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.

GB92] to formally capture the notion of logical system. Interpreting institutions as functors, and morphisms and representations of institutions as natural transformations, we give elegant proofs for the completeness of the categories of institutions with morphisms and representations, respectively, show that the duality between morphisms and representations of institutions comes from an adjointness between categories of functors, and prove the cocompleteness of the categories of institutions over small signatures with morphisms and representations, respectively. Category: F.3, F.4

We show that for any behavioral Sigma-specification B there is an ordinary algebraic specification ~ B over a larger signature, such that a model behaviorally satisfies B if and only if it satisfies ~ B, where is the information hiding operator exporting only the Sigma-theorems of ~ B. The idea is to add machinery for contexts and experiments (sorts, operations and equations), use it, and then hide it. We develop a procedure, called unhiding, that takes a finite B and produces a finite ~ B. The practical aspect of this procedure is that one can use any standard equational or inductive theorem prover to derive behavioral theorems, even if neither equational reasoning nor induction is sound for behavioral satisfaction.

This paper introduces the novel concept of inclusive institution as a foundational framework for studying logic-independent module compositionality, defines specification modules as specifications allowing both public and private signatures, and shows that an internal property of modules, called conservatism, is crucial for compositional semantics.

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.