130 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
Acceptability with general orderings
We present a new approach to termination analysis of logic programs. The
essence of the approach is that we make use of general orderings (instead of
level mappings), like it is done in transformational approaches to logic
program termination analysis, but we apply these orderings directly to the
logic program and not to the term-rewrite system obtained through some
transformation. We define some variants of acceptability, based on general
orderings, and show how they are equivalent to LD-termination. We develop a
demand driven, constraint-based approach to verify these
acceptability-variants.
The advantage of the approach over standard acceptability is that in some
cases, where complex level mappings are needed, fairly simple orderings may be
easily generated. The advantage over transformational approaches is that it
avoids the transformation step all together.
{\bf Keywords:} termination analysis, acceptability, orderings.Comment: To appear in "Computational Logic: From Logic Programming into the
Future
Homeomorphic Embedding for Online Termination of Symbolic Methods
Well-quasi orders in general, and homeomorphic embedding in particular, have gained popularity to ensure the termination of techniques for program analysis, specialisation, transformation, and verification. In this paper we survey and discuss this use of homeomorphic embedding and clarify the advantages of such an approach over one using well-founded orders. We also discuss various extensions of the homeomorphic embedding relation. We conclude with a study of homeomorphic embedding in the context of metaprogramming, presenting some new (positive and negative) results and open problems
A hybrid approach to conjunctive partial evaluation of logic programs
Conjunctive partial deduction is a well-known technique for the partial evaluation of logic programs. The original formulation follows the so called online approach where all termination decisions are taken on-the-fly. In contrast, offline partial evaluators first analyze the source program and produce an annotated version so that the partial evaluation phase should only follow these annotations to ensure the termination of the process. In this work, we introduce a lightweight approach to conjunctive partial deduction that combines some of the advantages of both online and offline styles of partial evaluation. © 2011 Springer-Verlag.This work has been partially supported by the Spanish Ministerio de Ciencia e
InnovaciĂłn under grant TIN2008-06622-C03-02 and by the Generalitat Valenciana
under grant ACOMP/2010/042.Vidal Oriola, GF. (2011). A hybrid approach to conjunctive partial evaluation of logic programs. En Logic-Based Program Synthesis and Transformation. Springer Verlag (Germany). 6564:200-214. https://doi.org/10.1007/978-3-642-20551-4_13S2002146564Ben-Amram, A., Codish, M.: A SAT-Based Approach to Size Change Termination with Global Ranking Functions. In: Ramakrishnan, C.R., Rehof, J. (eds.) TACAS 2008. LNCS, vol. 4963, pp. 218–232. Springer, Heidelberg (2007)Bruynooghe, M., De Schreye, D., Martens, B.: A General Criterion for Avoiding Infinite Unfolding during Partial Deduction of Logic Programs. In: Saraswat, V., Ueda, K. (eds.) Proc. 1991 Int’l Symp. on Logic Programming, pp. 117–131 (1991)Christensen, N.H., Glück, R.: Offline Partial Evaluation Can Be as Accurate as Online Partial Evaluation. ACM Transactions on Programming Languages and Systems 26(1), 191–220 (2004)Codish, M., Taboch, C.: A Semantic Basis for the Termination Analysis of Logic Programs. Journal of Logic Programming 41(1), 103–123 (1999)De Schreye, D., Glück, R., Jørgensen, J., Leuschel, M., Martens, B., Sørensen, M.H.: Conjunctive Partial Deduction: Foundations, Control, Algorihtms, and Experiments. Journal of Logic Programming 41(2&3), 231–277 (1999)Hruza, J., Stepánek, P.: Speedup of logic programs by binarization and partial deduction. TPLP 4(3), 355–380 (2004)Jones, N.D., Gomard, C.K., Sestoft, P.: Partial Evaluation and Automatic Program Generation. Prentice-Hall, Englewood Cliffs (1993)Leuschel, M.: Homeomorphic Embedding for Online Termination of Symbolic Methods. In: Mogensen, T.Æ., Schmidt, D.A., Sudborough, I.H. (eds.) The Essence of Computation. LNCS, vol. 2566, pp. 379–403. Springer, Heidelberg (2002)Leuschel, M.: The DPPD (Dozens of Problems for Partial Deduction) Library of Benchmarks (2007), http://www.ecs.soton.ac.uk/~mal/systems/dppd.htmlLeuschel, M., Elphick, D., Varea, M., Craig, S., Fontaine, M.: The Ecce and Logen Partial Evaluators and Their Web Interfaces. In: Proc. of PEPM 2006, pp. 88–94. IBM Press (2006)Leuschel, M., Vidal, G.: Fast Offline Partial Evaluation of Large Logic Programs. In: Hanus, M. (ed.) LOPSTR 2008. LNCS, vol. 5438, pp. 119–134. Springer, Heidelberg (2009)Lloyd, J.W., Shepherdson, J.C.: Partial Evaluation in Logic Programming. Journal of Logic Programming 11, 217–242 (1991)Somogyi, Z.: A System of Precise Modes for Logic Programs. In: Shapiro, E.Y. (ed.) Proc. of Third Int’l Conf. on Logic Programming, pp. 769–787. The MIT Press, Cambridge (1986
Convex Hull Abstraction in Specialisation of CLP Programs
We introduce an abstract domain consisting of atomic formulas constrained by linear arithmetic constraints (or convex hulls). This domain is used in an algorithm for specialization of constraint logic programs. The algorithm incorporates in a single phase both top-down goal directed propagation and bottom-up answer propagation, and uses a widening on the convex hull domain to ensure termination. We give examples to show the precision gained by this approach over other methods in the literature for specializing constraint logic programs. The specialization method can also be used for ordinary logic programs containing arithmetic, as well as constraint logic programs. Assignments, inequalities and equalities with arithmetic expressions can be interpreted as constraints during specialization, thus increasing the amount of specialization that can be achieved.We introduce an abstract domain consisting of atomic formulas constrained by linear arithmetic constraints (or convex hulls). This domain is used in an algorithm for specialization of constraint logic programs. The algorithm incorporates in a single phase both top-down goal directed propagation and bottom-up answer propagation, and uses a widening on the convex hull domain to ensure termination. We give examples to show the precision gained by this approach over other methods in the literature for specializing constraint logic programs. The specialization method can also be used for ordinary logic programs containing arithmetic, as well as constraint logic programs. Assignments, inequalities and equalities with arithmetic expressions can be interpreted as constraints during specialization, thus increasing the amount of specialization that can be achieved.</p
A Finite Representation of the Narrowing Space
The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-319-14125-1_4Narrowing basically extends rewriting by allowing free variables
in terms and by replacing matching with unification. As a consequence,
the search space of narrowing becomes usually infinite, as in
logic programming. In this paper, we introduce the use of some operators
that allow one to always produce a finite data structure that still represents
all the narrowing derivations. Furthermore, we extract from this
data structure a novel, compact equational representation of the (possibly
infinite) answers computed by narrowing for a given initial term.
Both the finite data structure and the equational representation of the
computed answers might be useful in a number of areas, like program
comprehension, static analysis, program transformation, etc.Nishida, N.; Vidal, G. (2013). A Finite Representation of the Narrowing Space. En Logic-Based Program Synthesis and Transformation. Springer. 54-71. doi:10.1007/978-3-319-14125-1_4S5471Albert, E., Vidal, G.: The Narrowing-Driven Approach to Functional Logic Program Specialization. New Generation Computing 20(1), 3–26 (2002)Alpuente, M., Falaschi, M., Vidal, G.: Partial Evaluation of Functional Logic Programs. ACM Transactions on Programming Languages and Systems 20(4), 768–844 (1998)Alpuente, M., Falaschi, M., Vidal, G.: Compositional Analysis for Equational Horn Programs. In: RodrĂguez-Artalejo, M., Levi, G. (eds.) ALP 1994. LNCS, vol. 850, pp. 77–94. Springer, Heidelberg (1994)Antoy, S., Ariola, Z.: Narrowing the Narrowing Space. In: Hartel, P.H., Kuchen, H. (eds.) PLILP 1997. LNCS, vol. 1292, pp. 1–15. Springer, Heidelberg (1997)Arts, T., Giesl, J.: Termination of term rewriting using dependency pairs. 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Theoretical Computer Science 367(1–2), 162–202 (2006)Escobar, S., Meseguer, J.: Symbolic Model Checking of Infinite-State Systems Using Narrowing. In: Baader, F. (ed.) RTA 2007. LNCS, vol. 4533, pp. 153–168. Springer, Heidelberg (2007)Fribourg, L.: SLOG: A Logic Programming Language Interpreter Based on Clausal Superposition and Rewriting. In: Proceedings of the Symposium on Logic Programming, pp. 172–185. IEEE Press (1985)Gnaedig, I., Kirchner, H.: Proving weak properties of rewriting. Theoretical Computer Science 412(34), 4405–4438 (2011)Hanus, M.: The integration of functions into logic programming: From theory to practice. Journal of Logic Programming 19&20, 583–628 (1994)Hanus, M. (ed.): Curry: An integrated functional logic language (vers. 0.8.3) (2012). http://www.curry-language.orgHermenegildo, M., Rossi, F.: On the Correctness and Efficiency of Independent And-Parallelism in Logic Programs. In: Lusk, E., Overbeck, R. (eds.) Proceedings of the 1989 North American Conf. on Logic Programming, pp. 369–389. The MIT Press, Cambridge (1989)Hölldobler, S. (ed.): Foundations of Equational Logic Programming. LNCS, vol. 353. Springer, Heidelberg (1989)Meseguer, J., Thati, P.: Symbolic Reachability Analysis Using Narrowing and its Application to Verification of Cryptographic Protocols. Electronic Notes in Theoretical Computer Science 117, 153–182 (2005)Middeldorp, A., Okui, S.: A Deterministic Lazy Narrowing Calculus. Journal of Symbolic Computation 25(6), 733–757 (1998)Nishida, N., Sakai, M., Sakabe, T.: Generation of Inverse Computation Programs of Constructor Term Rewriting Systems. IEICE Transactions on Information and Systems J88–D–I(8), 1171–1183 (2005) (in Japanese)Nishida, N., Sakai, M., Sakabe, T.: Partial Inversion of Constructor Term Rewriting Systems. In: Giesl, J. (ed.) RTA 2005. LNCS, vol. 3467, pp. 264–278. Springer, Heidelberg (2005)Nishida, N., Vidal, G.: Program inversion for tail recursive functions. In: Schmidt-SchauĂź, M. (ed.) Proceedings of the 22nd International Conference on Rewriting Techniques and Applications. LIPIcs, vol. 10, pp. 283–298. Schloss Dagstuhl - Leibniz-Zentrum fĂĽr Informatik (2011)Nishida, N., Vidal, G.: Computing More Specific Versions of Conditional Rewriting Systems. In: Albert, E. (ed.) LOPSTR 2012. LNCS, vol. 7844, pp. 137–154. Springer, Heidelberg (2013)Nutt, W., RĂ©ty, P., Smolka, G.: Basic Narrowing Revisited. Journal of Symbolic Computation 7(3/4), 295–317 (1989)Ohlebusch, E.: Advanced Topics in Term Rewriting. Springer, London, UK (2002)Palamidessi, C.: Algebraic Properties of Idempotent Substitutions. In: Paterson, M. (ed.) ICALP 1990. LNCS, vol. 443, pp. 386–399. Springer, Heidelberg (1990)Ramos, J.G., Silva, J., Vidal, G.: Fast Narrowing-Driven Partial Evaluation for Inductively Sequential Systems. In: Danvy, O., Pierce, B.C. (eds.) 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