  Relating formal grammars is a hard problem that balances between language
equivalence (which is known to be undecidable) and grammar identity (which is
trivial). In this paper, we investigate several milestones between those two
extremes and propose a methodology for inconsistency management in grammar
engineering. While conventional grammar convergence is a practical approach
relying on human experts to encode differences as transformation steps, guided
grammar convergence is a more narrowly applicable technique that infers such
transformation steps automatically by normalising the grammars and establishing
a structural equivalence relation between them. This allows us to perform a
case study with automatically inferring bidirectional transformations between
11 grammars (in a broad sense) of the same artificial functional language:
parser specifications with different combinator libraries, definite clause
grammars, concrete syntax definitions, algebraic data types, metamodels, XML
schemata, object models.
