A Coq Mechanization of JavaScript Regular Expression Semantics: Executable, Proven-Safe, and Faithful

Core Concepts

Faithfully mechanizing ECMAScript regexes in Coq ensures safety, usability, and future-proofing.

Abstract

The content discusses the first faithful mechanization of JavaScript regular expression matching in an interactive theorem prover. It highlights challenges faced during the process and demonstrates the usability and versatility of the mechanization through various analyses and experiments. The mechanization can be extracted to OCaml for an executable engine that aligns with the official Test262 conformance test suite. The complexity of ECMAScript regex semantics is explored, emphasizing extended features unique to JavaScript. The paper addresses issues with existing formal models of JavaScript regexes and presents a shallow-embedded Coq mechanization technique. Encoding potentially failing operations using an error monad ensures correctness while handling non-local operations with zipper contexts enables context-aware processing. Arbitrary recursion is managed through a fuel-based solution to ensure termination. New semantic properties are derived and mechanized to validate the ECMAScript specification's correctness.

Stats

33 pages of pseudocode translated into Coq definitions. More than 30% of JavaScript npm packages rely on regexes. Multiple revisions of ECMAScript standard with significant additions or refactorings in regex section. Matcher functions follow specific control-flow ending in mismatch or continuation call. Contextualized sub-regexes represented using zippers for navigation.

Quotes

"We present an executable, proven-safe, faithful and future-proof Coq mechanization of ECMAScript regexes." - Authors "The official ECMAScript regex standard is verbose and complex." - Content "Assertions are used extensively in the specification to clarify algorithms." - ECMA 2023

Key Insights Distilled From

A Coq Mechanization of JavaScript Regular Expression Semantics

by Noé ... at arxiv.org 03-19-2024

https://arxiv.org/pdf/2403.11919.pdf

Deeper Inquiries

How does encoding potentially failing operations using an error monad impact the overall correctness?

Encoding potentially failing operations using an error monad ensures that assertions and other potential failures in the ECMAScript specification are faithfully represented in the Coq mechanization. By utilizing this approach, we can maintain close adherence to the original pseudocode while also providing a mechanism to handle errors and assertion failures within the Coq environment. This method allows us to capture and address potential issues that may arise during execution, ensuring that the mechanization remains aligned with the intended behavior outlined in the specification. Additionally, by incorporating these error-handling mechanisms, we can verify and prove properties related to correctness, such as absence of crashes or out-of-bounds array accesses.

How do non-local operations encoded with zipper contexts impact context-aware processing?

Non-local operations encoded with zipper contexts play a crucial role in enabling context-aware processing within the Coq mechanization of JavaScript regular expressions. The use of zipper contexts allows for efficient navigation through complex data structures like ASTs (Abstract Syntax Trees) by maintaining information about both individual nodes and their relationships within a larger structure. In this case, when dealing with regexes where certain functions require knowledge of their position relative to other elements in the AST or even at higher levels of nesting, zipper contexts provide a way to track this contextual information effectively. By leveraging zipper contexts, we can accurately relate sub-regexes back to their parent regexes or root structures, facilitating precise context-aware processing required for various functionalities specified in ECMAScript.

How can the fuel-based solution for arbitrary recursion ensure termination without deviating from the original pseudocode?

The fuel-based solution for handling arbitrary recursion ensures termination without deviating from the original pseudocode by introducing an additional parameter representing "fuel" into recursive functions. This fuel parameter acts as a form of resource constraint that limits recursive calls based on available units of fuel provided during function invocation. As each recursive call consumes one unit of fuel until it reaches zero, functions will terminate when they run out of fuel rather than infinitely recursing. By incorporating this approach into non-terminating functions specified in ECMAScript regex matching algorithms – such as RepeatMatcher – we establish a structured mechanism for controlling recursion depth and preventing infinite loops while remaining faithful to the original specifications outlined in pseudocode format. Through formal verification methods supported by Coq's type system and proof capabilities, we can ensure that these modified functions adhere to termination requirements set forth by both theoretical considerations and practical implementation needs without straying from established algorithmic logic prescribed by ECMAScript standards.