A Category Theoretic Interpretation of Gandy's Principles for Mechanisms

Abstract

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.

Physical computing: a category theoretic perspective on physical computation and system compositionality

“…This principle invites further exploration of the theoretical limits of ideal physical computing machines, particularly their relation to category theory. Interestingly, Gandy's machines have attracted a category-theoretic axiomatic treatment of update rules to finite objects [51]. Future work will deepen our understanding of these relationships and the role of our categorical model in physical computation.…”