Proof Diagrams for Multiplicative Linear Logic

TL;DR

This paper introduces a novel interpretation of proof nets for multiplicative linear logic using string diagrams, enabling efficient verification of soundness and correctness in linear time.

Contribution

It presents a new framework translating proof nets into string diagrams, simplifying correctness verification at the cost of standard proof equivalence.

Findings

Soundness and well-typeness can be verified in linear time

The interpretation simplifies the proof net correctness checking process

Standard proof equivalence is not preserved in the new framework

Abstract

The original idea of proof nets can be formulated by means of interaction nets syntax. Additional machinery as switching, jumps and graph connectivity is needed in order to ensure correspondence between a proof structure and a correct proof in sequent calculus. In this paper we give an interpretation of proof nets in the syntax of string diagrams. Even though we lose standard proof equivalence, our construction allows to define a framework where soundness and well-typeness of a diagram can be verified in linear time.