  Automatic Program Repair (APR) has garnered significant attention as a
practical research domain focused on automatically fixing bugs in programs.
While existing APR techniques primarily target imperative programming languages
like C and Java, there is a growing need for effective solutions applicable to
declarative software specification languages. This paper presents a systematic
investigation into the capacity of Large Language Models (LLMs) for repairing
declarative specifications in Alloy, a declarative formal language used for
software specification. We propose a novel repair pipeline that integrates a
dual-agent LLM framework, comprising a Repair Agent and a Prompt Agent. Through
extensive empirical evaluation, we compare the effectiveness of LLM-based
repair with state-of-the-art Alloy APR techniques on a comprehensive set of
benchmarks. Our study reveals that LLMs, particularly GPT-4 variants,
outperform existing techniques in terms of repair efficacy, albeit with a
marginal increase in runtime and token usage. This research contributes to
advancing the field of automatic repair for declarative specifications and
highlights the promising potential of LLMs in this domain.
