Martin C. Henson

ZB 2002:Formal Specification and Development in Z and B

Alloy: A Logical Modelling Language.- An Outline Pattern Language for Z: Five Illustrations and Two Tables.- Patterns to Guide Practical Refactoring: Examples Targetting Promotion in Z.- Reuse of Specification Patterns with the B Method.- Composing Specifications Using Communication.- When Concurrent Control Meets Functional Requirements, or Z + Petri-Nets.- How to Diagnose a Modern Car with a Formal B Model?.- Parallel Hardware Design in B.- Operation Refinement and Monotonicity in the Schema Calculus.- Using Coupled Simulations in Non-atomic Refinement.- An Analysis of Forward Simulation Data Refinement.- B#: Toward a Synthesis between Z and B.- Introducing Backward Refinement into B.- Expression Transformers in B-GSL.- Probabilistic Termination in B.- Probabilistic Invariants for Probabilistic Machines.- Proving Temporal Properties of Z Specifications Using Abstraction.- Compositional Verification for Object-Z.- Timed CSP and Object-Z.- Object Orientation without Extending Z.- Comparison of Formalisation Approaches of UML Class Constructs in Z and Object-Z.- Towards Practical Proofs of Class Correctness.- Automatically Generating Information from a Z Specification to Support the Classification Tree Method.- Refinement Preserves PLTL Properties.- Proving Event Ordering Properties for Information Systems.- ZML: XML Support for Standard Z.- Formal Derivation of Spanning Trees Algorithms.- Using B Refinement to Analyse Compensating Business Processes.- A Formal Specification in B of a Medical Decision Support System.- Extending B with Control Flow Breaks.- Towards Dynamic Population Management of Abstract Machines in the B Method.

Logics of Specification Languages

Preludium.- An Overview.- The Languages.- Abstract State Machines for the Classroom.- The event-B Modelling Method: Concepts and Case Studies.- A Methodological Guide to the CafeOBJ Logic.- Casl - the Common Algebraic Specification Language.- Duration Calculus.- The Logic of the RAISE Specification Language.- The Specification Language TLA+.- The Typed Logic of Partial Functions and the Vienna Development Method.- Z Logic and Its Applications.- Postludium.- Reviews.

An analysis of total correctness refinement models for partial relation semantics I

This is the first of a series of papers devoted to the thorough investigation of (total correctness) refinement based on an underlying partial relational model. In this paper we restrict attention to operation refinement. We explore four theories of refinement based on an underlying partial relation model for specifications, and we show that they are all equivalent. This, in particular, sheds some light on the relational completion operator (lifted-totalisation) due to Woodcock which underlies data refinement in, for example, the specification language Z. It further leads to two simple alternative models which are also equivalent to the others.

Operation refinement and monotonicity in the schema calculus

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 to four schema operations for three notions of operation refinement. The mathematical connection between the equational schema logic and monotonicity is discussed and evaluated.

An analysis of forward simulation data refinement

This paper investigates data refinement by forward simulation for specifications whose semantics is given by partial relations. The most well-known example of such a semantics is that for Z. The standard model-theoretic approach is based on totalisation and lifting. The paper examines this model, exploring and isolating the precise roles played by lifting and totalisation in the standard account by introducing a simpler, normative theory of forward simulation data refinement (SF-refinement) which captures refinement directly in the language and in terms of the natural properties of preconditions and postconditions. This theory is used in conjunction with four other model-theoretic approaches to determine the extent to which the standard approach is canonical, and the extent to which it is arbitrary.

A Logic for Schema-Based Program Development

Abstract.We show how a theory of specification refinement and program development can be constructed as a conservative extension of our existing logic for Z. The resulting system can be set up as a development method for a Z-like specification language, or as a generalisation of a refinement calculus (with a novel semantics). In addition to the technical development we illustrate how the theory can be used in practice.

Program development in the constructive set theory TK

We present a constructive theory of types and kinds designed with program development as the major desideratum. We show how this theory may be employed to derive programs from proofs of specifications (that is, demonstrations that specifications are satisfiable) and how the infrastructure of the theory supports the transformational development of programs in a natural way.

Program Development and Specification Refinement in the Schema Calculus

We introduce a framework for program development and specification refinement in the schema calculus of Z. We provide illustrative examples outlining the major design decisions based on an interpretation of operation schemas as sets of programs.

A Constructive Set Theory for Program Development

We present a constructive theory of types and kinds (called TK5) designed with program development as the major desideratum. We motivate its definition with respect to existing research in the area of program logics (in particular Martin-Lofs theory of types) and establish suitable infrastructure for program extraction from proofs of specifications.

A Logic for the Schema Calculus

In this paper we introduce and investigate a logic for the schema calculus of Z. The schema calculus is arguably the reason for Z’s popularity but so far no true calculus (a sound system of rules for reasoning about schema expressions) has been given. Presentations to date have either failed to provide a calculus (e.g. the draft standard [3]) or have fallen back on informal descriptions at a syntactic level (most text books e.g. [7]). Alongside the calculus, we introduce a derived equational logic; this enables us to formalise properly the informal notions of schema expression equality to be found in the literature.