Not so many years ago, it would have been difficult to find more than a handful of examples of the use of formal methods in industry. Today however, the industrial application of formal methods is becoming increasingly common in a variety of application areas, particularly those with a safety, security or financially critical aspects. Furthermore, in situations where a particularly high level of assurance is required, formal proof is broadly accepted as being of value. Perhaps the major benefit of formalisation is that it enables formal symbolic manip ulation of elements of a design and hence can provide developers with a variety of analyses which facilitate the detection of faults. Proof is just one of these possible formal activities, others, such as test case generation and animation, have also been shown to be effective bug finders. Proof can be used for both validation and verifi cation. Validation of a specification can be achieved by proving formal statements conjectured about the required behaviours of the system. Verification of the cor rectness of successive designs can be achieved by proof of a prescribed set of proof obligations generated from the specifications.

Errata, detected in Taylor's Logarithms. London: 4to, 1792. [sic] 14.18.3 6 Kk Co-sine of 3398 3298 - Nautical Almanac (1832) In the list of ERRATA detected in Taylor's Logarithms, for cos. 4° 18'3", read cos. 14° 18'2". - Nautical Almanac (1833) ERRATUM ofthe ERRATUM ofthe ERRATA of TAYLOR'S Logarithms. For cos. 4° 18'3", read cos. 14° 18' 3". - Nautical Almanac (1836) In the 1820s, an Englishman named Charles Babbage designed and partly built a calculating machine originally intended for use in deriving and printing logarithmic and other tables used in the shipping industry. At that time, such tables were often inaccurate, copied carelessly, and had been instrumental in causing a number of maritime disasters. Babbage's machine, called a 'Difference Engine' because it performed its cal culations using the principle of partial differences, was intended to substantially reduce the number of errors made by humans calculating the tables. Babbage had also designed (but never built) a forerunner of the modern printer, which would also reduce the number of errors admitted during the transcription of the results. Nowadays, a system implemented to perform the function of Babbage's engine would be classed as safety-critical. That is, the failure of the system to produce correct results could result in the loss of human life, mass destruction of property (in the form of ships and cargo) as well as financial losses and loss of competitive advantage for the shipping firm.

Abstract: "The most powerful tools for analysis of formal specifications are general-purpose theorem provers and model checkers, but these tools provide scant methodological support. Conversely, those approaches that do provide a well-developed method generally have less powerful automation. It is natural, therefore, to try to combine the better developed methods with the more powerful general-purpose tools. An obstacle is that the methods and the tools often employ very different logics. We argue that methods are separable from their logics and are largely concerned with the structure and organization of specifications. We propose a technique called structural embedding that allows the structural elements of a method to be supported by a general-purpose tool, while substituting the logic of the tool for that of the method. We have found this technique quite effective and we provide some examples of its application. We also suggest how general-purpose systems could be restructured to support this activity better."

This book constitutes the refereed proceedings of the 5th International Conference on Abstract State Machines, Alloy, B, TLA, VDM, and Z, ABZ 2016, held in Linz, Austria, in May 2016. The 17 full and 15 short papers presented in this volume were carefully reviewed and selected from 61 submissions. They record the latest research developments in state-based formal methods Abstract State Machines, Alloy, B, Circus, Event-B, TLS+, VDM and Z.

This book summarizes work done by the authors under the Esprit Tool Use project (1985-1990), at GMD in Karlsruhe and at Berlin University of Technology. It provides a comprehensive description of the generic development language Deva designed by the authors. Much of the research reported in this monograph is inspired by the work of Michel Sintzoff on formal program development; he contributed an enlightening Foreword. Deva is essentially a typed functional language with certain deduction rules. The difference with ordinary languages is, of course, the application domain: the types serve here to express propositions such as specifications or programs, rather than just data classes. Its practical applicability was tested on several non-trivial case studies. The whole book is written using the DVWEB system, a WEB for Deva, beeing implemented at the Berlin University of Technology.

This book constitutes the refereed proceedings of the 4th International Conference on Frontiers of Combining Systems, FroCoS 2002, held in Santa Margherita Ligure, Italy, in April 2002. The 14 revised full papers presented together with 3 invited papers were carefully reviewed and selected from 35 submissions. Among the topics covered are combination of logics, combination of constraint solving techniques, combination of decision procedures, combination problems in verification, modular problems of theorem proving, and the integration of decision procedures and other solving processes into constraint programming and deduction systems.