12-The Typed Logic of Partial Functions and the

12-The Typed Logic of Partial Functions and the - The Typed...

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The Typed Logic of Partial Functions and the Vienna Development Method John S. Fitzgerald Centre for Software Reliability, Newcastle University, Newcastle upon Tyne, NE1 7RU, United Kingdom, John.Fitzgerald@ncl.ac.uk For Harry Fitzgerald, Engineer (1928–2004) Summary. Decisions about the logic underpinning a formal speciFcation language have important consequences for the utility of the formalism. This chapter describes the major features of the typed Logic of Partial ±unctions (LP±) as it has been im- plemented in support of the Vienna Development Method’s SpeciFcation Language, VDM-SL. It compares attempts to realise the logic in di²erent environments: a user- centred proof support tool, a speciFcation interpreter and an automated proof tool. ±uture directions in integrated proof support for the language are suggested. 1 Introduction The logic that underpins a specifcation language has great practical signif- cance, directly a±ecting the capabilities o² the tools that are so necessary to the success²ul application o² the language in pro²essional practice. Decisions regarding logic are there²ore influenced by methodological and pragmatic con- cerns, as well as by the desire to provide an intuitive and elegant theory. The Vienna Development Method’s Specifcation Language (VDM-SL) has a long history o² use, both as a vehicle ²or research and as a tool in the development o² computer-based systems. Machine support ²or the coding and analysis ²or VDM specifcations has been available ²or VDM-SL ²or well over a decade, and there is considerable experience at proving properties o² specifcations and refnements in the ²ormalism. Nevertheless, the logic underpinning VDM, and its susceptibility to machine support, remain the subject o² debate and research. The Logic o² Partial Functions (LPF) is closely associated with VDM, although its potential ²or application goes well beyond that particular ²ormal- ism. The aims o² this chapter are to give an account o² LPF and attempts to realise it in various support environments ²or VDM, ranging ²rom an inter-
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454 John S. Fitzgerald preter to automated provers, and to identify the next steps in the provision of integrated support for reasoning about VDM speciFcations. In order to understand the requirements for a logic supporting VDM-SL, it is worth reviewing the distinguishing characteristics of the speciFcation lan- guage and a little of its history (Sect. 2). The key features of Typed LP±, notably the handling of undeFned terms, are introduced in Sects. 3 and 4. Us- ing LP± to reason about models expressed in VDM-SL entails the addition of types and other relevant features, discussed in Sect. 5. Contrasting approaches to tool support for LP±-based reasoning in VDM-SL are discussed in Sect. 6, leading to a discussion of future directions and concluding remarks (Sect. 7).
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This note was uploaded on 03/31/2010 for the course CAS 707 taught by Professor Ridhakhedri during the Spring '10 term at McMaster University.

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12-The Typed Logic of Partial Functions and the - The Typed...

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