A Category Theoretic Interpretation of Gandy's Principles for Mechanisms

04/23/2019

∙

by   Joseph Razavi, et al.

∙

0

∙

share

Based on Gandy's principles for models of computation we give category-theoretic axioms describing locally deterministic updates to finite objects. Rather than fixing a particular category of states, we describe what properties such a category should have. The computation is modelled by a functor that encodes updating the computation, and we give an abstract account of such functors. We show that every updating functor satisfying our conditions is computable.