This paper studies the composition of modules that can hide information, over a very general class of logical systems called inclusive institutions. Two semantics are given for composition of such modules using five familiar operations, and a property called conservativity is shown necessary and sufficient for these semantics to agree. The first semantics extracts the visible properties of the result of composing the visible and hidden parts of modules, while the second uses only the visible properties of the components; the semantics agree when the visible consequences of hidden information are enough to determine the result of the composition. A number of "laws of software composition" are proved relating the composition operations. Inclusive institutions simplify many proofs.

Parameterized programming is extended to higher order modules, by extending views, which fit actual parameters to formal parameters in a flexible way, to morphisms, with higher order module expressions to compose modules into systems. A category theoretic semantics is outlined, and examples in BOBJ show the power of morphisms.

In this paper we show how by means of a categorical framework we can compose systems of concurrent object modules satisfying some interaction rules given by a specification. Module interaction can be either synchronous or asynchronous and both cases are considered separately. The behaviour of object modules is modelled by labelled prime event structures. The category of labelled prime event structures has (co)products. A product in the category of labelled prime event structures is given accordingly to Winskel and Nielsen but denotes parallel composition in a sense that does not have much practical interest. For synchronously communicating modules, by applying to the product a restriction on the allowed life cycles by means of the categorical concept of a functor induced by a co bration and a morphism on labels, we achieve the desired joint behaviour. A way to model asynchronous composition of modules is to construct a coproduct and extend it by their interaction rules. At the end of ...

This paper studies the composition of modules that can hide information, over a very general class of logical systems called inclusive institutions. Two semantics are given for compositions using five familiar operations, and a property called conservativity is shown necessary and sufficient for these semantics to agree. The first semantics extracts the visible properties of the result of composing both the visible and hidden parts of modules, while the second uses only the visible properties of the components. Several "laws of software composition" are given, which demonstrate the power of inclusive institutions to simplify proofs.