If you haven't read it, you might be interested in the paper Alimarine et al, "There and Back Again: Arrows for Invertible Programming" which can be found at http://www.st.cs.ru.nl/papers/2005/alia2005-biarrowsHaskellWorkshop.pdf Dan Weston Greg Meredith wrote:
Haskellians,
But, along these lines i have been wondering for a while... the monad laws present an alternative categorification of monoid. At least it's alternative to monoidoid. In the spirit of this thought, does anyone know of an expansion of the monad axioms to include an inverse action? Here, i am following an analogy
monoidoid : monad :: groupoid : ???
i did a search of the literature, but was probably using the wrong terminology to try to find references. i would be very grateful for anyone who might point me in the right direction.
My intuition tells me this could be quite generally useful to computing in situation where boxing and updating have natural (or yet to be discovered) candidates for undo operations. i'm given to understand reversible computing might be a good thing to be thinking about if QC ever gets real... ;-)
Best wishes,
--greg