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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 <wad...@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. >