1General introduction- 11 Formal methods- 12 VDM development- 13 The IPSE 25 project- 14 Proof assistant requirements- 2 Introduction to mural- 21 General introduction- 22 The proof assistant- 23 The VDM support tool- 24 Reasoning about developments- 3 Instantiation- 31 Symbolic logic in mural- 32 Classical first order predicate calculus- 33 Some common data types- 34 More complicated formulations- 35 The theory of VDM- 36 Some other logics- 4 Foundation- 41 Preamble- 42 Syntax- 43 Natural Deduction rules- 44 Rule Schemas and instantiation- 45 The mural store- 46 Syntactic contexts and well-formedness- 47 Proofs- 48 Morphisms- 49 Pattern matching- 410 Reading the full specification- 411 Limitations of the mural approach- 5 The tactic language- 51 Mechanising proof in mural- 52 The language- 53 The implementation of tactics- 54 Examples- 6 Implementing the mural proof assistant- 61 The process of implementation- 62 The implementation- 63 Lessons learnt and advice to the young- 64 The future- 65 The final word- 7 Supporting formal software development- 71 Abstract specification- 72 Relating specifications- 73 Support for reasoning about formal developments- 8 The mural VDM Support Tool- 81 Specifying VDM developments in VDM- 82 Theories from specifications- 83 Scope for growth- 9 Foundations of specification animation- 91 Approaches to animation- 92 Denotational semantics of symbolic execution- 93 Operational semantics of symbolic execution- 94 Theories to support symbolic execution- 95 Conclusions- 10 Case Studies- 101 Specifications in VDM- 102 Transformation of VDM into mural -theories- 103 A watchdog for a reactor system- 104 An algorithm for topological sorting- 105 Theories for VDM in mural- 11 Conclusions- 111 Experimental use of mural- 112 Detailed observations- 113 Further developments- 114 Summary- Appendices- A Summary of VDM Notation- B Glossary of terms- C The Specification of the Proof Assistant- C1 The Raw Syntax- C2 Subterm Access and Editing- C3 Sequents and Rules- C4 Instantiation and Pattern-matching- C5 Signatures- C6 Theories- C7 Morphisms and Theory Morphisms- C8 Proofs- C9 The Store- D The specification of the animation tool- D1 Data structure and some auxiliary functions- D2 Operations- E The Theorem Prover's House

Mural: A Formal Development Support System

This report was prepared to supplement a forthcoming chapter on formal methods in the FAA Digital Systems Validation Handbook1. Its purpose is to outline the technical basis for formal methods in computer science, to explain the use of formal methods in the specification and verification of software and hardware requirements, designs, and implementations, to identify the benefits, weaknesses, and difficulties in applying these methods to digital systems used in critical applications, and to suggest factors for consideration when formal methods are offered in support of certification. The report assumes a serious interest in the engineering of critical systems, and a willingness to read occasional mathematical formulas and specialized terminology, but assumes no special background in formal logic or mathematical specification techniques. (An appendix provides a rapid introduction to formal logic for those to whom this topic is new.) The discussion should be accessible to most people with an engineering background. It may also be of use to those who develop or advocate formal methods and are interested in their use to support certification of critical systems. The particular focus of this report is computer systems used on-board aircraft. Some background on these systems is provided so that those concerned with critical computer systems in other contexts may be able to reinterpret the airplane-specific material to suit their own field. Digital Systems Validation Handbook–Volume II. Federal Aviation Administration Technical Center, Atlantic City, NJ, February 1989. DOT/FAA/CT-88/10. The chapter on Formal Methods will probably form part of Volume III.

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Formal Methods and the Certification of Critical Systems

Formal methods rely on the correctness of the formal requirements specification, but this correctness cannot be proved. This paper discusses the use of software tools to assist in the validation of formal specifications and advocates a system by which Z specifications may be animated as Prolog programs. Two Z/Prolog translation strategies are explored; formal program synthesis and structure simulation. The paper explains why the former proved to be unsuccessful and describes the techniques developed for implementing the latter approach, with the aid of case studies.

Software development: two approaches to animation of Z specifications using Prolog

Before a system can be formally defined, it is common to write a specification in a natural language as the basis for the formal definition. Natural languages are not well suited for this task; documentation written in a natural language is often ambiguous and imprecise. Inspection of real documentation also reveals that, without special training, most writers do not produce concise, clear or consistent statements. We present here an experimental interface to a general-purpose natural-language processing system designed to control the writing of specification statements in a natural language. The interface is designed to reduce the degree of imprecision and ambiguity in the natural-language statements, as well as contributing to the writing of shorter statements, with clear structure and punctuation. We compare our approach to similar work in this area. 1. INTRODUCTIO N

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A Method for Controlling the Production of Specifications in Natural Language

In this paper the possibilities to automate black-box testing through formal requirement specifications are explored. More precisely, the formal method VDM (Vienna Development Method) serves to demonstrate that abstract requirement models can be used as test oracles for concrete software. The automation of the resulting testing frame-work is based on modern CASE-tools that support a light-weight approach to formal methods. The specification language used is VDMSL, but the results are easily transferred into similar model oriented methods such as B, Z or RAISE.

Automated Black-Box Testing with Abstract VDM Oracles

A case study is presented in which the Vienna development method (VDM), a formal specification and development methodology, was used during the analysis phase of the assessment of a prototype nuclear reactor protection system. The VDM specification was also translated into the logic language Prolog to animate the specification and to provide a diverse implementation for use in back-to-back testing. It is claimed that this technique provides a visible and effective method of analysis which is superior to the informal alternatives.

P. K. D. Froome

Papers

The application of formal methods to the assessment of high integrity software