rio-0.1.22.0: A standard library for Haskell

Safe Haskell | Safe-Inferred
Language | Haskell2010

RIO.Seq

Contents

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

Description

`Seq`. Import as:

    import qualified RIO.Seq as Seq

Synopsis

- data Seq a where
  - pattern Empty :: Seq a
  - pattern (:|>) :: Seq a -> a -> Seq a
  - pattern (:<|) :: a -> Seq 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
- unstableSort :: Ord a => Seq a -> Seq a
- unstableSortBy :: (a -> a -> Ordering) -> 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' :: (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

# Documentation

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 (:|>) :: Seq a -> a -> Seq a infixl 5 | A bidirectional pattern synonym viewing the rear of a non-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

#### Instances

Instances details

MonadFix Seq | Since: containers-0.5.11
Instance details Defined in Data.Sequence.Internal Methods mfix :: (a -> Seq a) -> Seq a #
MonadZip Seq |
     mzipWith = zipWith
     munzip = unzip
Since: containers-0.5.10.1
Instance details Defined in Data.Sequence.Internal Methods mzip :: Seq a -> Seq b -> Seq (a, b) # mzipWith :: (a -> b -> c) -> Seq a -> Seq b -> Seq c # munzip :: Seq (a, b) -> (Seq a, Seq b) #
Foldable Seq |
Instance details Defined in Data.Sequence.Internal Methods fold :: Monoid m => Seq m -> m # foldMap :: Monoid m => (a -> m) -> Seq a -> m # foldMap' :: Monoid m => (a -> m) -> Seq a -> m # foldr :: (a -> b -> b) -> b -> Seq a -> b # foldr' :: (a -> b -> b) -> b -> Seq a -> b # foldl :: (b -> a -> b) -> b -> Seq a -> b # foldl' :: (b -> a -> b) -> b -> Seq a -> b # foldr1 :: (a -> a -> a) -> Seq a -> a # foldl1 :: (a -> a -> a) -> Seq a -> a # toList :: Seq a -> [a] # null :: Seq a -> Bool # length :: Seq a -> Int # elem :: Eq a => a -> Seq a -> Bool # maximum :: Ord a => Seq a -> a # minimum :: Ord a => Seq a -> a # sum :: Num a => Seq a -> a # product :: Num a => Seq a -> a #
Eq1 Seq | Since: containers-0.5.9
Instance details Defined in Data.Sequence.Internal Methods liftEq :: (a -> b -> Bool) -> Seq a -> Seq b -> Bool #
Ord1 Seq | Since: containers-0.5.9
Instance details Defined in Data.Sequence.Internal Methods liftCompare :: (a -> b -> Ordering) -> Seq a -> Seq b -> Ordering #
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) # liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [Seq a] # liftReadPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec (Seq a) # liftReadListPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec [Seq a] #
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 # liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [Seq a] -> ShowS #
Traversable Seq |
Instance details Defined in Data.Sequence.Internal Methods traverse :: Applicative f => (a -> f b) -> Seq a -> f (Seq b) # sequenceA :: Applicative f => Seq (f a) -> f (Seq a) # mapM :: Monad m => (a -> m b) -> Seq a -> m (Seq b) # sequence :: Monad m => Seq (m a) -> m (Seq a) #
Alternative Seq | Since: containers-0.5.4
Instance details Defined in Data.Sequence.Internal Methods empty :: Seq a # (<|>) :: Seq a -> Seq a -> Seq a # some :: Seq a -> Seq [a] # many :: Seq a -> Seq [a] #
Applicative Seq | Since: containers-0.5.4
Instance details Defined in Data.Sequence.Internal Methods pure :: a -> Seq a # (<*>) :: Seq (a -> b) -> Seq a -> Seq b # liftA2 :: (a -> b -> c) -> Seq a -> Seq b -> Seq c # (*>) :: Seq a -> Seq b -> Seq b # (<*) :: Seq a -> Seq b -> Seq a #
Functor Seq |
Instance details Defined in Data.Sequence.Internal Methods fmap :: (a -> b) -> Seq a -> Seq b # (<$) :: a -> Seq b -> Seq a #
Monad Seq |
Instance details Defined in Data.Sequence.Internal Methods (>>=) :: Seq a -> (a -> Seq b) -> Seq b # (>>) :: Seq a -> Seq b -> Seq b # return :: a -> Seq a #
MonadPlus Seq |
Instance details Defined in Data.Sequence.Internal Methods mzero :: Seq a # mplus :: Seq a -> Seq a -> Seq a #
UnzipWith Seq |
Instance details Defined in Data.Sequence.Internal Methods unzipWith' :: (x -> (a, b)) -> Seq x -> (Seq a, Seq b)
Hashable1 Seq | Since: hashable-1.3.4.0
Instance details Defined in Data.Hashable.Class Methods liftHashWithSalt :: (Int -> a -> Int) -> Int -> Seq a -> Int #
Lift a => Lift (Seq a :: Type) | Since: containers-0.6.6
Instance details Defined in Data.Sequence.Internal Methods lift :: Quote m => Seq a -> m Exp # liftTyped :: forall (m :: Type -> Type). Quote m => Seq a -> Code m (Seq a) #
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) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Seq a) # toConstr :: Seq a -> Constr # dataTypeOf :: Seq a -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Seq a)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Seq a)) # gmapT :: (forall b. Data b => b -> b) -> Seq a -> Seq a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Seq a -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Seq a -> r # gmapQ :: (forall d. Data d => d -> u) -> Seq a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Seq a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Seq a -> m (Seq a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Seq a -> m (Seq a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Seq a -> m (Seq a) #
a ~ Char => IsString (Seq a) | Since: containers-0.5.7
Instance details Defined in Data.Sequence.Internal Methods fromString :: String -> Seq a #
Monoid (Seq a) |
Instance details Defined in Data.Sequence.Internal Methods mempty :: Seq a # mappend :: Seq a -> Seq a -> Seq a # mconcat :: [Seq a] -> Seq a #
Semigroup (Seq a) | Since: containers-0.5.7
Instance details Defined in Data.Sequence.Internal Methods (<>) :: Seq a -> Seq a -> Seq a # sconcat :: NonEmpty (Seq a) -> Seq a # stimes :: Integral b => b -> Seq a -> Seq a #
IsList (Seq a) |
Instance details Defined in Data.Sequence.Internal Associated Types
type Item (Seq a) |
Instance details Defined in Data.Sequence.Internal type Item (Seq a) = a
Methods fromList :: [Item (Seq a)] -> Seq a # fromListN :: Int -> [Item (Seq a)] -> Seq a # toList :: Seq a -> [Item (Seq a)] #
Read a => Read (Seq a) |
Instance details Defined in Data.Sequence.Internal Methods readsPrec :: Int -> ReadS (Seq a) # readList :: ReadS [Seq a] # readPrec :: ReadPrec (Seq a) # readListPrec :: ReadPrec [Seq a] #
Show a => Show (Seq a) |
Instance details Defined in Data.Sequence.Internal Methods showsPrec :: Int -> Seq a -> ShowS # show :: Seq a -> String # showList :: [Seq a] -> ShowS #
NFData a => NFData (Seq a) |
Instance details Defined in Data.Sequence.Internal Methods rnf :: Seq a -> () #
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 #
Hashable v => Hashable (Seq v) | Since: hashable-1.3.4.0
Instance details Defined in Data.Hashable.Class Methods hashWithSalt :: Int -> Seq v -> Int # hash :: Seq v -> Int #
type Item (Seq a) |
Instance details Defined in Data.Sequence.Internal type Item (Seq a) = a

# 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 the `Seq` counterpart of `Control.Monad.`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 # foldMap :: Monoid m => (a -> m) -> ViewL a -> m # foldMap' :: Monoid m => (a -> m) -> ViewL a -> m # foldr :: (a -> b -> b) -> b -> ViewL a -> b # foldr' :: (a -> b -> b) -> b -> ViewL a -> b # foldl :: (b -> a -> b) -> b -> ViewL a -> b # foldl' :: (b -> a -> b) -> b -> ViewL a -> b # foldr1 :: (a -> a -> a) -> ViewL a -> a # foldl1 :: (a -> a -> a) -> ViewL a -> a # toList :: ViewL a -> [a] # null :: ViewL a -> Bool # length :: ViewL a -> Int # elem :: Eq a => a -> ViewL a -> Bool # maximum :: Ord a => ViewL a -> a # minimum :: Ord a => ViewL a -> a # sum :: Num a => ViewL a -> a # product :: Num a => ViewL a -> a #
Traversable ViewL |
Instance details Defined in Data.Sequence.Internal Methods traverse :: Applicative f => (a -> f b) -> ViewL a -> f (ViewL b) # sequenceA :: Applicative f => ViewL (f a) -> f (ViewL a) # mapM :: Monad m => (a -> m b) -> ViewL a -> m (ViewL b) # sequence :: Monad m => ViewL (m a) -> m (ViewL a) #
Functor ViewL |
Instance details Defined in Data.Sequence.Internal Methods fmap :: (a -> b) -> ViewL a -> ViewL b # (<$) :: a -> ViewL b -> ViewL a #
Generic1 ViewL |
Instance details Defined in Data.Sequence.Internal Associated Types
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-0.6.8-inplace" '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)))
Methods from1 :: ViewL a -> Rep1 ViewL a # to1 :: Rep1 ViewL a -> ViewL a #
Lift a => Lift (ViewL a :: Type) | Since: containers-0.6.6
Instance details Defined in Data.Sequence.Internal Methods lift :: Quote m => ViewL a -> m Exp # liftTyped :: forall (m :: Type -> Type). Quote m => ViewL a -> Code m (ViewL a) #
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) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (ViewL a) # toConstr :: ViewL a -> Constr # dataTypeOf :: ViewL a -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (ViewL a)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (ViewL a)) # gmapT :: (forall b. Data b => b -> b) -> ViewL a -> ViewL a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> ViewL a -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> ViewL a -> r # gmapQ :: (forall d. Data d => d -> u) -> ViewL a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> ViewL a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> ViewL a -> m (ViewL a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> ViewL a -> m (ViewL a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> ViewL a -> m (ViewL a) #
Generic (ViewL a) |
Instance details Defined in Data.Sequence.Internal Associated Types
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-0.6.8-inplace" '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))))
Methods from :: ViewL a -> Rep (ViewL a) x # to :: Rep (ViewL a) x -> ViewL a #
Read a => Read (ViewL a) |
Instance details Defined in Data.Sequence.Internal Methods readsPrec :: Int -> ReadS (ViewL a) # readList :: ReadS [ViewL a] # readPrec :: ReadPrec (ViewL a) # readListPrec :: ReadPrec [ViewL a] #
Show a => Show (ViewL a) |
Instance details Defined in Data.Sequence.Internal Methods showsPrec :: Int -> ViewL a -> ShowS # show :: ViewL a -> String # showList :: [ViewL a] -> ShowS #
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 #
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-0.6.8-inplace" '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)))
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-0.6.8-inplace" '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))))

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 # foldMap :: Monoid m => (a -> m) -> ViewR a -> m # foldMap' :: Monoid m => (a -> m) -> ViewR a -> m # foldr :: (a -> b -> b) -> b -> ViewR a -> b # foldr' :: (a -> b -> b) -> b -> ViewR a -> b # foldl :: (b -> a -> b) -> b -> ViewR a -> b # foldl' :: (b -> a -> b) -> b -> ViewR a -> b # foldr1 :: (a -> a -> a) -> ViewR a -> a # foldl1 :: (a -> a -> a) -> ViewR a -> a # toList :: ViewR a -> [a] # null :: ViewR a -> Bool # length :: ViewR a -> Int # elem :: Eq a => a -> ViewR a -> Bool # maximum :: Ord a => ViewR a -> a # minimum :: Ord a => ViewR a -> a # sum :: Num a => ViewR a -> a # product :: Num a => ViewR a -> a #
Traversable ViewR |
Instance details Defined in Data.Sequence.Internal Methods traverse :: Applicative f => (a -> f b) -> ViewR a -> f (ViewR b) # sequenceA :: Applicative f => ViewR (f a) -> f (ViewR a) # mapM :: Monad m => (a -> m b) -> ViewR a -> m (ViewR b) # sequence :: Monad m => ViewR (m a) -> m (ViewR a) #
Functor ViewR |
Instance details Defined in Data.Sequence.Internal Methods fmap :: (a -> b) -> ViewR a -> ViewR b # (<$) :: a -> ViewR b -> ViewR a #
Generic1 ViewR |
Instance details Defined in Data.Sequence.Internal Associated Types
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-0.6.8-inplace" '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))
Methods from1 :: ViewR a -> Rep1 ViewR a # to1 :: Rep1 ViewR a -> ViewR a #
Lift a => Lift (ViewR a :: Type) | Since: containers-0.6.6
Instance details Defined in Data.Sequence.Internal Methods lift :: Quote m => ViewR a -> m Exp # liftTyped :: forall (m :: Type -> Type). Quote m => ViewR a -> Code m (ViewR a) #
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) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (ViewR a) # toConstr :: ViewR a -> Constr # dataTypeOf :: ViewR a -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (ViewR a)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (ViewR a)) # gmapT :: (forall b. Data b => b -> b) -> ViewR a -> ViewR a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> ViewR a -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> ViewR a -> r # gmapQ :: (forall d. Data d => d -> u) -> ViewR a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> ViewR a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> ViewR a -> m (ViewR a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> ViewR a -> m (ViewR a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> ViewR a -> m (ViewR a) #
Generic (ViewR a) |
Instance details Defined in Data.Sequence.Internal Associated Types
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-0.6.8-inplace" '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)))
Methods from :: ViewR a -> Rep (ViewR a) x # to :: Rep (ViewR a) x -> ViewR a #
Read a => Read (ViewR a) |
Instance details Defined in Data.Sequence.Internal Methods readsPrec :: Int -> ReadS (ViewR a) # readList :: ReadS [ViewR a] # readPrec :: ReadPrec (ViewR a) # readListPrec :: ReadPrec [ViewR a] #
Show a => Show (ViewR a) |
Instance details Defined in Data.Sequence.Internal Methods showsPrec :: Int -> ViewR a -> ShowS # show :: ViewR a -> String # showList :: [ViewR a] -> ShowS #
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 #
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-0.6.8-inplace" '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))
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-0.6.8-inplace" '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)))

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

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

# 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' :: (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 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

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`.