models for specifications and schema operations which are monotonic. This leads us to explore a number of theoretical and pragmatic questions: the former concern logics for modular refinement; the latter explore the use of novel schema calculi in practice. 1

We present an algorithm called Tar ("Thread-modular Abstraction Refinement") for model checking safety properties of concurrent software. The Tar algorithm uses thread-modular assume-guarantee reasoning to overcome the exponential complexity in the control state of multithreaded

Refinement calculi for imperative programs provide an integrated framework for programs and specifications and allow one to develop programs from specifications in a systematic fashion. The semantics of these calculi has traditionally been de ned in terms of predicate transformers and poses several

The schema calculus of Z provides a means for expressing structured, modular specifications. Extending this modularity to program development requires the monotonicity of these operators with respect to refinement. This paper provides a thorough mathematical analysis of monotonicity with respect

of data. Up to now, schema mappings have typically been specified manually or have been derived using mapping-design systems that automatically generate a schema mapping from a visual specification of the relationship between two schemas. We present a novel paradigm and develop a system

The schema calculus operators of Z provide an excellent means for expressing modular specifications but not for undertaking modular reasoning: it is well-known that these operators have poor monotonicity properties. The paper addresses three topics in this context: first, we provide a thorough

of the axiom rule to the atomic case is not adequate for this type of calculi. A novel proviso for the axiom rule and corresponding provisos for the left and right definition rules are introduced with an accompanying discussion and suggestions for possible applications in the domain of declarative

aims at the modular development and implementation of distributed interactive systems through several abstraction levels by stepwise refinement. 1 Chapter 1 Methods for System Development A (distributed) system consists of a family of interacting, conceptually or spatially distributed components. A

of absorption as well as the standard tableau calculus to directly handle the (absorbed) nominal schema axioms. We implement the resulting extension of standard tableau calculi in a novel reasoning system and we integrate further optimisations. In our empirical evaluation, we show the effect

-known optimisation of absorption as well as the standard tableau calculus to directly handle the (absorbed) nominal schema axioms. We implement the resulting extension of standard tableau calculi in a novel reasoning system and we integrate further optimisations. In our empirical evaluation, we show the effect