[TYPES] What algebra am I thinking of?

Radu Grigore radugrigore at gmail.com
Tue Mar 27 04:03:11 EDT 2018

You might want to look at vector addition systems, aka Petri Nets.
"Displacements" are from Z^d, but current values are from N^d, as in your
case. But, unlike your case, the dimension d is typically finite.

The restriction to nonnegative integers makes all sorts of problems harder
than they'd otherwise be.

On Tue, Mar 27, 2018 at 6:19 AM Philip Wadler <wadler at inf.ed.ac.uk> wrote:

> [ The Types Forum, http://lists.seas.upenn.edu/mailman/listinfo/types-list
> ]
> Consider a blockchain managing several different resources. Over time, new
> resources may be added or deleted. Each input to or output from a
> transaction is associated with a value, where each value consists of
> associating zero or more resources with amounts, where the amounts are
> natural numbers (that is, integers greater than or equal to zero).
> What kind of algebra do values correspond to? It seems similar to vector
> spaces, except:
>   (a) adding or deleting resources increases or decreases the number of
> dimensions in the vector space
>   (b) the scalars in the vector space are natural numbers rather than reals
> What algebra am I thinking of? Cheers, -- P
> .   \ Philip Wadler, Professor of Theoretical Computer Science,
> .   /\ School of Informatics, University of Edinburgh
> .  /  \ and Senior Research Fellow, IOHK
> . http://homepages.inf.ed.ac.uk/wadler/
> The University of Edinburgh is a charitable body, registered in
> Scotland, with registration number SC005336.

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