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Invariants, Well-Founded Statements and Real-Time Program Algebra

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FM 2014: Formal Methods (FM 2014)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 8442))

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Abstract

Program algebras based on Kleene algebra abstract the essential properties of programming languages in the form of algebraic laws. The proof of a refinement law may be expressed in terms of the algebraic properties of programs required for the law to hold, rather than directly in terms of the semantics of a language. This has the advantage that the law is then valid for any programming language that satisfies the axioms of the algebra.

In this paper we explore the notion of well-founded statements and their relationship to well-founded relations and iterations. The laws about well-founded statements and relations are combined with invariants to derive a simpler proof of a while-loop introduction law. The algebra is then applied to a real-time programming language. The main difference is that tests within conditions and loops take time to evaluate and during that time the values of program inputs may change. This requires new definitions for conditionals and while loops but the proofs of the introduction laws for these constructs can still make use of the more basic algebraic properties of iterations.

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Authors and Affiliations

  1. School of Information Technology and Electrical Engineering, The University of Queensland, Brisbane, 4072, Australia

    Ian J. Hayes & Larissa Meinicke

Authors
  1. Ian J. Hayes
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  2. Larissa Meinicke
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Editor information

Editors and Affiliations

  1. School of Computing Science, Newcastle University, NE1 7RU, Newcastle, UK

    Cliff Jones

  2. Data Abstraction (Pty) Ltd., 7 Saint David’s Park, Saint David’s Place, Parktown, Johannesburg, South Africa

    Pekka Pihlajasaari

  3. Information System Technology and Design, Singapore University of Technology and Design, 20 Dover Road, 138682, Singapore

    Jun Sun

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Hayes, I.J., Meinicke, L. (2014). Invariants, Well-Founded Statements and Real-Time Program Algebra. In: Jones, C., Pihlajasaari, P., Sun, J. (eds) FM 2014: Formal Methods. FM 2014. Lecture Notes in Computer Science, vol 8442. Springer, Cham. https://doi.org/10.1007/978-3-319-06410-9_23

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  • DOI: https://doi.org/10.1007/978-3-319-06410-9_23

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-06409-3

  • Online ISBN: 978-3-319-06410-9

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