Toy compression implementations

This code is provided in the hope that someone might find it interesting/entertaining, and to demonstrate what an excellent programming language Haskell truly is. (A working polymorphic LZW implementation in 10 lines? Try that in Java!)

This is 'toy' code. Please don't try to use it to compress multi-GB of data. It has not been thoroughly checked for correctly, and I shudder to think what the time and space complexity would be like! However, it is enlightening and entertaining to see how many algorithms you can implement with a handful of lines...

MathematicalOrchid 16:46, 15 February 2007 (UTC)

module Compression where

import Data.List


-- Run-length encoding

encode_RLE :: (Eq x) => [x] -> [(Int,x)]
encode_RLE = map (\xs -> (length xs, head xs)) . groupBy (==)

decode_RLE :: [(Int,x)] -> [x]
decode_RLE = concatMap (uncurry replicate)


-- Limpel-Ziv-Welsh compression (Recommend using [Word8] or [SmallAlpha] for input!)

encode_LZW :: (Eq x, Enum x, Bounded x) => [x] -> [Int]
encode_LZW [] = []
encode_LZW (x:xs) = work init [x] xs where
  init = map (\x -> [x]) $ enumFromTo minBound maxBound
  work table buffer []     = [maybe undefined id (elemIndex buffer table)]
  work table buffer (x:xs) =
    let new = buffer ++ [x]
    in  case elemIndex new table of
          Nothing -> maybe undefined id (elemIndex buffer table) : work (table ++ [new]) [x] xs
          Just _  -> work table new xs

-- TODO: Matching decode_LZW function.

-- TODO: Huffman encoding.

-- TODO: Arithmetic coding.

It may also be useful to add the following for test purposes:

import Data.Word

data SmallAlpha = AA | BB | CC | DD deriving (Show, Eq, Ord, Enum, Bounded)

parse1 'a' = AA
parse1 'b' = BB
parse1 'c' = CC
parse1  _  = DD -- For safety

parse = map parse1

Anybody know how to use newtype to make a type like Char but with minBound and maxBound much closer together?