Compositionality and compatibility of parameterization and parameter passing in specification languages

Abstract

In this paper we continue previous work by Sannella, Sokolowski and Tarlecki on parameterization in specification languages. Within the loose approach, we define specification and model level semantics for two kinds of parameterizations (parameterized specifications and specifications of parameterized data types) and describe, in a compositional manner, parameter passing at both levels. Moreover, the specification and the model level semantics of parameter passing are shown to be compatible. We also show that the results obtained do not only apply to the loose approach but can also be directly applicable to the initial framework, and in general to any other kind of monomorphic framework (i.e., a framework where all specifications are monomorphic). In particular, the results obtained generalize and extend previous results for the initial approach. Finally, to obtain our results, new categorical constructions of multiple pushouts, amalgamations and extensions, which generalize standard notions of pushouts, amalgamations and extensions, had to be introduced.