Data.Compressed.Internal.LZ78

Compression algorithms are all about exploiting redundancy. When applying an expensive Reducer to a redundant source, it may be better to extract the structural redundancy that is present. LZ78 is a compression algorithm that does so, without requiring the dictionary to be populated with all of the possible values of a data type unlike its later refinement LZW, and which has fewer comparison reqirements during encoding than its earlier counterpart LZ77.

Lempel-Ziv 78

data Token a

Constructors

Token !Int a

Instances

Functor Token

Methods

fmap :: (a -> b) -> Token a -> Token b

(<$) :: a -> Token b -> Token a

Foldable Token

Methods

fold :: Monoid m => Token m -> m

foldMap :: Monoid m => (a -> m) -> Token a -> m

foldr :: (a -> b -> b) -> b -> Token a -> b

foldr' :: (a -> b -> b) -> b -> Token a -> b

foldl :: (b -> a -> b) -> b -> Token a -> b

foldl' :: (b -> a -> b) -> b -> Token a -> b

foldr1 :: (a -> a -> a) -> Token a -> a

foldl1 :: (a -> a -> a) -> Token a -> a

toList :: Token a -> [a]

null :: Token a -> Bool

length :: Token a -> Int

elem :: Eq a => a -> Token a -> Bool

maximum :: Ord a => Token a -> a

minimum :: Ord a => Token a -> a

sum :: Num a => Token a -> a

product :: Num a => Token a -> a

Traversable Token

Methods

traverse :: Applicative f => (a -> f b) -> Token a -> f (Token b)

sequenceA :: Applicative f => Token (f a) -> f (Token a)

mapM :: Monad m => (a -> m b) -> Token a -> m (Token b)

sequence :: Monad m => Token (m a) -> m (Token a)

Comonad Token

Methods

extract :: Token a -> a

duplicate :: Token a -> Token (Token a)

extend :: (Token a -> b) -> Token a -> Token b

Extend Token

Methods

duplicated :: Token a -> Token (Token a)

extended :: (Token a -> b) -> Token a -> Token b

Eq a => Eq (Token a)

Methods

(==) :: Token a -> Token a -> Bool

(/=) :: Token a -> Token a -> Bool

Ord a => Ord (Token a)

Methods

compare :: Token a -> Token a -> Ordering

(<) :: Token a -> Token a -> Bool

(<=) :: Token a -> Token a -> Bool

(>) :: Token a -> Token a -> Bool

(>=) :: Token a -> Token a -> Bool

max :: Token a -> Token a -> Token a

min :: Token a -> Token a -> Token a

Hashable a => Hashable (Token a)

Methods

hashWithSalt :: Int -> Token a -> Int

hash :: Token a -> Int

data LZ78 a

An LZ78 compressed Generator.

Constructors

Cons !(Token a) (LZ78 a)

Nil

Instances

Monad LZ78

Methods

(>>=) :: LZ78 a -> (a -> LZ78 b) -> LZ78 b

(>>) :: LZ78 a -> LZ78 b -> LZ78 b

return :: a -> LZ78 a

fail :: String -> LZ78 a

Functor LZ78

Methods

fmap :: (a -> b) -> LZ78 a -> LZ78 b

(<$) :: a -> LZ78 b -> LZ78 a

Applicative LZ78

Methods

pure :: a -> LZ78 a

(<*>) :: LZ78 (a -> b) -> LZ78 a -> LZ78 b

liftA2 :: (a -> b -> c) -> LZ78 a -> LZ78 b -> LZ78 c

(*>) :: LZ78 a -> LZ78 b -> LZ78 b

(<*) :: LZ78 a -> LZ78 b -> LZ78 a

Foldable LZ78

Methods

fold :: Monoid m => LZ78 m -> m

foldMap :: Monoid m => (a -> m) -> LZ78 a -> m

foldr :: (a -> b -> b) -> b -> LZ78 a -> b

foldr' :: (a -> b -> b) -> b -> LZ78 a -> b

foldl :: (b -> a -> b) -> b -> LZ78 a -> b

foldl' :: (b -> a -> b) -> b -> LZ78 a -> b

foldr1 :: (a -> a -> a) -> LZ78 a -> a

foldl1 :: (a -> a -> a) -> LZ78 a -> a

toList :: LZ78 a -> [a]

null :: LZ78 a -> Bool

length :: LZ78 a -> Int

elem :: Eq a => a -> LZ78 a -> Bool

maximum :: Ord a => LZ78 a -> a

minimum :: Ord a => LZ78 a -> a

sum :: Num a => LZ78 a -> a

product :: Num a => LZ78 a -> a

MonadZip LZ78

Methods

mzip :: LZ78 a -> LZ78 b -> LZ78 (a, b)

mzipWith :: (a -> b -> c) -> LZ78 a -> LZ78 b -> LZ78 c

munzip :: LZ78 (a, b) -> (LZ78 a, LZ78 b)

Zip LZ78

Methods

zipWith :: (a -> b -> c) -> LZ78 a -> LZ78 b -> LZ78 c

zip :: LZ78 a -> LZ78 b -> LZ78 (a, b)

zap :: LZ78 (a -> b) -> LZ78 a -> LZ78 b

Indexable LZ78

Methods

index :: LZ78 a -> Key LZ78 -> a

Lookup LZ78

Methods

lookup :: Key LZ78 -> LZ78 a -> Maybe a

Adjustable LZ78

Methods

adjust :: (a -> a) -> Key LZ78 -> LZ78 a -> LZ78 a

replace :: Key LZ78 -> a -> LZ78 a -> LZ78 a

FoldableWithKey LZ78

Methods

toKeyedList :: LZ78 a -> [(Key LZ78, a)]

foldMapWithKey :: Monoid m => (Key LZ78 -> a -> m) -> LZ78 a -> m

foldrWithKey :: (Key LZ78 -> a -> b -> b) -> b -> LZ78 a -> b

foldlWithKey :: (b -> Key LZ78 -> a -> b) -> b -> LZ78 a -> b

Pointed LZ78

Methods

point :: a -> LZ78 a

Eq a => Eq (LZ78 a)

Methods

(==) :: LZ78 a -> LZ78 a -> Bool

(/=) :: LZ78 a -> LZ78 a -> Bool

Ord a => Ord (LZ78 a)

Methods

compare :: LZ78 a -> LZ78 a -> Ordering

(<) :: LZ78 a -> LZ78 a -> Bool

(<=) :: LZ78 a -> LZ78 a -> Bool

(>) :: LZ78 a -> LZ78 a -> Bool

(>=) :: LZ78 a -> LZ78 a -> Bool

max :: LZ78 a -> LZ78 a -> LZ78 a

min :: LZ78 a -> LZ78 a -> LZ78 a

(Read a, Hashable a, Eq a) => Read (LZ78 a)

Methods

readsPrec :: Int -> ReadS (LZ78 a)

readList :: ReadS [LZ78 a]

readPrec :: ReadPrec (LZ78 a)

readListPrec :: ReadPrec [LZ78 a]

Show a => Show (LZ78 a)

Methods

showsPrec :: Int -> LZ78 a -> ShowS

show :: LZ78 a -> String

showList :: [LZ78 a] -> ShowS

Generator (LZ78 a)

Associated Types

type Elem (LZ78 a) :: *

Methods

mapReduce :: (Reducer e m, Monoid m) => (Elem (LZ78 a) -> e) -> LZ78 a -> m

mapTo :: (Reducer e m, Monoid m) => (Elem (LZ78 a) -> e) -> m -> LZ78 a -> m

mapFrom :: (Reducer e m, Monoid m) => (Elem (LZ78 a) -> e) -> LZ78 a -> m -> m

type Key LZ78

type Key LZ78 = Int

type Elem (LZ78 a)

type Elem (LZ78 a) = a

Encoding

encode :: (Hashable a, Eq a) => [a] -> LZ78 a

O(n) Construct an LZ78-compressed Generator using a HashMap internally.

encodeOrd :: Ord a => [a] -> LZ78 a

O(n log n) Contruct an LZ78-compressed Generator using a Map internally.

encodeEq :: Eq a => [a] -> LZ78 a

O(n^2) Contruct an LZ78-compressed Generator using a list internally, requires an instance of Eq, less efficient than encode.

Decoding (reduce)

decode :: LZ78 a -> [a]

A type-constrained reduce operation

Recoding

recode :: (Eq a, Hashable a) => LZ78 a -> LZ78 a

O(n). Recompress with Hashable

recodeOrd :: Ord a => LZ78 a -> LZ78 a

O(n log n). Recompress with Ord

recodeEq :: Eq a => LZ78 a -> LZ78 a

O(n^2). Recompress with Eq

Unsafe (exposes internal structure)

data Entry i a

Constructors

Entry !i a

Instances

Functor (Entry i)

Methods

fmap :: (a -> b) -> Entry i a -> Entry i b

(<$) :: a -> Entry i b -> Entry i a

Comonad (Entry i)

Methods

extract :: Entry i a -> a

duplicate :: Entry i a -> Entry i (Entry i a)

extend :: (Entry i a -> b) -> Entry i a -> Entry i b

Extend (Entry i)

Methods

duplicated :: Entry i a -> Entry i (Entry i a)

extended :: (Entry i a -> b) -> Entry i a -> Entry i b

Eq i => Eq (Entry i a)

Methods

(==) :: Entry i a -> Entry i a -> Bool

(/=) :: Entry i a -> Entry i a -> Bool

Ord i => Ord (Entry i a)

Methods

compare :: Entry i a -> Entry i a -> Ordering

(<) :: Entry i a -> Entry i a -> Bool

(<=) :: Entry i a -> Entry i a -> Bool

(>) :: Entry i a -> Entry i a -> Bool

(>=) :: Entry i a -> Entry i a -> Bool

max :: Entry i a -> Entry i a -> Entry i a

min :: Entry i a -> Entry i a -> Entry i a

(Read a, Read i) => Read (Entry i a)

Methods

readsPrec :: Int -> ReadS (Entry i a)

readList :: ReadS [Entry i a]

readPrec :: ReadPrec (Entry i a)

readListPrec :: ReadPrec [Entry i a]

(Show a, Show i) => Show (Entry i a)

Methods

showsPrec :: Int -> Entry i a -> ShowS

show :: Entry i a -> String

showList :: [Entry i a] -> ShowS

Hashable i => Hashable (Entry i a)

Methods

hashWithSalt :: Int -> Entry i a -> Int

hash :: Entry i a -> Int

entries :: LZ78 a -> LZ78 (Entry Int a)

exposes internal structure