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Abstract. Csp-Casl is but one of the many languages, Bernd Krieg-Brückner (BKB) was influential to: From the initial idea of working towards an integration of the process algebra Csp with the algebraic specification language Casl, over the concrete design of the language’s syntax, to the tool’s side where the theorem prover Isabelle should provide the common platform, BKB provided inspiration and guidance, funding, and also a helping hand when needed. This paper provides a survey on the technology developed so far for Csp-Casl, covering results of theoretical nature, an industrial case study, tool support as well as a testing approach. In honour of BKB’s 60th birthday, this survey documents what has become out of one of BKB’s visions. 1

Abstract. We present the integration of refinement method of VSE verification tool, successfully used in industrial applications, in the Heterogeneous Tool Set HETS. The connection is done via introducing the dynamic logic underlying VSE and two logic translations in the logic graph of HETS. Thus the logic-independent layers of HETS are not modified and its proof management formalism can be applied to VSE specifications. 1

The central idea of the Heterogeneous Tool Set (HETS) is to provide a general framework for formal methods integration and proof management. One can think of HETS acting like a motherboard where different expansion cards can be plugged in, the expansion cards here being individual logics (with their analysis

Inclusion systems have been introduced in algebraic specification theory as a categorical structure supporting the development of a general abstract logic-independent approach to the algebra of specification (or programming) modules. Here we extend the concept of indexed categories and their Grothendieck flattenings to inclusion systems. An important practical significance of the resulting Grothendieck inclusion systems is that they allow the development of module algebras for multi-logic heterogeneous specification frameworks. At another level, we show that several inclusion systems in use in some syntactic (signatures, deductive theories) or semantic contexts (models) appear as Grothendieck inclusion systems too. We also study several general properties of Grothendieck inclusion systems.

The central idea of the Heterogeneous Tool Set (HETS) is to provide a general framework for formal methods integration and proof management. One can think of HETS acting like a motherboard where different expansion cards can be plugged in, the expansion cards here being individual logics (with their analysis

Abstract. The error-prone process of formal specification and verification of large systems requires an efficient, evolutionary formal development approach. Development graphs have been designed to support such an approach. They can formally represent the actual state of a software development comprising specification and verification work in a structured way and assist the user in her evolutionary development by the incorporated change management support. In this paper we extend this work with respect to heterogeneous development graphs allowing one to make use of different institutions, i.e. logics, for specifying and verifying large developments. We also push forward the idea of stringent locality of definitions by introducing pre-signatures and pre-signature morphisms, which allow us to build up signatures in an incremental and parametric way. 1