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A Provably Correct Translation of the λ-Calculus into a Mathematical Model of C++

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Abstract

We introduce a translation of the simply typed λ-calculus into C++, and give a mathematical proof of the correctness of this translation. For this purpose we develop a suitable fragment of C++ together with a denotational semantics. We introduce a formal translation of the λ-calculus into this fragment, and show that this translation is correct with respect to the denotational semantics. We show as well a completeness result, namely that by translating λ-terms we obtain essentially all C++ terms in this fragment. We introduce a mathematical model for the evaluation of programs of this fragment, and show that the evaluation computes the correct result with respect to this semantics.

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Authors and Affiliations

  1. Faculty of Information System and Quantitative Science, University of Technology MARA, 40450, Shah Alam, Selangor D.E., Malaysia

    Rose H. Abdul Rauf

  2. Department of Computer Science, University of Wales Swansea, Singleton Park, Swansea, SA2 8PP, UK

    Ulrich Berger & Anton Setzer

Authors
  1. Rose H. Abdul Rauf
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  2. Ulrich Berger
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  3. Anton Setzer
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Correspondence to Rose H. Abdul Rauf.

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Supported by EPSRC grant GR/S30450/01.

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Abdul Rauf, R.H., Berger, U. & Setzer, A. A Provably Correct Translation of the λ-Calculus into a Mathematical Model of C++. Theory Comput Syst 43, 298–321 (2008). https://doi.org/10.1007/s00224-007-9062-1

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  • DOI: https://doi.org/10.1007/s00224-007-9062-1

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