[Haskell-cafe] Invertible functions list

Hi, I would to create a list of tuples (or something similar) of invertible functions [((a -> b), (b -> a)), ((b -> c), (c -> b)), .... Such that I could call forward invertibleFuctionList domainValue = ? -- composite all the functions backward invertibleFuctionList rangeValue = forward (reverse invertibleFuctionList) rangeValue -- or something similar I would also like to concat them. This sounds like a job for GADT that someone might have already tackled. Any ideas? -Jonathan