A categorical reduction system for linear logic
Logic in Computer Science
2020-10-09 v2
Abstract
Diagram chasing is not an easy task. The coherence holds in a generalized sense if we have a mechanical method to judge whether given two morphisms are equal to each other. A simple way to this end is to reform a concerned category into a calculus, where the instructions for the diagram chasing are given in the form of rewriting rules. We apply this idea to the categorical semantics of the linear logic. We build a calculus directly on the free category of the semantics. It enables us to perform diagram chasing as essentially one-way computations led by the rewriting rules. We verify the weak termination property of this calculus. This gives the first step towards the mechanization of diagram chasing.
Cite
@article{arxiv.1912.00629,
title = {A categorical reduction system for linear logic},
author = {Ryu Hasegawa},
journal= {arXiv preprint arXiv:1912.00629},
year = {2020}
}