Summary. A semantics for the Clear specification language is given. The language of set theory is employed to present constructions corresponding to Clear's specification-combining operations, which are then used as the basis for a denotational semantics. This is in contrast to Burstall and Goguen's 1980 semantics which described the meanings of these operations

In this paper we continue previous work from 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 the two 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, for obtaining all our results, new categorical constructions of multiple pushouts, amalgamations and extensions, gen...