## 4th Refinement Workshop: Proceedings of the 4th Refinement Workshop, organised by BCS-FACS, 9–11 January 1991, CambridgeThis volume contains the proceedings ofthe 4th Refinement Workshop which was organised by the British Computer Society specialist group in Formal Aspects of Computing Science and held in Wolfson College, Cambridge, on 9-11 January, 1991. The term refinement embraces the theory and practice of using formal methods for specifying and implementing hardware and software. Most of the achievements to date in the field have been in developing the theoretical framework for mathematical approaches to programming, and on the practical side in formally specifying software, while more recently we have seen the development of practical approaches to deriving programs from their speCifications. The workshop gives a fair picture of the state of the art: it presents new theories for reasoning about software and hardware and case studies in applying known theory to interesting small-and medium-scale problems. We hope the book will be Of interest both to researchers in formal methods, and to software engineers in industry who want to keep abreast of possible applications of formal methods in industry. The programme consisted both of invited talks and refereed papers. The invited speakers were Ib S0rensen, Jean-Raymond Abrial, Donald MacKenzie, Ralph Back, Robert Milne, Mike Read, Mike Gordon, and Robert Worden who gave the introductory talk. This is the first refinement workshop that solicited papers for refereeing, and despite a rather late call for papers the response was excellent. |

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### Contents

Introductory Talk to the | 1 |

Specialising Abstract Programs | 34 |

A Refinement Case Study Using the Abstract Machine | 51 |

Copyright | |

14 other sections not shown

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### Common terms and phrases

abstract data type algorithm allow application assertions assumption axioms behaviour binary Bool C.A.R. Hoare circuit components concrete concurrent systems construct constructor correctness data refinement defined definition defn denotes derivation element empty environment eqJist equivalence ev.time example export F Event finite formal methods formula function generalised guar hence implementation input instruction number interface invariant is-empty Lemma List livelock logic mathematical maxsize module node notation notion object operational semantics operations output parameter parametrised Past(C,S PointModule post-condition postcondition Pre-order predicate procedures process algebra programming language Programming Research Group proof graphs proof lattice proof obligations properties prove refinement calculus refinement diagram refinement relation reification Rename restriction result satisfy schema semantics sequence sequential simulation Spawn(C synchronisation techniques Theorem theory traces transition true type theory untimed variables verification Workers Z notation