Formal Aspects of Computing

, Volume 28, Issue 3, pp 469–497 | Cite as

A language-independent proof system for full program equivalence

  • Ştefan CiobâcăEmail author
  • Dorel Lucanu
  • Vlad Rusu
  • Grigore Roşu
Original Article


Two programs are fully equivalent if, for the same input, either they both diverge or they both terminate with the same result. Full equivalence is an adequate notion of equivalence for programs written in deterministic languages. It is useful in many contexts, such as capturing the correctness of program transformations within the same language, or capturing the correctness of compilers between two different languages. In this paper we introduce a language-independent proof system for full equivalence, which is parametric in the operational semantics of two languages and in a state-similarity relation. The proof system is sound: a proof tree establishes the full equivalence of the programs given to it as input. We illustrate it on two programs in two different languages (an imperative one and a functional one), that both compute the Collatz sequence. The Collatz sequence is an interesting case study since it is not known whether the sequence terminates or not; nevertheless, our proof system shows that the two programs are fully equivalent (even if we cannot establish termination or divergence of either one).


Matching logic Programming language semantics Program equivalence Full equivalence Programming language aggregation 


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Copyright information

© British Computer Society 2016

Authors and Affiliations

  • Ştefan Ciobâcă
    • 1
    Email author
  • Dorel Lucanu
    • 1
  • Vlad Rusu
    • 2
  • Grigore Roşu
    • 3
  1. 1.Faculty of Computer Science“Alexandru Ioan Cuza” UniversityIasiRomania
  2. 2.InriaLilleFrance
  3. 3.University of Illinois at Urbana-ChampaignChampaignUSA

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