[Haskell-cafe] Invertible functions list

[Antoine Latter]

On Mon, Dec 28, 2009 at 10:32 PM, Jonathan Fischoff
<jonathangfischoff at gmail.com> wrote:
> 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?

It looks like the thrist package should help you out:

http://hackage.haskell.org/cgi-bin/hackage-scripts/package/thrist

You could define some sort of type Iso:

data Iso a b = Iso (a -> b) (b -> a)

And then build a Thrist and fold over it, the functions forward and
backwards can both be implemented with right-folds.