Formal Verification for JavaScript Regular Expressions: a Proven Semantics and its Applications

2025-07-17

AI Summary

This paper addresses the lack of a formal, faithful, and practical semantic model for modern regular expressions—particularly those with backtracking semantics. We present the first mechanized semantics for JavaScript regular expressions, fully supporting backtracking and provably equivalent to the ECMAScript specification. Our approach leverages the Coq proof assistant (Rocq) to achieve full mechanization: we introduce *contextual equivalence* as a novel behavioral characterization of regexes and deliver the first formal correctness proof of the PikeVM algorithm; additionally, we explicitly model the complete backtracking tree to precisely capture all matches and their priority order. Key contributions include: (1) the first fully verified semantic model for JavaScript regular expressions; (2) a concise, faithful, and complete formalization of backtracking semantics; and (3) foundational support for verifying regex rewriting rules and formally guaranteeing mainstream engine algorithms.

Technology Category

• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

We present the first mechanized, succinct, practical, complete, and proven-faithful semantics for a modern regular expression language with backtracking semantics. We ensure its faithfulness by proving it equivalent to a preexisting line-by-line embedding of the official ECMAScript specification of JavaScript regular expressions. We demonstrate its practicality by presenting two real-world applications. First, a new notion of contextual equivalence for modern regular expressions, which we use to prove or disprove rewrites drawn from previous work. Second, the first formal proof of the PikeVM algorithm used in many real-world engines. In contrast with the specification and other formalization work, our semantics captures not only the top-priority match, but a full backtracking tree recording all possible matches and their respective priority. All our definitions and results have been mechanized in the Rocq proof assistant.

Problem

• Mechanized semantics for JavaScript regex with backtracking
• Proving contextual equivalence for regex rewrites
• Formal verification of PikeVM algorithm in regex engines

Innovation

• Mechanized semantics for JavaScript regex
• Contextual equivalence for regex rewrites
• Formal proof of PikeVM algorithm