Grammar Repair with Examples and Tree Automata: Extended Version

TL;DR

This paper introduces a novel method for repairing ambiguous context-free grammars using tree automata learned from examples, ensuring unambiguous, user-preferred syntax suitable for parser generation.

Contribution

It presents a new tree automata learning algorithm and an efficient intersection method, enabling automated grammar repair based on user examples, improving parser correctness.

Findings

The approach effectively repairs ambiguous grammars in case studies.

The algorithms are proven sound and implemented in the Greta tool.

Automated grammar repair aligns with user preferences for syntax.

Abstract

Context-free grammars (CFGs) are the de-facto formalism for declaratively describing concrete syntax for programming languages and generating parsers. One of the major challenges in defining a desired syntax is ruling out all possible ambiguities in the CFG productions that determine scoping rules as well as operator precedence and associativity. Practical tools for parser generation typically apply ad-hoc approaches for resolving such ambiguities, which might result in a parser's behavior that contradicts the intents of the language designer. In this work, we present a user-friendly approach to soundly repair grammars with ambiguities, which is inspired by the programming by example line of research in automated program synthesis. At the heart of our approach is the interpretation of both the initial CFG and additional examples that define the desired restrictions in precedence and associativity, as tree automata (TAs). The technical novelties of our approach are (1) a new TA learning algorithm that constructs an automaton based on the original grammar and examples that encode the user's preferred ways of resolving ambiguities all in a single TA, and (2) an efficient algorithm for TA intersection that utilises reachability analysis and optimizations that significantly reduce the size of the resulting automaton, which results in idiomatic CFGs amenable to parser generators. We have proven the soundness of the algorithms, and implemented our approach in a tool called Greta, demonstrating its effectiveness on a series of case studies.