7 research outputs found
Combining norms to prove termination
Automatic termination analyzers typically measure the size of terms applying norms which are mappings from terms to the natural numbers. This paper illustrates how to enable the use of size functions defined as tuples of these simpler norm functions. This approach enables us to simplify the problem of deriving automatically a candidate norm with which to prove termination. Instead of deriving a single, complex norm function, it is sufficient to determine a collection of simpler norms, some combination of which, leads to a proof of termination. We propose that a collection of simple norms, one for each of the recursive data-types in the program, is often a suitable choice. We first demonstrate the power of combining norm functions and then the adequacy of combining norms based on regular-types
A decidable subclass of finitary programs
Answer set programming - the most popular problem solving paradigm based on
logic programs - has been recently extended to support uninterpreted function
symbols. All of these approaches have some limitation. In this paper we propose
a class of programs called FP2 that enjoys a different trade-off between
expressiveness and complexity. FP2 programs enjoy the following unique
combination of properties: (i) the ability of expressing predicates with
infinite extensions; (ii) full support for predicates with arbitrary arity;
(iii) decidability of FP2 membership checking; (iv) decidability of skeptical
and credulous stable model reasoning for call-safe queries. Odd cycles are
supported by composing FP2 programs with argument restricted programs
Inference of termination conditions for numerical loops in Prolog
We present a new approach to termination analysis of numerical computations
in logic programs. Traditional approaches fail to analyse them due to non
well-foundedness of the integers. We present a technique that allows overcoming
these difficulties. Our approach is based on transforming a program in a way
that allows integrating and extending techniques originally developed for
analysis of numerical computations in the framework of query-mapping pairs with
the well-known framework of acceptability. Such an integration not only
contributes to the understanding of termination behaviour of numerical
computations, but also allows us to perform a correct analysis of such
computations automatically, by extending previous work on a constraint-based
approach to termination. Finally, we discuss possible extensions of the
technique, including incorporating general term orderings.Comment: To appear in Theory and Practice of Logic Programming. To appear in
Theory and Practice of Logic Programmin
A Transformational Approach to Resource Analysis with Typed-Norms
In order to automatically infer the resource consumption of programs, analyzers track how data sizes change along a program s execution. Typically, analyzers measure the sizes of data by applying norms which are mappings from data to natural numbers that represent the sizes of the corresponding data. When norms are defined by taking type information into account, they are named typed-norms. The main contribution of this paper is a transformational approach to resource analysis with typed-norms. The analysis is based on a transformation of the program into an intermediate abstract program in which each variable is abstracted with respect to all considered norms which are valid for its type. We also sketch a simple analysis that can be used to automatically infer the required, useful, typed-norms from programs.This work was funded partially by the EU project FP7-ICT-610582 ENVISAGE: Engineering Virtualized Services (http://www.envisage-project.eu) and by the Spanish projects TIN2008-05624 and TIN2012-38137. Raúl Gutiérrez is also partially supported by a Juan de la Cierva Fellowship from the Spanish MINECO, ref. JCI-2012-13528.Albert Albiol, EM.; Genaim, S.; Gutiérrez Gil, R. (2014). A Transformational Approach to Resource Analysis with Typed-Norms. Lecture Notes in Computer Science. 8901:38-53. https://doi.org/10.1007/978-3-319-14125-1_3S38538901Albert, E., Arenas, P., Genaim, S., Gómez-Zamalloa, M., Puebla, G.: Cost Analysis of Concurrent OO Programs. In: Yang, H. (ed.) APLAS 2011. LNCS, vol. 7078, pp. 238–254. Springer, Heidelberg (2011)Albert, E., Arenas, P., Genaim, S., Puebla, G., Zanardini, D.: Cost Analysis of Java Bytecode. In: De Nicola, R. (ed.) ESOP 2007. LNCS, vol. 4421, pp. 157–172. Springer, Heidelberg (2007)Albert, E., Arenas, P., Genaim, S., Puebla, G., Zanardini, D.: Removing Useless Variables in Cost Analysis of Java Bytecode. In: Proc. of SAC 2008, pp. 368–375. ACM (2008)Alonso, D., Arenas, P., Genaim, S.: Handling Non-linear Operations in the Value Analysis of COSTA. In: Proc. of BYTECODE 2011. ENTCS, vol. 279, pp. 3–17. Elsevier (2011)Bossi, A., Cocco, N., Fabris, M.: Proving Termination of Logic Programs by Exploiting Term Properties. In: Proc. of TAPSOFT 1991. LNCS, vol. 494, pp. 153–180. Springer (1991)Bruynooghe, M., Codish, M., Gallagher, J., Genaim, S., Vanhoof, W.: Termination Analysis of Logic Programs through Combination of Type-Based norms. TOPLAS 29(2), Art. 10 (2007)Claessen, K., Hughes, J.: QuickCheck: A Lightweight Tool for Random Testing of Haskell Programs. In: Proc. of ICFP 2000, pp. 268–279. ACM (2000)Fähndrich, M.: Static Verification for Code Contracts. In: Cousot, R., Martel, M. (eds.) SAS 2010. LNCS, vol. 6337, pp. 2–5. Springer, Heidelberg (2010)Genaim, S., Codish, M., Gallagher, J.P., Lagoon, V.: Combining Norms to Prove Termination. In: Cortesi, A. (ed.) VMCAI 2002. LNCS, vol. 2294, pp. 123–138. Springer, Heidelberg (2002)Johnsen, E.B., Hähnle, R., Schäfer, J., Schlatte, R., Steffen, M.: ABS: A Core Language for Abstract Behavioral Specification. In: Aichernig, B.K., de Boer, F.S., Bonsangue, M.M. (eds.) Formal Methods for Components and Objects. LNCS, vol. 6957, pp. 142–164. Springer, Heidelberg (2011)King, A., Shen, K., Benoy, F.: Lower-bound Time-complexity Analysis of Logic Programs. In: Proc. of ILPS 1997, pp. 261–275. MIT Press (1997)Serrano, A., Lopez-Garcia, P., Bueno, F., Hermenegildo, M.: Sized Type Analysis for Logic Programs. In: Tech. Comms. of ICLP 2013. Cambridge U. Press (2013) (to appear)Spoto, F., Mesnard, F., Payet, É.: A Termination Analyser for Java Bytecode based on Path-Length. TOPLAS 32(3), Art. 8 (2010)Vallée-Rai, R., Hendren, L., Sundaresan, V., Lam, P., Gagnon, E., Co, P.: Soot - a Java Optimization Framework. In: Proc. of CASCON 1999. pp. 125–135. IBM (1999)Vasconcelos, P.: Space Cost Analysis using Sized Types. Ph.D. thesis, School of CS, University of St. Andrews (2008)Vasconcelos, P.B., Hammond, K.: Inferring Cost Equations for Recursive, Polymorphic and Higher-Order Functional Programs. In: Trinder, P., Michaelson, G.J., Peña, R. (eds.) IFL 2003. LNCS, vol. 3145, pp. 86–101. Springer, Heidelberg (2004)Wegbreit, B.: Mechanical Program Analysis. Commun. ACM 18(9), 528–539 (1975