LZW routine in Haskell using Monads - haskell

Question

I'm trying to implement LZW compression in Haskell using Monads, here is my code so far with test cases:
{-# LANGUAGE FlexibleInstances #-}
{-# LANGUAGE MultiParamTypeClasses #-}
{-# LANGUAGE FlexibleContexts #-}
import Control.Monad.State
import Control.Monad.Writer
import Data.Char (chr, ord)
import Data.List (isPrefixOf, maximumBy)
import Data.Function
import Test.QuickCheck
type Dictionary = [String]
dictionary :: Dictionary
dictionary = [[chr x] | x <- [0..127]]
test_dictionary =
[ map ord (concat dictionary) == [0..127]
, all (\str -> length str == 1) dictionary
]
prefixes :: String -> Dictionary -> [(Int, String)]
prefixes str dict = [(x, dict!!x) | x <- [0..length dict - 1], isPrefixOf (dict!!x) str]
test_prefixes =
[ prefixes "" dictionary == []
, prefixes "appletree" [] == []
, prefixes "appletree" ["ap", "apple", "tree", "pear"] == [(0, "ap"), (1, "apple")]
, prefixes "babe" dictionary == [(98, "b")]
]
longest :: [(Int, String)] -> (Int, String)
longest prefs = maximumBy (compare `on` (\(x,y) -> length y)) prefs
test_longest =
[ longest [(30, "a"), (20, "abc"), (15, "ab")] == (20, "abc")
, longest [(30, "a"), (20, "abc"), (15, "abc")] == (15, "abc")
]
instance MonadState Dictionary ((->) Dictionary) where
get = \s -> s
munch :: MonadState Dictionary m => String -> m (Int, String, String)
munch str = do
dict <- get
let longst = longest (prefixes str dict)
return (fst longst, snd longst, [str!!x | x <- [length (snd longst)..length str - 1]])
test_munch =
[ evalState (munch "a") ["a"] == (0, "a", "")
, evalState (munch "appletree") ["a"] == (0, "a", "ppletree")
, evalState (munch "peach") ["a", "ba", "b"] == (1, "ba", "be")
]
instance MonadState m (StateT Dictionary ((->) m)) where
append :: MonadState Dictionary m => String -> String -> m ()
append s "" = return ()
append s w = do
dict <- get
let newWord = s ++ (take 1 w)
if (notElem newWord dict)
then do
put (dict++[newWord])
else return ()
test_append =
[ execState (append "a" "") [] == []
, execState (append "a" "") dictionary == dictionary
, execState (append "a" "bc") [] == ["ab"]
, execState (append "a" "bc") ["ab"] == ["ab"]
]
encode :: String -> WriterT [Int] (State Dictionary) ()
encode "" = return ()
encode w = do
dict <- get
let (a, b, c) = (munch w) dict
if length dict < 256
then do
tell [a]
put ((append b c) dict)
encode c
else return ()
test_encode =
[ evalState (execWriterT (encode "")) [] == []
, evalState (execWriterT (encode "aaa")) ["a"] == [0, 1]
, evalState (execWriterT (encode "aaaa")) ["a"] == [0, 1, 0]
, evalState (execWriterT (encode "aaaaa")) ["a"] == [0, 1, 1]
, evalState (execWriterT (encode "abababab")) ["a", "b"] == [0, 1, 2, 4, 1]
, evalState (execWriterT (encode "aaabbbccc")) dictionary
== [97, 128, 98, 130, 99, 132]
]
decode :: [Int] -> WriterT String (State Dictionary) ()
decode [] = return ()
decode [x] = do
dict <- get
tell (dict!!x)
decode (x:xs) = do
dict <- get
let f = dict!!x
let s = if(length dict > head xs)
then dict!!head xs
else f
tell f
put (append f s) dict
decode xs
test_decode =
[ evalState (execWriterT (decode [])) [] == []
, evalState (execWriterT (decode [0])) ["a"] == "a"
, evalState (execWriterT (decode [0, 1, 1, 0])) ["a", "b"] == "abba"
, evalState (execWriterT (decode [0, 1, 2, 0])) ["a", "b"] == "ababa"
, evalState (execWriterT (decode [0, 1, 2, 4, 1])) ["a", "b"] == "abababab"
, evalState (execWriterT (decode [97, 128, 98, 130, 99, 132])) dictionary
== "aaabbbccc"
]
compress :: String -> [Int]
compress w = evalState (execWriterT (encode w)) dictionary
test_compress =
[ compress "" == []
, compress "a" == [97]
, compress "aaa" == [97, 128]
, compress "aaabbbccc" == [97, 128, 98, 130, 99, 132]
]
decompress :: [Int] -> String
decompress list = evalState (execWriterT (decode list)) dictionary
test_decompress =
[ decompress [] == ""
, decompress [97] == "a"
, decompress [97, 128] == "aaa"
, decompress [97, 128, 98, 130, 99, 132] == "aaabbbccc"
]
prop_compressDecompress :: String -> Bool
prop_compressDecompress w = do
let tmp = [chr (div (ord x) 2) | x <- w]
decompress (compress tmp) == tmp
compressFile :: FilePath -> FilePath -> IO ()
compressFile source target = do
s <- readFile source
let compressed = compress s
let chars = [chr x | x <- compressed]
writeFile target chars
decompressFile :: FilePath -> FilePath -> IO ()
decompressFile source target = do
s <- readFile source
let code = [ord x | x <- s]
let decompressed = decompress code
writeFile target decompressed
allTests = [test_dictionary, test_prefixes, test_longest, test_munch, test_append
,test_encode
--, test_decode, test_compress, test_decompress
]
main = do
--quickCheck prop_compressDecompress
print (allTests, and (concat allTests))
With this code I get the following error (referring to the use of put in "encode" and "decode" functions) :
Main.hs#80:13-80:16 No instance for (MonadState () (StateT Dictionary Data.Functor.Identity.Identity)) arising from a use of put
I've tried to define this instance but the best I could achieve is a "functional dependencies conflict between instance declarations" error.
I know there is more simple solutions without Monads but I have to use them, also the types of the functions are not to be modified.
Could you give me any help about what I'm doing wrong here?

Answer 1

You don't need to write any instances. You're simply using append and munch in a wrong way.
append has type MonadState Dictionary m => String -> String -> m ().
If f and s are strings, then append f s yields a state-modifying action that eventually returns a ().
put has type MonadState s m => s -> m (). put replaces the current state with the s argument.
In the light of this, put (append f s) dict makes little sense. You're supposed to supply put a single argument. And you don't have to do anything with dict there; a core point of using the State monad is that the state is left implicit, and there is no need to pass it around.
Also, append f s by itself already updates the state. So what you want here is simply append f s, instead of put (append x y) dict.
There's a similar error in encode with munch; it has a single String argument, so (munch w) dict is erroneous. Again, no need to touch dict. Also, because munch w yields a monadic result, you must bind the result with <- instead of let. So, you should replace let (a, b, c) = (much w dict) with (a, b, c) <- munch w.

Answer 2

put ((append b c) dict)
looks wrong. append is already a monadic action, so it should be enough to use
append b c