Abstract. Development graphs are a tool for dealing with structured specifications in a formal program development in order to ease the management of change and reusing proofs. Often, different aspects of a software system have to be specified in different logics, since the construction of a huge logic covering all needed features would be too complex to be feasible. Therefore, we introduce heterogeneous development graphs as a means to cope with heterogeneous specifications. We cover both the semantics and the proof theory of heterogeneous development graphs. A proof calculus can be obtained either by combining proof calculi for the individual logics, or by representing these in some “universal ” logic like higher-order logic in a coherent way and then “borrowing” its calculus for the heterogeneous language. 1

We provide a semantic basis for heterogeneous specifications that not only involve different logics, but also different kinds of translations between these. We show that Grothendieck institutions based on spans of (co)morphisms can serve as a unifying framework providing a simple but powerful semantics for heterogeneous specification.

Abstract. We present a semantics for architectural specifications in Casl, including an extended static analysis compatible with modeltheoretic requirements. The main obstacle here is the lack of amalgamation for Casl models. To circumvent this problem, we extend the Casl logic by introducing enriched signatures, where subsort embeddings form a category rather than just a preorder. The extended model functor has amalgamation, which makes it possible to express the amalgamability conditions in the semantic rules in static terms. Using these concepts, we develop the semantics at various levels in an institution-independent fashion.

Partiality is a fact of life, but at present explicitly partial algebraic specifications lack tools and have limited proof methods. We propose a sound and complete way to support execution and formal reasoning of explicitly partial algebraic specifications within the total framework of membership equational logic (MEL) which has a high-performance interpeter (Maude) and proving tools. This is accomplished by a sound and complete mapping PMEL ! MEL of partial membership equational (PMEL) theories into total ones.

CafeOBJ is an executable industrial strength multi-logic algebraic speci cation language which is a modern successor of OBJ and incorporates several new algebraic speci cation paradigms.

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