Change Actions: Models of Generalised Differentiation
Logic in Computer Science
2020-07-23 v3
Abstract
Cai et al. have recently proposed change structures as a semantic framework for incremental computation. We generalise change structures to arbitrary cartesian categories and propose the notion of change action model as a categorical model for (higher-order) generalised differentiation. Change action models naturally arise from many geometric and computational settings, such as (generalised) cartesian differential categories, group models of discrete calculus, and Kleene algebra of regular expressions. We show how to build canonical change action models on arbitrary cartesian categories, reminiscent of the F\`aa di Bruno construction.
Cite
@article{arxiv.1902.05465,
title = {Change Actions: Models of Generalised Differentiation},
author = {Mario Alvarez-Picallo and C. -H. Luke Ong},
journal= {arXiv preprint arXiv:1902.05465},
year = {2020}
}