[Haskell-cafe] Re: monads and groups -- instead of loops

Dan Weston westondan at imageworks.com
Wed Aug 1 22:08:43 EDT 2007

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


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

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