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