compareWithBackspace.hs

pop :: [a] -> [a]
pop [] = []
pop (x:xs) = xs

compareWithBackspace :: String -> String -> Bool
compareWithBackspace xs ys = compare' s1 s2
  where s1 = buildStack xs
        s2 = buildStack ys

buildStack :: String -> String
buildStack xs =  buildStack' xs []

buildStack' :: String -> String -> String
buildStack' [] ys = ys
buildStack' ('#':xs) ys = buildStack' xs $ pop ys
buildStack' (x:xs) ys = buildStack' xs (x:ys)

compare' :: Eq a => [a] -> [a] -> Bool
compare' xs ys = and $ (length xs == length ys) : (zipWith (==) xs ys)

gistfile1.txt

GHCi, version 8.0.2: http://www.haskell.org/ghc/  :? for help
Prelude> :l compareWithBackspace.hs
[1 of 1] Compiling Main             ( compareWithBackspace.hs, interpreted )
Ok, modules loaded: Main.
*Main> compareWithBackspace "a##c" "#a#c"
True
*Main> compareWithBackspace "xy##" "z#w#"
True