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Localized Operational Termination in General Logics

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Book cover Software, Services, and Systems

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 8950))

Abstract

Termination can be thought of as the property of programs ensuring that every input is given an answer in finite time. There are, however, many different (combinations of) programming paradigms and languages for these paradigms. Is a common formal definition of termination of programs in any (or most) of these programming languages possible? The notion of operational termination provides a general definition of termination which relies on the logic-based description of (the operational semantics of) a programming language. The key point is capturing termination as the absence of infinite inference, that is: all proof attempts must either successfully terminate, or they must fail in finite time. This global notion is well-suited for most declarative languages, where programs are theories in a logic whose inference system is specialized to each theory to characterize its computations. Other programming languages (e.g., imperative languages) and applications (e.g., the evaluation of specific expressions and goals in functional and logic programs) require a more specialized treatment which pays attention not just to theories, but to specific formulas to be proved within the given theory. For instance, the execution of an imperative program can be viewed as a proof of an specific formula (representing the program) within the computational logic describing the operational semantics of the programming language. In such cases, an appropriate definition of termination should focus on proving the absence of infinite proofs for computations localized to specific goals. In this paper we generalize the global notion of operational termination to this new setting and adapt the recently introduced OT-framework for mechanizing proofs of operational termination to support proofs of localized operational termination.

Partially supported by NSF grant CNS 13-19109. Salvador Lucas’ research, developed during a sabbatical year at the UIUC, was also supported by the EU (FEDER), MECD grant PRX12/00214, MINECO projects TIN2010-21062-C02-02 and TIN 2013-45732-C4-1-P, and GV projects BEST/2014/026 and PROMETEO/2011/052.

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Author information

Authors and Affiliations

  1. CS Dept., University of Illinois at Urbana-Champaign, IL, USA

    Salvador Lucas & José Meseguer

  2. DSIC, Universitat Politècnica de València, Spain

    Salvador Lucas

Authors
  1. Salvador Lucas
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  2. José Meseguer
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Editor information

Editors and Affiliations

  1. IMT Institute for Advanced Studies Lucca, Piazza S. Francesco, 19, 55100, Lucca, Italy

    Rocco De Nicola

  2. Ludwig-Maximilians-Universität München, Germany

    Rolf Hennicker

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Lucas, S., Meseguer, J. (2015). Localized Operational Termination in General Logics. In: De Nicola, R., Hennicker, R. (eds) Software, Services, and Systems. Lecture Notes in Computer Science, vol 8950. Springer, Cham. https://doi.org/10.1007/978-3-319-15545-6_9

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  • DOI: https://doi.org/10.1007/978-3-319-15545-6_9

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-15544-9

  • Online ISBN: 978-3-319-15545-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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