. Data b => b -> b) -> ViewR a -> ViewR a Source # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> ViewR a -> r Source # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> ViewR a -> r Source # gmapQ :: (forall d. Data d => d -> u) -> ViewR a -> [u] Source # gmapQi :: Int -> (forall d. Data d => d -> u) -> ViewR a -> u Source # gmapM :: Monad m => (forall d. Data d => d -> m d) -> ViewR a -> m (ViewR a) Source # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> ViewR a -> m (ViewR a) Source # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> ViewR a -> m (ViewR a) Source #
Generic (ViewR a) # |
Instance details Defined in Data.Sequence.Internal Associated Types type Rep (ViewR a) :: Type -> Type Source # Methods from :: ViewR a -> Rep (ViewR a) x Source # to :: Rep (ViewR a) x -> ViewR a Source #
Read a => Read (ViewR a) # |
Instance details Defined in Data.Sequence.Internal Methods readsPrec :: Int -> ReadS (ViewR a) Source # readList :: ReadS [ViewR a] Source # readPrec :: ReadPrec (ViewR a) Source # readListPrec :: ReadPrec [ViewR a] Source #
Show a => Show (ViewR a) # |
Instance details Defined in Data.Sequence.Internal Methods showsPrec :: Int -> ViewR a -> ShowS Source # show :: ViewR a -> String Source # showList :: [ViewR a] -> ShowS Source #
Eq a => Eq (ViewR a) # |
Instance details Defined in Data.Sequence.Internal Methods (==) :: ViewR a -> ViewR a -> Bool # (/=) :: ViewR a -> ViewR a -> Bool #
Ord a => Ord (ViewR a) # |
Instance details Defined in Data.Sequence.Internal Methods compare :: ViewR a -> ViewR a -> Ordering # (<) :: ViewR a -> ViewR a -> Bool # (<=) :: ViewR a -> ViewR a -> Bool # (>) :: ViewR a -> ViewR a -> Bool # (>=) :: ViewR a -> ViewR a -> Bool # max :: ViewR a -> ViewR a -> ViewR a # min :: ViewR a -> ViewR a -> ViewR a #
Generic1 ViewR # |
Instance details Defined in Data.Sequence.Internal Associated Types type Rep1 ViewR :: k -> Type Source # Methods from1 :: forall (a :: k). ViewR a -> Rep1 ViewR a Source # to1 :: forall (a :: k). Rep1 ViewR a -> ViewR a Source #
type Rep (ViewR a) # | Since: containers-0.5.8
Instance details Defined in Data.Sequence.Internal type Rep (ViewR a) = D1 ('MetaData "ViewR" "Data.Sequence.Internal" "containers-0.6.4.1" 'False) (C1 ('MetaCons "EmptyR" 'PrefixI 'False) (U1 :: Type -> Type) :+: C1 ('MetaCons ":>" ('InfixI 'LeftAssociative 5) 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (Seq a)) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)))
type Rep1 ViewR # | Since: containers-0.5.8
Instance details Defined in Data.Sequence.Internal type Rep1 ViewR = D1 ('MetaData "ViewR" "Data.Sequence.Internal" "containers-0.6.4.1" 'False) (C1 ('MetaCons "EmptyR" 'PrefixI 'False) (U1 :: Type -> Type) :+: C1 ('MetaCons ":>" ('InfixI 'LeftAssociative 5) 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec1 Seq) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1))

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

chunksOf :: Int -> Seq a -> Seq (Seq a) #

\(O \Bigl(\bigl(\frac{n}{c}\bigr) \log c\Bigr)\). `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 \( O \Bigl( \bigl(\frac{n}{c} - 1\bigr) (\log (c + 1)) + 1 \Bigr) \)

Since: containers-0.5.8

## 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 slightly faster.

Since: containers-0.3.0

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 slightly faster.

Since: containers-0.3.0

sortOn :: Ord b => (a -> b) -> Seq a -> Seq a #

\( O(n \log n) \). `sortOn` sorts the specified `Seq` by comparing the results of a key function applied to each element. ``sortOn` f` is equivalent to ``sortBy` (`compare` ``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` ``on`` f)` will be faster than ``sortOn` f`.

Since: containers-0.5.11

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`.

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`.

Since: containers-0.3.0

unstableSortOn :: Ord b => (a -> b) -> Seq a -> Seq a #

\( O(n \log n) \). `unstableSortOn` sorts the specified `Seq` by comparing the results of a key function applied to each element. ``unstableSortOn` f` is equivalent to ``unstableSortBy` (`compare` ``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` ``on`` f)` will be faster than ``unstableSortOn` f`.

Since: containers-0.5.11

# Indexing

lookup :: Int -> Seq a -> Maybe a #

\( O(\log(\min(i,n-i))) \). 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`.

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

    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 `Map` `m` at key `k`, you could use

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

Since: containers-0.5.8

(!?) :: Seq a -> Int -> Maybe a #

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

Since: containers-0.5.8

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.

    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 `(!?)`.

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. `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.

Since: containers-0.5.8

adjust' :: forall a. (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. 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

Since: containers-0.5.8

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.

insertAt :: Int -> a -> Seq a -> Seq a #

\( O(\log(\min(i,n-i))) \). ``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]

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

Since: containers-0.5.8

deleteAt :: Int -> Seq a -> Seq a #

\( O(\log(\min(i,n-i))) \). 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]

Since: containers-0.5.8

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`.

foldMapWithIndex :: Monoid m => (Int -> a -> m) -> Seq a -> m #

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.

traverseWithIndex :: Applicative f => (Int -> a -> f b) -> Seq a -> f (Seq b) #

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

Since: containers-0.5.8

reverse :: Seq a -> Seq a #

\( O(n) \). The reverse of a sequence.

intersperse :: a -> Seq a -> Seq a #

\( O(n) \). 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]

Since: containers-0.5.8

## Zips and unzip

zip :: Seq a -> Seq b -> Seq (a, b) #

\( O(\min(n_1,n_2)) \). `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 #

\( O(\min(n_1,n_2)) \). `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) #

\( O(\min(n_1,n_2,n_3)) \). `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 #

\( O(\min(n_1,n_2,n_3)) \). `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) #

\( O(\min(n_1,n_2,n_3,n_4)) \). `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 #

\( O(\min(n_1,n_2,n_3,n_4)) \). `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`.

unzip :: Seq (a, b) -> (Seq a, Seq b) #

Unzip a sequence of pairs.

    unzip ps = ps `seq` (fmap fst ps) (fmap snd ps)

Example:

    unzip $ fromList [(1,"a"), (2,"b"), (3,"c")] =
      (fromList [1,2,3], fromList ["a", "b", "c"])

See the note about efficiency at `unzipWith`.

Since: containers-0.5.11

unzipWith :: (a -> (b, c)) -> Seq a -> (Seq b, Seq c) #

\( O(n) \). Unzip a sequence using a function to divide elements.

     unzipWith f xs == unzip (fmap f xs)

Efficiency note:

`unzipWith` produces its two results in lockstep. If you calculate `unzipWith f xs` and fully force either of the results, then the entire structure of the other one will be built as well. This behavior allows the garbage collector to collect each calculated pair component as soon as it dies, without having to wait for its mate to die. If you do not need this behavior, you may be better off simply calculating the sequence of pairs and using `fmap` to extract each component sequence.

Since: containers-0.5.11