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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Vydané v:	Formal aspects of computing Ročník 28; číslo 3; s. 469 - 497
Hlavní autori:	Ciobâcă, Ştefan, Lucanu, Dorel, Rusu, Vlad, Roşu, Grigore
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	London Springer London 01.05.2016 Association for Computing Machinery Springer Verlag
Predmet:	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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Abstract	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).
AbstractList	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). Two programs are mutually equivalent if, for the same input, either they both diverge or they both terminate with the same result. Mutual 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 mutual equivalence, which is para-metric in the operational semantics of two languages and in a state-similarity relation. The proof system is sound: if it terminates then it establishes the mutual 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 wether the sequence terminates or not; nevertheless, our proof system shows that the two programs are mutually equivalent (even if we cannot establish termination or divergence of either one).
Author	Lucanu, Dorel Ciobâcă, Ştefan Rusu, Vlad Roşu, Grigore
Author_xml	– sequence: 1 givenname: Ştefan surname: Ciobâcă fullname: Ciobâcă, Ştefan email: stefan.ciobaca@gmail.com organization: Faculty of Computer Science, “Alexandru Ioan Cuza” University – sequence: 2 givenname: Dorel surname: Lucanu fullname: Lucanu, Dorel organization: Faculty of Computer Science, “Alexandru Ioan Cuza” University – sequence: 3 givenname: Vlad surname: Rusu fullname: Rusu, Vlad organization: Inria – sequence: 4 givenname: Grigore surname: Roşu fullname: Roşu, Grigore organization: University of Illinois at Urbana-Champaign
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Keywords	Program equivalence Matching logic Programming language aggregation Programming language semantics Full equivalence
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References	Traian-Florin Şerbănuţă, Grigore Roşu, José Meseguer (2009) A rewriting logic approach to operational semantics. Information and Computation, 207(2):305–340 Nick Benton, Chung-Kil Hur (2009) Biorthogonality, step-indexing and compiler correctness. In ICFP 2009, pp 97–108 Davide Sangiorgi, Naoki Kobayashi, Eijiro Sumii (2011) Environmental bisimulations for higher-order languages. ACM Transactions on Programming Languages and Systems, 33(1):5 Grigore Roşu, Chucky Ellison, Wolfram Schulte (2010) Matching logic: An alternative to Hoare/Floyd logic. In AMAST 2010, volume 6486 of LNCS, pp 142–162 Fabio Somenzi, Andreas Kuehlmann (2006) Electronic Design Automation For Integrated Circuits Handbook, volume 2, chapter 4: Equivalence Checking. CRC Press George Necula (2000) Translation validation for an optimizing compiler. In PLDI 2000, pp 83–94. ACM José Meseguer, Grigore Roşu (2004) Rewriting logic semantics: From language specifications to formal analysis tools. 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References_xml	– reference: Chung-Kil Hur, Derek Dreyer, Georg Neis, Viktor Vafeiadis (2012) The marriage of bisimulations and kripke logical relations. In POPL 2012, pp 59–72 – reference: Fabio Somenzi, Andreas Kuehlmann (2006) Electronic Design Automation For Integrated Circuits Handbook, volume 2, chapter 4: Equivalence Checking. CRC Press – reference: Grigore Roşu (2015) Matching logic—extended abstract. In RTA 2015, volume 36 of LIPIcs, pp 5–21 – reference: Davide Sangiorgi, Naoki Kobayashi, Eijiro Sumii (2011) Environmental bisimulations for higher-order languages. ACM Transactions on Programming Languages and Systems, 33(1):5 – reference: José Meseguer, Grigore Roşu (2004) Rewriting logic semantics: From language specifications to formal analysis tools. In IJCAR 2004, volume 3097 of LNCS, pp 1–44 – reference: Sagar Chaki, Arie Gurfinkel, Ofer Strichman (2012) Regression verification for multi-threaded programs. 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Snippet	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... Two programs are mutually equivalent if, for the same input, either they both diverge or they both terminate with the same result. Mutual equivalence is an...
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SubjectTerms	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
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Title	A language-independent proof system for full program equivalence
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