Data.Edison.Seq.BraunSeq

One-sided Braun sequences. All running times are as listed in Data.Edison.Seq except the following:

• lview, lcons, ltail* O( log n )
• rcons, rview, rhead*, rtail*, size O( log^2 n )
• copy, inBounds, lookup*, update, adjust O( log i )
• append O( n1 log n2 )
• concat O( n + m log m )
• drop, splitAt O( i log n )
• subseq O( i log n + len )
• reverseOnto O( n1 log n2 )
• concatMap, (>>=) O( n * t + m log m ), where n is the length of the input sequence m is the length of the output sequence and t is the running time of f

By keeping track of the size, we could get rcons, rview, rhead*, and rtail* down to O(log n) as well; furthermore, size would be O( 1 ).

References:

• Rob Hoogerwoord. "A symmetric set of efficient list operations". Journal of Functional Programming, 2(4):505--513, 1992.
• Rob Hoogerwoord. "A Logarithmic Implementation of Flexible Arrays". Mathematics of Program Construction (MPC'92), pages 191-207.
• Chris Okasaki. "Three algorithms on Braun Trees". Journal of Function Programming 7(6):661-666. Novemebr 1997.

Sequence Type

data Seq a

Instances

Monad Seq

Functor Seq

Applicative Seq

Sequence Seq

Alternative Seq

MonadPlus Seq

Eq a => Eq (Seq a)

Ord a => Ord (Seq a)

Read a => Read (Seq a)

Show a => Show (Seq a)

Arbitrary a => Arbitrary (Seq a)

CoArbitrary a => CoArbitrary (Seq a)

Monoid (Seq a)

Sequence Operations

empty :: Seq a

singleton :: a -> Seq a

lcons :: a -> Seq a -> Seq a

rcons :: a -> Seq a -> Seq a

append :: Seq a -> Seq a -> Seq a

lview :: Monad m => Seq a -> m (a, Seq a)

lhead :: Seq a -> a

ltail :: Seq a -> Seq a

rview :: Monad m => Seq a -> m (a, Seq a)

rhead :: Seq a -> a

rtail :: Seq a -> Seq a

lheadM :: Monad m => Seq a -> m a

ltailM :: Monad m => Seq a -> m (Seq a)

rheadM :: Monad m => Seq a -> m a

rtailM :: Monad m => Seq a -> m (Seq a)

null :: Seq a -> Bool

size :: Seq a -> Int

concat :: Seq (Seq a) -> Seq a

reverse :: Seq a -> Seq a

reverseOnto :: Seq a -> Seq a -> Seq a

fromList :: [a] -> Seq a

toList :: Seq a -> [a]

map :: (a -> b) -> Seq a -> Seq b

concatMap :: (a -> Seq b) -> Seq a -> Seq b

fold :: (a -> b -> b) -> b -> Seq a -> b

fold' :: (a -> b -> b) -> b -> Seq a -> b

fold1 :: (a -> a -> a) -> Seq a -> a

fold1' :: (a -> a -> a) -> Seq a -> a

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

foldr1' :: (a -> a -> a) -> Seq a -> a

foldl1 :: (a -> a -> a) -> Seq a -> a

foldl1' :: (a -> a -> a) -> Seq a -> a

reducer :: (a -> a -> a) -> a -> Seq a -> a

reducer' :: (a -> a -> a) -> a -> Seq a -> a

reducel :: (a -> a -> a) -> a -> Seq a -> a

reducel' :: (a -> a -> a) -> a -> Seq a -> a

reduce1 :: (a -> a -> a) -> Seq a -> a

reduce1' :: (a -> a -> a) -> Seq a -> a

copy :: Int -> a -> Seq a

inBounds :: Int -> Seq a -> Bool

lookup :: Int -> Seq a -> a

lookupM :: Monad m => Int -> Seq a -> m a

lookupWithDefault :: a -> Int -> Seq a -> a

update :: Int -> a -> Seq a -> Seq a

adjust :: (a -> a) -> Int -> Seq a -> Seq a

mapWithIndex :: (Int -> a -> b) -> Seq a -> Seq b

foldrWithIndex :: (Int -> a -> b -> b) -> b -> Seq a -> b

foldrWithIndex' :: (Int -> a -> b -> b) -> b -> Seq a -> b

foldlWithIndex :: (b -> Int -> a -> b) -> b -> Seq a -> b

foldlWithIndex' :: (b -> Int -> a -> b) -> b -> Seq a -> b

take :: Int -> Seq a -> Seq a

drop :: Int -> Seq a -> Seq a

splitAt :: Int -> Seq a -> (Seq a, Seq a)

subseq :: Int -> Int -> Seq a -> Seq a

filter :: (a -> Bool) -> Seq a -> Seq a

partition :: (a -> Bool) -> Seq a -> (Seq a, Seq a)

takeWhile :: (a -> Bool) -> Seq a -> Seq a

dropWhile :: (a -> Bool) -> Seq a -> Seq a

splitWhile :: (a -> Bool) -> Seq a -> (Seq a, Seq a)

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

zip3 :: Seq a -> Seq b -> Seq c -> Seq (a, b, c)

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

zipWith3 :: (a -> b -> c -> d) -> Seq a -> Seq b -> Seq c -> Seq d

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

unzip3 :: Seq (a, b, c) -> (Seq a, Seq b, Seq c)

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

unzipWith3 :: (a -> b) -> (a -> c) -> (a -> d) -> Seq a -> (Seq b, Seq c, Seq d)

strict :: Seq a -> Seq a

strictWith :: (a -> b) -> Seq a -> Seq a

Unit testing

structuralInvariant :: Seq a -> Bool

Documentation

moduleName :: String