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 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 Innovación 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

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 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. 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Forward Slicing by Conjunctive Partial Deduction and Argument Filtering

Program slicing is a well-known methodology that aims at identifying the program statements that (potentially) affect the values computed at some point of interest. Within imperative programming, this technique has been successfully applied to debugging, specialization, merging, reuse, maintenance, etc. Due to its declarative nature, adapting the slicing notions and techniques to a logic programming setting is not an easy task. In this work, we define the first, semantics-preserving, forward slicing technique for logic programs. Our approach relies on the application of a conjunctive partial deduction algorithm for a precise propagation of information between calls. We do not distinguish between static and dynamic slicing since partial deduction can naturally deal with both static and dynamic data. Furthermore, this approach can quite easily be implemented by adding a new code generator on top of existing partial deduction systems. A slicing tool has been implemented in ECCE, where a post-processing transformation to remove redundant arguments has been added. Experiments conducted on a wide variety of programs are encouraging and demonstrate the usefulness of our approach, both as a classical slicing method and as a technique for code size reduction