The rising popularity of declarative languages and the hard to debug nature thereof have motivated the need for applicable, automated repair techniques for such languages. However, despite significant advances in the program repair of imperative languages, there is a dearth of repair techniques for declarative languages. This paper presents BeAFix, an automated program repair technique for faulty models written in Alloy, a declarative language based on first-order relational logic. BeAFix is backed with a novel strategy for bounded exhaustive, yet scalable, exploration of the spaces of fix candidates and a formally rigorous, sound pruning of such spaces. Moreover, different from the state-of-the-art in Alloy program repair, that relies on the availability of unit tests, BeAFix does not require tests and can work with assertions that are naturally used in declarative languages. Our experience with using BeAFix to repair thousands of real-world faulty models, collected by other researchers, corroborates its ability to effectively generate correct repairs and outperform the state-of-the-art.