Partial Pushout Semantics of Generics in DOL

Till Mossakowski; Bernd Krieg-Brückner
In: Theoretical Computer Science (TCS), Vol. 0, Pages 0-1, 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 \emph{partial} maps. We introduce a notion of MipMap institution that can serve as a semantic background for a partial pushout semantics of generics with filtering.

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