This might be pertinent:

Alimarine et al, "There and Back Again: Arrows for Invertible Programming"
http://www.cs.ru.nl/A.vanWeelden/bi-arrows/

Jonathan Fischoff 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?

-Jonathan


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