I was hoping that

let notBoth1 a b = not (a == 1 && b == 1) in
groupBy notBoth1  [1,1,2,3,1,1,4,5,6,1]

would give me

[[1],[1,2,3,1],[1,4,5,6,1]]

but instead I get

[[1],[1,2,3],[1],[1,4,5,6],[1]]

It seems that groupBy assumes transitivity in the argument function. I have a new implementation that does not make this assumption. Of course, the implications of changing this function's behavior are troubling.

groupBy' :: (a -> a -> Bool) -> [a] -> [[a]]
groupBy' p (x : xs) = go [x] xs
    where
      go (x : xs) (y : zs) | p x y = go (y : x : xs) zs
      go g (y : zs) = reverse g : go [y] zs
      go g [] = [reverse g]