Partial pushout semantics of generics in DOL

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 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.