A language-independent proof system for full program equivalence

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 p...

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Veröffentlicht in:Formal aspects of computing Jg. 28; H. 3; S. 469 - 497
Hauptverfasser: Ciobâcă, Ştefan, Lucanu, Dorel, Rusu, Vlad, Roşu, Grigore
Format: Journal Article
Sprache:Englisch
Veröffentlicht: London Springer London 01.05.2016
Association for Computing Machinery
Springer Verlag
Schlagworte:
Compilers
Computer Science
Equivalence
Languages
Logic in Computer Science
Math Applications in Computer Science
Original Article
Programming Languages
Proving
Semantics
Sequences
Sound
Theory of Computation
Transformations
Program equivalence
Matching logic
Programming language aggregation
Programming language semantics
Full equivalence
ISSN:0934-5043, 1433-299X
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Zusammenfassung: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).
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ISSN:0934-5043
1433-299X
DOI:10.1007/s00165-016-0361-7