Simplified Parsing Expression Derivatives

TL;DR

This paper introduces a simplified and more efficient derivative parsing algorithm for parsing expression grammars, improving performance and space bounds while providing a formal correctness proof.

Contribution

It presents a new derivative parsing algorithm that is simpler, faster, and more space-efficient than previous methods, with a formal correctness proof.

Findings

Improves worst-case space and runtime bounds by a linear factor

Reduces runtime by about half in practical scenarios

Provides a formal proof of correctness for the new algorithm

Abstract

This paper presents a new derivative parsing algorithm for parsing expression grammars; this new algorithm is both simpler and faster than the existing parsing expression derivative algorithm presented by Moss. This new algorithm improves on the worst-case space and runtime bounds of the previous algorithm by a linear factor, as well as decreasing runtime by about half in practice. A proof of correctness for the new algorithm is included in this paper, a result not present in earlier work.