Automated Termination Proofs with AProVE

Giesl, Jürgen; Thiemann, René; Schneider–Kamp, Peter; Falke, Stephan

doi:10.1007/978-3-540-25979-4_15

Cited by 110 publications

(74 citation statements)

References 27 publications

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“…Each function in the program Π terminates on each input for which the precondition holds, and similarly for each postcondition. Tools such as [14,1] or techniques developed for ACL2 [20] could be used to establish this property. Base theory solver soundness: The underlying solver is complete and sound for the (quantifier-free) formulas in the base theory.…”

Section: Properties Of Our Proceduresmentioning

confidence: 99%

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Satisfiability Modulo Recursive Programs

2011

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Abstract. We present a semi-decision procedure for checking satisfiability of expressive correctness properties of recursive first-order functional programs. In our approach, both properties and programs are expressed in the same language, a subset of Scala. We implemented our procedure and integrated it with the Z3 SMT solver and the Scala compiler. Our procedure is sound for counterexamples and for proofs of terminating functions. It is terminating and thus complete for many important classes of specifications, including all satisfiable formulas and all formulas where recursive functions satisfy certain syntactic restrictions. Using our system, Leon, we verified detailed correctness properties for functional data structure implementations, as well as syntax tree manipulations. We have found our system to be fast for both finding counterexamples and finding correctness proofs, and to scale to larger programs than alternative techniques.

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Section: Properties Of Our Proceduresmentioning

confidence: 99%

“…These systems have been applied to a number of industrial-scale case studies in hardware and software verification [18,21]. Recent systems based on functional programs include VeriFun [31] and AProVE [14]. Moreover, computable specifications form important parts of many case studies in proof assistants Coq [5] and Isabelle [23].…”

Section: Related Workmentioning

confidence: 99%

Satisfiability Modulo Recursive Programs

2011

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“…Termination analysis has received a considerable attention for at least two decades, and nowadays several powerful tools for the automatic termination analysis of different programming languages and computational models exist Giesl et al 2004;Cook et al 2006;Albert et al 2007;Spoto et al 2010;Giesl et al 2011]. Two important aspects of termination analysis tools are their scalability and their ability to handle a large class of programs.…”

Section: Introductionmentioning

confidence: 99%

On the Termination of Integer Loops

Ben-Amram

Genaim

Masud

2012

Lecture Notes in Computer Science

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In this paper we study the decidability of termination of several variants of simple integer loops, without branching in the loop body and with affine constraints as the loop guard (and possibly a precondition). We show that termination of such loops is undecidable in some cases, in particular, when the body of the loop is expressed by a set of linear inequalities where the coefficients are from Z∪{r} with r an arbitrary irrational; when the loop is a sequence of instructions, that compute either linear expressions or the step function; and when the loop body is a piecewise linear deterministic update with two pieces. The undecidability result is proven by a reduction from counter programs, whose termination is known to be undecidable. For the common case of integer linear-constraint loops with rational coefficients we have not succeeded in proving either decidability or undecidability of termination, but we show that a Petri net can be simulated with such a loop; this implies some interesting lower bounds. For example, termination for a partially-specified input is at least EXPSPACE-hard.

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“…The two techniques for automated proofs of termination of narrowing, corresponding to Chapters 4 and 5, have been implemented in the tool [Narradar], consisting of over 10.000 lines of Haskell code developed solely by the author. narradar itself makes use of other tools, including modern SMT solvers as [Yices] and, in earlier versions, of the termination tool AProVE [Giesl et al, 2004].…”

Section: Plan Of the Thesismentioning

confidence: 99%

“…The former is trivially finite by the Dependency Graph processor of Theorem 4.41. The latter can be solved by any modern termination tool implementing the DP method, such as Aprove [Giesl et al, 2004], Mu-Term [Alarcón et al, 2007], or the small, RPO based reduction pair solver in our tool [Narradar].…”

Section: The Argument Filtering Processormentioning

confidence: 99%

Termination of Narrowing: Automated Proofs and Modularity Properties

López¹

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In 1936, Alan Turing proved that the halting problem, that is, deciding whether a program terminates, is an undecidable problem for most practical programming languages. Even so, termination is so relevant that a vast number of techniques for proving the termination of programs have been researched in the recent decades. Term rewriting systems provide an abstract theoretical framework ideally suited for the study of termination. In term rewriting systems, evaluation of a term corresponds to the left-to-right, non-deterministic application of rewriting rules.Narrowing is a generalization of term rewriting that provides a mechanism for automated reasoning. For instance, given a set of rules defining addition and multiplication with natural numbers, rewriting allows to perform evaluation of arithmetic expressions, whereas narrowing allows to solve equations with variables over arithmetic expressions. This thesis constitutes an in-depth study of the termination properties of narrowing. The contributions are as follows.First, we identify classes of systems where narrowing behaves well, in the sense that it always terminates for any system belonging to these classes. Many methods of analysis, such as the semantics-based analysis of program properties by means of narrowing, benefit from this characterization.Second, we develop an automatic method to prove termination of narrowing for a given system, based on the abstract framework of dependency pairs. For the first time, such an automatic method is not restricted to specific classes of TRSs and hence is universally applicable.Third, we propose another automatic method to prove termination of narrowing from a given term, also on top of the framework of dependency pairs. Termination from a given term is relevant for many applications, including the termination analysis of programming languages. Our method generalizes the current state-of-the-art, enabling the study of termination of logic programs in terms of the termination of narrowing, something which was not possible previously.Fourth and last, the modularity properties of the termination of narrowing are considered in detail. That is, given two systems A and B where narrowing is terminating, determine whether it is still terminating in the union system. This notion of modularity has implications in many of the applications of narrowing. We develop the case of combining systems for equational unification.Furthermore, the automated approaches of the second and third contributions above have been implemented in Narradar, our tool for automatic proofs of termination of narrowing. ResumenEn 1936 Alan Turing demostró que el halting problem, esto es, el problema de decidir si un programa termina o no, es un problema indecidible para la inmensa mayoría de los lenguajes de programación. A pesar de ello, la terminación es un problema tan relevante que en lasúltimas décadas un gran número de técnicas han sido desarrolladas para demostrar la terminación de forma automática de la máxima cantidad posible de programas. Los...

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Automated Termination Proofs with AProVE

Cited by 110 publications

References 27 publications

Satisfiability Modulo Recursive Programs

Satisfiability Modulo Recursive Programs

On the Termination of Integer Loops

Termination of Narrowing: Automated Proofs and Modularity Properties

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