[TYPES] What algebra am I thinking of?

Matthew Meola mlmeola at gmail.com
Tue Mar 27 02:49:44 EDT 2018

I think this might be a module over a semiring. The natural numbers with
+,* form a semiring and then, over resources, would form a module over the

For the dimensional issue, you might treat it as infinite dimensional
because there are infinitely many potential resources even if not all are
available at the moment. And then take the set of sequences with finitely
many nonzero terms. This a subspace and is infinite dimensional at least
for the vector space R-infinity. Maybe that holds for this case as well.

On Tue, Mar 27, 2018 at 01:21 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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