A Category Theoretic Interpretation of Gandy's Principles for Mechanisms

TL;DR

This paper provides a category-theoretic framework for Gandy's principles, modeling locally deterministic updates in computation without fixing a specific state category, and proves such updates are computable.

Contribution

It introduces axioms for categories of states and characterizes computable updating functors within this abstract setting.

Findings

Every updating functor satisfying the axioms is computable.

The framework generalizes Gandy's principles using category theory.

Provides an abstract account of computation updates via functors.

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.