Cyclic proofs of program termination in separation logic

Brotherston, J G.; Bornat, Richard; Calcagno, Cristiano

doi:10.1145/1328438.1328453

Cited by 46 publications

(58 citation statements)

References 19 publications

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“…Our experiments show that AProVE is substantially more powerful than all other tools. In particular, AProVE succeeds for all problems of [9] 17 and for 85 % of the examples from LinkedList and HashMap. There, AProVE '11, Julia, resp.…”

Section: Experiments and Conclusionmentioning

confidence: 92%

“…We implemented our contributions in the tool AProVE [18] (using the SMT Solver Z3 [14]) and evaluated it on a collection of 387 JBC programs. It consists of all 13 268 Java programs of the Termination Problem Data Base (used in the International Termination Competition); the examples length, visit, iterate from this paper; 14 a variant of visit on graphs; 15 3 well-known challenge problems from [9]; 57 (non-terminating) examples from [8]; and all 60 methods of java.util.LinkedList and java.util.HashMap from Oracle's standard Java distribution. 16 Apart from list algorithms, the collection also contains many programs on integers, arrays, trees, or graphs.…”

Section: Experiments and Conclusionmentioning

confidence: 99%

“…Thus, we can now express that by following some field of an object, one eventually reaches another specific object. In this way, we can also prove termination of well-known algorithms like the in-place reversal for pan-handle lists [9] automatically.…”

Section: Introductionmentioning

confidence: 99%

“…Up to now, transformational approaches could not deal with such programs. Similar to related approaches based on separation logic [4,5,9,10,28,32], our technique relies on suitable predicates describing properties of the heap. Like [28], but in contrast to several previous works, our technique derives these heap predicates automatically from the input program and it works automatically for arbitrary data structures (i.e., not only for lists).…”

Section: Introductionmentioning

confidence: 99%

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Automated Termination Proofs for Java Programs with Cyclic Data

Brockschmidt

Musiol

Otto

et al. 2012

Computer Aided Verification

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Abstract. In earlier work, we developed a technique to prove termination of Java programs automatically: first, Java programs are automatically transformed to term rewrite systems (TRSs) and then, existing methods and tools are used to prove termination of the resulting TRSs. In this paper, we extend our technique in order to prove termination of algorithms on cyclic data such as cyclic lists or graphs automatically. We implemented our technique in the tool AProVE and performed extensive experiments to evaluate its practical applicability.

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Section: Experiments and Conclusionmentioning

confidence: 92%

Section: Experiments and Conclusionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Automated Termination Proofs for Java Programs with Cyclic Data

Brockschmidt

Musiol

Otto

et al. 2012

Computer Aided Verification

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“…Our approach is based upon heuristic search in a formal system of cyclic proofs, adapted from the cyclic termination proofs in [8]. A cyclic proof is a derivation tree possibly containing back-links, which identify leaves of the tree with arbitrary interior nodes.…”

Section: Introductionmentioning

confidence: 99%

Cyclic Abduction of Inductively Defined Safety and Termination Preconditions

Brotherston

Gorogiannis

2014

Static Analysis

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Abstract. We introduce cyclic abduction: a new method for automatically inferring safety and termination preconditions of heap-manipulating while programs, expressed as inductive definitions in separation logic. Cyclic abduction essentially works by searching for a cyclic proof of the desired property, abducing definitional clauses of the precondition as necessary in order to advance the proof search process. We provide an implementation, Caber, of our cyclic abduction method, based on a suite of heuristically guided tactics. It is often able to automatically infer preconditions describing lists, trees, cyclic and composite structures which, in other tools, previously had to be supplied by hand.

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Intuitionistic Podelski-Rybalchenko Theorem and Equivalence Between Inductive Definitions and Cyclic Proofs

Berardi¹,

Tatsuta

2018

Coalgebraic Methods in Computer Science

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A cyclic proof system gives us another way of representing inductive and coinductive definitions and efficient proof search. Podelski-Rybalchenko termination theorem is important for program termination analysis. This paper first shows that Heyting arithmetic HA proves Kleene-Brouwer theorem for induction and Podelski-Rybalchenko theorem for induction. Then by using this theorem this paper proves the equivalence between the provability of the intuitionistic cyclic proof system and that of the intuitionistic system of Martin-Lof's inductive definitions when both systems contain HA.

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Cyclic proofs of program termination in separation logic

Cited by 46 publications

References 19 publications

Automated Termination Proofs for Java Programs with Cyclic Data

Automated Termination Proofs for Java Programs with Cyclic Data

Cyclic Abduction of Inductively Defined Safety and Termination Preconditions

Intuitionistic Podelski-Rybalchenko Theorem and Equivalence Between Inductive Definitions and Cyclic Proofs

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