Syntax Repair as Language Intersection

TL;DR

This paper presents a novel syntax repair technique for context-free languages that models repairs as language intersections, enabling efficient, provably complete, and state-of-the-art syntax error correction.

Contribution

It introduces a new formal language intersection approach for syntax repair, connecting formal language theory with program analysis to improve repair efficiency and completeness.

Findings

Polylogarithmic parallel time decidability for syntax repair

Enumeration algorithm based on Brzozowski derivative

State-of-the-art results on Python syntax repair benchmark

Abstract

We introduce a new technique for repairing syntax errors in arbitrary context-free languages. This technique models syntax repair as a language intersection problem by defining a finite language that provably generates every syntactically valid repair within a given edit distance. Leveraging a theoretical connection between the Bar-Hillel construction from formal language theory and CFL reachability from program analysis, we show that repairability in a finite number of typographic edits is polylogarithmic parallel time decidable and provide an enumeration algorithm based on the Brzozowski derivative. Finally, we evaluate this algorithm and its implementation, demonstrating state-of-the-art results on a Python syntax repair benchmark.