Grammar convergence is a method that helps discovering relationships between different grammars of the same language or different language versions. The key element of the method is the operational, transformation-based representation of those relationships. Given input grammars for convergence, they are transformed until they are structurally equal. The transformations are composed from primitive operators; properties of these operators and the composed chains provide quantitative and qualitative insight into the relationships between the grammars at hand. We describe a refined method for grammar convergence, and we use it in a major study, where we recover the relationships between all the grammars that occur in the different versions of the Java Language Specification (JLS). The relationships are represented as grammar transformation chains that capture all accidental or intended differences between the JLS grammars. This method is mechanized and driven by nominal and structural differences between pairs of grammars that are subject to asymmetric, binary convergence steps. We present the underlying operator suite for grammar transformation in detail, and we illustrate the suite with many examples of transformations on the JLS grammars. We also describe the extraction effort, which was needed to make the JLS grammars amenable to automated processing. We include substantial metadata about the convergence process for the JLS so that the effort becomes reproducible and transparent.
R. Lämmel, V. Zaytsev. Recovering Grammar Relationships for the Java Language Specification, Software Quality Journal, 19:2, pages 333–378, Springer Netherlands, March 2011.

Grammar convergence is a lightweight verification method for establishing and maintaining the correspondence between grammar knowledge ingrained in all kinds of software artifacts, e.g., object models, XML schemas, parser descriptions, or language documents. The central idea is to extract grammars from diverse software artifacts, and to transform the grammars until they become syntactically identical. The present paper introduces and illustrates the basics of grammar convergence.
R. Lämmel, V. Zaytsev. An Introduction to Grammar Convergence. In Proceedings of 7th International Conference on Integrated Formal Methods (iFM 2009), LNCS 5423, pages 246–260. Springer, February 2009.

The process of grammar convergence (involving grammar extraction and transformation for structural equivalence) contains a range of technical challenges. These need to be addressed in order for the method to deliver useful results. The paper describes a DSL and the infrastructure behind it that automates the convergence process, hides negligible backend details, aids development/debugging and enables application of grammar convergence technology to large scale projects. The necessity of having a strong framework is explained by listing case studies. Domain elements such as extractors and transformation operators are described to illustrate the issues we successfully addressed.
V. Zaytsev. Language Convergence Infrastructure. In João Miguel Fernandes, Ralf Lämmel, Joost Visser, João Saraiva, editors, Post-proceedings of the 3rd International Summer School on Generative and Transformational Techniques in Software Engineering (GTTSE 2009), LNCS 6491, pages 481–497, Springer-Verlag, January 2011.

We describe a completed effort to recover the relationships between all the grammars that occur in the different versions of the Java Language Specification (JLS). The relationships are represented as grammar transformations that capture all accidental or intended differences between the JLS grammars. This process is mechanized and it is driven by simple measures of nominal or structural differences between any pair of grammars involved. Our work suggests a form of consistency management for the JLS in particular, and language specifications in general.
R. Lämmel, V. Zaytsev. Recovering Grammar Relationships for the Java Language Specification. In Proceedings of the 9th IEEE International Working Conference on Source Code Analysis and Manipulation (SCAM 2009), pages 178–186, IEEE, September 2009.