Partial Pushout Semantics of Generics in DOL

Till Mossakowski; Bernd Krieg-Brückner

In: Theoretical Computer Science (TCS), Vol. 741, Pages 58-70, Elsevier, 2018.


We combine CASL’s pushout-style generic specification with DOL’s filtering, the latter being a syntactic removal of parts of a specification. The challenge is that now the body of a generic specification can remove parts of the formal parameter. This cannot be handled with usual pushout semantics, but calls for a semantics of “match, delete, glue in” as used in the theory of graph grammars. We hence employ Heindel’s theory of MipMap categories as a basis for the use of pushouts in categories of partialmaps. We introduce a notion of MipMap institution that can serve as a semantic background for a partial pushout seman-tics of generics with filtering.

Deutsches Forschungszentrum für Künstliche Intelligenz
German Research Center for Artificial Intelligence