Tile flipping in Haskell

I wanted a little bit of assistance with a tile-flipping puzzle, so I wrote this little bit of almost-Haskell code.

let zero = replicate 4 $ replicate 4 $ False
let gshow g = putStrLn $ unlines [[if v then '#' else '.' | v <- r] | r <- g]
let flips = [(-1,0),(0,0),(1,0),(0,-1),(0,1)]
let gflip (x,y) g = [ [ ((vi-x,ri-y) `elem` flips) /= v | (v,vi) <- zip r [0..]] | (r,ri) <- zip g [0..]]
let grid l = foldr gflip zero l

It doesn't compute solutions given a puzzle; rather, it shows the result of a series of flips.

Prelude> gshow $ grid [(1,1)]
.#..
###.
.#..
....

Prelude> gshow $ grid [(2,0),(1,2),(2,3)]
.###
.##.
##..
..##

I tried a version using 2-dimensional arrays instead of lists, but gshow and gflip turned out uglier than they already are. Suggestions welcome.