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(**) Eliminate consecutive duplicates of list elements.

compress :: Eq a => [a] -> [a]
compress = map head . group

We simply group equal values together (using, then take the head of each. Note that (with GHC) we must give an explicit type to compress otherwise we get:

Ambiguous type variable `a' in the constraint:
      `Eq a'
	arising from use of `group'	
    Possible cause: the monomorphism restriction applied to the following:
      compress :: [a] -> [a]
    Probable fix: give these definition(s) an explicit type signature
		  or use -fno-monomorphism-restriction

We can circumvent the monomorphism restriction by writing compress this way (See: section 4.5.4 of the report):

compress xs = map head $ group xs

An alternative solution is

compress (x:ys@(y:_))
    | x == y    = compress ys
    | otherwise = x : compress ys
compress ys = ys

Another possibility using foldr

compress :: (Eq a) => [a] -> [a]
compress = foldr skipDups []
    where skipDups x [] = [x]
          skipDups x acc
                | x == head acc = acc
                | otherwise = x : acc

A very simple approach:

compress []     = []
compress (x:xs) = [x] ++ (compress $ dropWhile (== x) xs)

Another approach, using foldr

compress :: Eq a => [a] -> [a]
compress x = foldr (\a b -> if a == (head b) then b else a:b) [last x] x