Theory of Computing Systems

, Volume 43, Issue 3–4, pp 298–321 | Cite as

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

  • Rose H. Abdul Rauf
  • Ulrich Berger
  • Anton Setzer


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.


Functional programming Object-oriented programming Inheritance Simply typed lambda-calculus Denotational semantics Kripke-style logical relation Correctness proof 


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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  • Rose H. Abdul Rauf
    • 1
  • Ulrich Berger
    • 2
  • Anton Setzer
    • 2
  1. 1.Faculty of Information System and Quantitative ScienceUniversity of Technology MARAShah AlamMalaysia
  2. 2.Department of Computer ScienceUniversity of Wales SwanseaSwanseaUK

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