A language-independent proof system for full program equivalence

Ştefan Ciobâcă, Dorel Lucanu, Vlad Rusu, Grigore Roşu

Research output: Contribution to journalArticlepeer-review


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).

Original languageEnglish (US)
Pages (from-to)469-497
Number of pages29
JournalFormal Aspects of Computing
Issue number3
StatePublished - May 1 2016


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

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Software


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