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

[Greg Meredith]

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

On 8/1/07, Greg Meredith <lgreg.meredith at biosimilarity.com> wrote:
>
> Haskellians,
>
> Though the actual metaphor in the monads-via-loops doesn't seem to fly
> with this audience, i like the spirit of the communication and the implicit
> challenge: find a pithy slogan that -- for a particular audience, like
> imperative programmers -- serves to uncover the essence of the notion. i
> can't really address that audience as my first real exposure to programming
> was scheme and i moved into concurrency and reflection after that and only
> ever used imperative languages as means to an end. That said, i think i
> found another metaphor that summarizes the notion for me. In the same way
> that the group axioms organize notions of symmetry, including addition,
> multiplication, reflections, translations, rotations, ... the monad(ic
> axioms) organize(s) notions of snapshot (return) and update (bind),
> including state, i/o, control, .... In short
>
> group : symmetry :: monad : update
>
> Best wishes,
>
> --greg
>
> --
> L.G. Meredith
> Managing Partner
> Biosimilarity LLC
> 505 N 72nd St
> Seattle, WA 98103
>
> +1 206.650.3740
>
> http://biosimilarity.blogspot.com




-- 
L.G. Meredith
Managing Partner
Biosimilarity LLC
505 N 72nd St
Seattle, WA 98103

+1 206.650.3740

http://biosimilarity.blogspot.com
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