We further investigate the use of LR-based parsing for languages generated by hyperedge replacement grammars (HRGs). Previous work successfully used predictive shift-reduce (PSR) parsing. Here, we turn our attention to positional LR (pLR) parsing. This approach has been devised to parse many kinds of non-string languages mainly in the domain of visual languages, such as iconic, box, box-and-arrows, and statechart-like languages, among others. Moreover, several tools based on positional parsers have been implemented so far.

In this paper, we give formal rules to translate HRGs into positional grammars: we first provide a simple translation to generic positional grammars and then define an algorithm to transform these grammars into well-formed positional grammars, i.e., grammars that are guaranteed to be parsable according to the positional parsing methodology. We show how the pLR parsing methodology applies to hypergraph languages, that it always guarantees the construction of a parser, and discuss the time and space complexity of the well-forming transformation. As a further contribution we implement our approach in a prototype tool and demonstrate it on the running example.