My master's thesis, A formal grammar definition to describe Multidimensional Languages, studies how to define and parse visual or multidimensional languages with a more practical and declarative formalism.
The work starts from the limits of existing approaches for visual languages, especially Positional Grammars and their extended variants: they are expressive and parser-friendly, but often difficult to write because of operational syntax and structural constraints.
The core contribution is a renewed definition of Multidimensional Grammars (MG), designed to be easier to read, easier to author, and still expressive enough to model non-trivial visual languages such as flow-based and diagrammatic notations.
The thesis then introduces an algorithm to convert MG into valid Positional Grammars so the same language can be parsed using existing parser-generation techniques. The implementation also includes tooling work, with an LSP-based language server and a conversion utility to make the formalism usable from modern editors and IDEs.
In short, the project sits at the intersection of formal languages, parsing, and developer tooling: the goal is to make multidimensional languages more approachable in practice without giving up rigor.