Copyright | (c) Ross Paterson 2005 (c) Louis Wasserman 2009 (c) Bertram Felgenhauer David Feuer Ross Paterson and Milan Straka 2014 |
---|---|
License | BSD-style |
Maintainer | [email protected] |
Portability | portable |
Safe Haskell | Safe |
Language | Haskell98 |
The Seq a
type represents a finite sequence of values of type a
.
Sequences generally behave very much like lists.
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
<|
, |>
, 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.><
splitAt
, take
and drop
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.
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
Functor
methods fmap
and <$
, along with mapWithIndex
Applicative
methods <*>
, *>
, and <*
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 the methods <$
and *>
, each of which take time and space proportional to the logarithm of the size of the result.
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
.
The implementation uses 2-3 finger trees annotated with sizes, as described in section 4.2 of
General-purpose finite sequences.
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 |
Monad Seq | |
Functor Seq | |
MonadFix Seq | Since: containers-0.5.11 |
Defined in Data.Sequence.Internal | |
Applicative Seq | Since: containers-0.5.4 |
Foldable Seq | |
Defined in Data.Sequence.Internal Methodsfold :: 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 elem :: Eq a => a -> Seq a -> Bool Source maximum :: Ord a => Seq a -> a Source minimum :: Ord a => Seq a -> a Source | |
Traversable Seq | |
Eq1 Seq | Since: containers-0.5.9 |
Ord1 Seq | Since: containers-0.5.9 |
Defined in Data.Sequence.Internal | |
Read1 Seq | Since: containers-0.5.9 |
Defined in Data.Sequence.Internal | |
Show1 Seq | Since: containers-0.5.9 |
MonadZip Seq |
mzipWith = zipWith munzip = unzip |
Alternative Seq | Since: containers-0.5.4 |
MonadPlus Seq | |
IsList (Seq a) | |
Eq a => Eq (Seq a) | |
Data a => Data (Seq a) | |
Defined in Data.Sequence.Internal Methodsgfoldl :: (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 | |
Ord a => Ord (Seq a) | |
Read a => Read (Seq a) | |
Show a => Show (Seq a) | |
a ~ Char => IsString (Seq a) | Since: containers-0.5.7 |
Defined in Data.Sequence.Internal MethodsfromString :: String -> Seq a Source | |
Semigroup (Seq a) | Since: containers-0.5.7 |
Monoid (Seq a) | |
NFData a => NFData (Seq a) | |
Defined in Data.Sequence.Internal | |
type Item (Seq a) | |
Defined in Data.Sequence.Internal |
Much like lists can be constructed and matched using the :
and []
constructors, sequences can be constructed and matched using the Empty
, :<|
, and :|>
pattern synonyms.
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
.
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])
\( O(1) \). 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
\( O(\log(\min(n_1,n_2))) \). 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.
Since: containers-0.5.6.2
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.
Since: containers-0.5.6.2
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 liftA2
and pure
.
replicateA n x = sequenceA (replicate n x)
replicateM :: Applicative m => Int -> m a -> m (Seq a) Source
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 Source
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
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)
.
Additional functions for deconstructing sequences are available via the Foldable
instance of Seq
.
\( O(1) \). Is this the empty sequence?
\( O(1) \). The number of elements in the sequence.
View of the left end of a sequence.
EmptyL | empty sequence |
a :< (Seq a) infixr 5 | leftmost element and the rest of the sequence |
Functor ViewL | |
Foldable ViewL | |
Defined in Data.Sequence.Internal Methodsfold :: 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 | |
Traversable ViewL | |
Eq a => Eq (ViewL a) | |
Data a => Data (ViewL a) | |
Defined in Data.Sequence.Internal Methodsgfoldl :: (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 | |
Ord a => Ord (ViewL a) | |
Read a => Read (ViewL a) | |
Show a => Show (ViewL a) | |
Generic (ViewL a) | Since: containers-0.5.8 |
Generic1 ViewL | Since: containers-0.5.8 |
type Rep (ViewL a) | |
Defined in Data.Sequence.Internal type Rep (ViewL a) = D1 ('MetaData "ViewL" "Data.Sequence.Internal" "containers-0.6.2.1" '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 | |
Defined in Data.Sequence.Internal type Rep1 ViewL = D1 ('MetaData "ViewL" "Data.Sequence.Internal" "containers-0.6.2.1" '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 Source
\( O(1) \). Analyse the left end of a sequence.
View of the right end of a sequence.
EmptyR | empty sequence |
(Seq a) :> a infixl 5 | the sequence minus the rightmost element, and the rightmost element |
Functor ViewR | |
Foldable ViewR | |
Defined in Data.Sequence.Internal Methodsfold :: 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 | |
Traversable ViewR | |
Eq a => Eq (ViewR a) | |
Data a => Data (ViewR a) | |
Defined in Data.Sequence.Internal Methodsgfoldl :: (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 | |
Ord a => Ord (ViewR a) | |
Read a => Read (ViewR a) | |
Show a => Show (ViewR a) | |
Generic (ViewR a) | Since: containers-0.5.8 |
Generic1 ViewR | Since: containers-0.5.8 |
type Rep (ViewR a) | |
Defined in Data.Sequence.Internal type Rep (ViewR a) = D1 ('MetaData "ViewR" "Data.Sequence.Internal" "containers-0.6.2.1" '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 | |
Defined in Data.Sequence.Internal type Rep1 ViewR = D1 ('MetaData "ViewR" "Data.Sequence.Internal" "containers-0.6.2.1" '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 Source
\( O(1) \). Analyse the right end of a sequence.
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.
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 \( i \)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) 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 \( i \)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) Source
\(O \Bigl(\bigl(\frac{n}{c}\bigr) \log c\Bigr)\). 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
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.
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 slightly faster.
Since: containers-0.3.0
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 slightly faster.
Since: containers-0.3.0
sortOn :: Ord b => (a -> b) -> Seq a -> Seq a Source
\( O(n \log n) \). 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 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
.
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
.
Since: containers-0.3.0
unstableSortOn :: Ord b => (a -> b) -> Seq a -> Seq a Source
\( O(n \log n) \). 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
lookup :: Int -> Seq a -> Maybe a Source
\( O(\log(\min(i,n-i))) \). 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 Source
\( O(\log(\min(i,n-i))) \). A flipped, infix version of lookup
.
Since: containers-0.5.8
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.
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 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. 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 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. 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 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.
insertAt :: Int -> a -> Seq a -> Seq a Source
\( O(\log(\min(i,n-i))) \). 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 Source
\( O(\log(\min(i,n-i))) \). 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) Source
\( O(\log(\min(i,n-i))) \). Split a sequence at a given position. splitAt i s = (take i s, drop i s)
.
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.
General folds are available via the Foldable
instance of Seq
.
foldMapWithIndex :: Monoid m => (Int -> a -> m) -> Seq a -> m Source
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.
mapWithIndex :: (Int -> a -> b) -> Seq a -> Seq b Source
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) Source
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 Source
\( O(n) \). The reverse of a sequence.
intersperse :: a -> Seq a -> Seq a Source
\( O(n) \). 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
zip :: Seq a -> Seq b -> Seq (a, b) Source
\( O(\min(n_1,n_2)) \). 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 Source
\( O(\min(n_1,n_2)) \). 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) Source
\( O(\min(n_1,n_2,n_3)) \). 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 Source
\( O(\min(n_1,n_2,n_3)) \). 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) Source
\( O(\min(n_1,n_2,n_3,n_4)) \). 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 Source
\( O(\min(n_1,n_2,n_3,n_4)) \). 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) Source
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) Source
\( O(n) \). 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
© The University of Glasgow and others
Licensed under a BSD-style license (see top of the page).
https://downloads.haskell.org/~ghc/8.8.3/docs/html/libraries/containers-0.6.2.1/Data-Sequence.html