| 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
Description
Finite sequences
The type represents a finite sequence of values of
type Seq aa.
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,
filterfilters a sequence in exactly the same way thatPrelude.filters a list. The only major exception is thefilterlookupfunction, 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 patternsEmpty,:<|, and:|>. See the detailed explanation in the "Pattern synonyms" section. - Logarithmic-time concatenation with
>< - Logarithmic-time splitting with
splitAt,takeanddrop - Logarithmic-time access to any element with
lookup,!?,index,insertAt,deleteAt,adjust', andupdate
- Constant-time access to both the front and the rear with
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
Seqis defineddata 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
Functormethodsfmapand<$, along withmapWithIndex - The
Applicativemethods<*>,*>, and<* - The zips:
zipWith,zip, etc. inits,tailsfromFunction,replicate,intersperse, andcycleTakingreversechunksOf
Note that the Monad method, >>=, is not particularly lazy. It will
take time proportional to the sum of the logarithms of the individual
result sequences to produce anything whatsoever.
Several functions take special advantage of sharing to produce results using much less time and memory than one might expect. These are documented individually for functions, but also include certain class methods:
<$ 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
- 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
- viewl :: Seq a -> ViewL a
- data ViewR 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
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
| MonadFix Seq # | Since: containers-0.5.11 |
| MonadZip Seq # |
|
| Foldable Seq # | |
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 # | |
| 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 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 |
| Traversable Seq # | |
| Alternative Seq # | Since: containers-0.5.4 |
| Applicative Seq # | Since: containers-0.5.4 |
| Functor Seq # | |
| Monad Seq # | |
| MonadPlus Seq # | |
| Data a => Data (Seq a) # | |
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 |
Defined in Data.Sequence.Internal Methods fromString :: String -> Seq a Source # | |
| Monoid (Seq a) # | |
| Semigroup (Seq a) # | Since: containers-0.5.7 |
| IsList (Seq a) # | |
| Read a => Read (Seq a) # | |
| Show a => Show (Seq a) # | |
| NFData a => NFData (Seq a) # | |
Defined in Data.Sequence.Internal | |
| Eq a => Eq (Seq a) # | |
| Ord a => Ord (Seq a) # | |
| type Item (Seq a) # | |
Defined in Data.Sequence.Internal | |
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
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) ys = (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
(<|) :: 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.
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). forms a sequence of length cycleTaking k xsk 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.
Deconstruction
Queries
Views
View of the left end of a sequence.
Instances
| Foldable ViewL # | |
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 # | |
| Traversable ViewL # | |
Defined in Data.Sequence.Internal | |
| Functor ViewL # | |
| Data a => Data (ViewL a) # | |
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) # | |
| Read a => Read (ViewL a) # | |
| Show a => Show (ViewL a) # | |
| Eq a => Eq (ViewL a) # | |
| Ord a => Ord (ViewL a) # | |
Defined in Data.Sequence.Internal | |
| Generic1 ViewL # | |
| type Rep (ViewL a) # | Since: containers-0.5.8 |
Defined in Data.Sequence.Internal type Rep (ViewL a) = D1 ('MetaData "ViewL" "Data.Sequence.Internal" "containers-0.6.5.1" '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 |
Defined in Data.Sequence.Internal type Rep1 ViewL = D1 ('MetaData "ViewL" "Data.Sequence.Internal" "containers-0.6.5.1" 'False) (C1 ('MetaCons "EmptyL" 'PrefixI 'False) (U1 :: TYPE LiftedRep -> 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))) | |
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
| Foldable ViewR # | |
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 # | |
| Traversable ViewR # | |
Defined in Data.Sequence.Internal | |
| Functor ViewR # | |
| Generic1 ViewR # | |
| Data a => Data (ViewR a) # | |
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) # | |
| Read a => Read (ViewR a) # | |
| Show a => Show (ViewR a) # | |
| Eq a => Eq (ViewR a) # | |
| Ord a => Ord (ViewR a) # | |
Defined in Data.Sequence.Internal | |
| type Rep1 ViewR # | Since: containers-0.5.8 |
Defined in Data.Sequence.Internal type Rep1 ViewR = D1 ('MetaData "ViewR" "Data.Sequence.Internal" "containers-0.6.5.1" '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)) | |
| type Rep (ViewR a) # | Since: containers-0.5.8 |
Defined in Data.Sequence.Internal type Rep (ViewR a) = D1 ('MetaData "ViewR" "Data.Sequence.Internal" "containers-0.6.5.1" '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))) | |
Scans
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.
is equivalent to takeWhileR p xs.reverse (takeWhileL p (reverse xs))
dropWhileL :: (a -> Bool) -> Seq a -> Seq a #
\( O(i) \) where \( i \) is the prefix length. returns
the suffix remaining after dropWhileL p xs.takeWhileL p xs
dropWhileR :: (a -> Bool) -> Seq a -> Seq a #
\( O(i) \) where \( i \) is the suffix length. returns
the prefix remaining after dropWhileR p xs.takeWhileR p xs
is equivalent to dropWhileR p xs.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.
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. is
equivalent to sortOn f, but has the
performance advantage of only evaluating sortBy (compare `on` f)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),
will be faster than
sortBy (compare `on` f).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.
is equivalent to unstableSortOn f,
but has the performance advantage of only evaluating unstableSortBy (compare `on` f)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),
will be faster than
unstableSortBy (compare `on` f).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
\( O(\log(\min(i,n-i))) \). 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, yields the empty sequence.
If the sequence contains fewer than take i si 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, yields the whole sequence.
If the sequence contains fewer than drop i si elements, the empty sequence
is returned.
insertAt :: Int -> a -> Seq a -> Seq a #
\( O(\log(\min(i,n-i))) \). inserts insertAt i x xsx 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
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 #
finds the index of the leftmost element that
satisfies findIndexL p xsp, if any exist.
findIndicesL :: (a -> Bool) -> Seq a -> [Int] #
finds all indices of elements that satisfy findIndicesL pp,
in ascending order.
findIndexR :: (a -> Bool) -> Seq a -> Maybe Int #
finds the index of the rightmost element that
satisfies findIndexR p xsp, if any exist.
findIndicesR :: (a -> Bool) -> Seq a -> [Int] #
finds all indices of elements that satisfy findIndicesR pp,
in descending order.
Folds
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
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.
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(fmapf 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