Abstract
Recently well-quasi orders in general, and homeomorphic embedding in particular, have gained popularity to ensure the termination of program analysis, specialisation and transformation techniques. In this paper we investigate and clarify for the first time, both intuitively and formally, the advantages of such an approach over one using well-founded orders. Notably we show that the homeomorphic embedding relation is strictly more powerful than a large class of involved well-founded approaches.
Part of the work was done while the author was Post-doctoral Fellow of the Fund for Scientific Research - Flanders Belgium (FWO) and visiting DIKU, University of Copenhagen.
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References
M. Alpuente, M. Falaschi, P. Julián, and G. Vidal. Spezialisation of lazy functional logic programs. In Proceedings PEPM’97, pages 151–162, Amsterdam, The Netherlands, 1997. ACM Press.
M. Alpuente, M. Falaschi, and G. Vidal. Narrowing-driven partial evaluation of functional logic programs. In H. Riis Nielson, editor, Proceedings ESOP’96, LNCS 1058, pages 45–61. Springer-Verlag, 1996.
K. R. Apt. Introduction to logic programming. In J. van Leeuwen, editor, Handbook of Theoretical Computer Science, chapter 10, pages 495–574. North-Holland Amsterdam, 1990.
R. Bol. Loop checking in partial deduction. The Journal of Logic Programming, 16(1&2):25–46, 1993.
M. Bruynooghe, D. De Schreye, and B. Martens. A general criterion for avoiding infnite unfolding during partial deduction. New Generation Computing, 11(1):47–79, 1992.
D. De Schreye and S. Decorte. Termination of logic programs: The never ending story. The Journal of Logic Programming, 19 & 20:199–260, May 1994.
N. Dershowitz. Termination of rewriting. Journal of Symbolic Computation, 3:69–116, 1987.
N. Dershowitz and J.-P. Jouannaud. Rewrite systems. In J. van Leeuwen, editor, Handbook of Theoretical Computer Science, Vol.B, pages 243–320. Elsevier, MIT Press, 1990.
N. Dershowitz and Z. Manna. Proving termination with multiset orderings. Communications of the ACM, 22(8):465–476, 1979.
J. Gallagher. Tutorial on specialisation of logic programs. In Proceedings PEPM’93, pages 88–98. ACM Press, 1993.
R. Glück, J. Jørgensen, B. Martens, and M. H. Sørensen. Controlling conjunctive partial deduction of definite logic programs. In H. Kuchen and S. Swierstra, editors, Proceedings PLILP’96, LNCS 1140, pages 152–166, Aachen, Germany, September 1996. Springer-Verlag.
R. Glück and M. H. Sørensen. A roadmap to supercompilation. In O. Danvy, R. Glück, and P. Thiemann, editors, Proceedings of the 1996 Dagstuhl Seminar on Partial Evaluation, LNCS 1110, pages 137–160, Schloß Dagstuhl, 1996. Springer-Verlag.
J. Gustedt. Algorithmic Aspects of Ordered Structures. PhD thesis, Technische Universität Berlin, 1992.
G. Higman. Ordering by divisibility in abstract algebras. Proceedings of the London Mathematical Society, 2:326–336, 1952.
G. Huet. Confluent reductions: Abstract properties and applications to term rewriting systems. Journal of the ACM, 27(4):797–821, 1980.
N. D. Jones. An introduction to partial evaluation. ACM Computing Surveys, 28(3):480–503, September 1996.
N. D. Jones, C. K. Gomard, and P. Sestoft. Partial Evaluation and Automatic Program Generation. Prentice Hall, 1993.
J. Jørgensen, M. Leuschel, and B. Martens. Conjunctive partial deduction in practice. In J. Gallagher, editor, Proceedings LOPSTR’96, LNCS 1207, pages 59–82, Stockholm, Sweden, August 1996. Springer-Verlag.
J. B. Kruskal. Well-quasi ordering, the tree theorem, and Vazsonyi’s conjecture. Transactions of the American Mathematical Society, 95:210–225, 1960.
L. Lafave and J. Gallagher. Constraint-based partial evaluation of rewriting-based functional logic programs. In N. Fuchs, editor, Proceedings LOPSTR’97, LNCS, Leuven, Belgium, July 1997. Springer-Verlag.
P. Lescanne. Well rewrite orderings and well quasi-orderings. Technical Report N∘ 1385, INRIA-Lorraine, France, January 1991.
M. Leuschel. The ECCE partial deduction system and the DPPD library of benchmarks. 1996–1998. Obtainable via http://www.cs.kuleuven.ac.be/~dtai.
M. Leuschel. Advanced Techniques for Logic Program Specialisation. PhD thesis, K.U. Leuven, May 1997. Accessible via http://www.cs.kuleuven.ac.be/~michael.
M. Leuschel. Homeomorphic Embedding for Online Termination. Technical Report, Department of Electronics and Computer Science, University of Southampton, 1998.
M. Leuschel and B. Martens. Global control for partial deduction through characteristic atoms and global trees. In O. Danvy, R. Glück, and P. Thiemann, editors, Proceedings of the 1996 Dagstuhl Seminar on Partial Evaluation, LNCS 1110, pages 263–283, Schloß Dagstuhl, 1996. Springer-Verlag.
M. Leuschel, B. Martens, and D. De Schreye. Controlling generalisation and polyvariance in partial deduction of normal logic programs. ACM Transactions on Programming Languages and Systems, 20(1):208–258, January 1998.
N. Lindenstrauss, Y. Sagiv, and A. Serebrenik. Unfolding the mystery of mergesort. In N. Fuchs, editor, Proceedings LOPSTR’97, LNCS, Leuven, Belgium, July 1997. Springer-Verlag.
J. W. Lloyd. Foundations of Logic Programming. Springer-Verlag, 1987.
J. W. Lloyd and J. C. Shepherdson. Partial evaluation in logic programming. The Journal of Logic Programming, 11(3&4):217–242, 1991.
R. Marlet. Vers une Formalisation de l’Évaluation Partielle. PhD thesis, Université de Nice-Sophia Antipolis, December 1994.
B. Martens. On the Semantics of Meta-Programming and the Control of Partial Deduction in Logic Programming. PhD thesis, K.U. Leuven, February 1994.
B. Martens and D. De Schreye. Automatic ifnite unfolding using well-founded measures. The Journal of Logic Programming, 28(2):89–146, August 1996.
B. Martens, D. De Schreye, and T. Horváth. Sound and complete partial deduction with unfolding based on well-founded measures. Theoretical Computer Science, 122(1–2):97–117, 1994.
B. Martens and J. Gallagher. Ensuring global termination of partial deduction while allowing flexible polyvariance. In L. Sterling, editor, Proceedings ICLP’95, pages 597–613, Kanagawa, Japan, June 1995. MIT Press.
J. Martin. Sonic partial deduction. Technical Report, Department of Electronics and Computer Science, University of Southampton, 1998.
P.-A. Melliès. On a duality between Kruskal and Dershowitz theorems. In K. G. Larsen, editor, Proceedings of ICALP’98, LNCS, Aalborg, Denmark, 1998. Springer-Verlag.
A. Middeldorp and H. Zantema. Simple termination of rewrite systems. Theoretical Computer Science, 175(1):127–158, 1997.
L. Plümer. Termination Proofs for Logic Programs. LNCS 446. Springer-Verlag, 1990.
L. Puel. Using unavoidable set of trees to generalize Kruskal’s theorem. Journal of Symbolic Computation, 8:335–382, 1989.
E. Ruf. Topics in Online Partial Evaluation. PhD thesis, Stanford University, March 1993.
D. Sahlin. Mixtus: An automatic partial evaluator for full Prolog. New Generation Computing, 12(1):7–51, 1993.
M. H. Sørensen and R. Glück. An algorithm of generalization in positive supercompilation. In J. W. Lloyd, editor, Proceedings ILPS’95, pages 465–479, Portland, USA, December 1995. MIT Press.
M. H. Sørensen, R. Glück and N.D. Jones. A positive supercompiler. Journal of Functional Programming, 1996.
J. Stillman. Computational Problems in Equational Theorem Proving. PhD thesis, State University of New York at Albany, 1988.
V. F. Turchin. The concept of a supercompiler. ACM Transactions on Programming Languages and Systems, 8(3):292–325, 1986.
W. Vanhoof and B. Martens. To parse or not to parse. In N. Fuchs, editor, Proceedings LOPSTR’97, LNCS, Leuven, Belgium, July 1997. Springer-Verlag.
D. Weise, R. Conybeare, E. Ruf, and S. Seligman. Automatic online partial evaluation. In Proceedings of the Conference on Functional Programming Languages and Computer Architectures, LNCS 523, pages 165–191, Harvard University, 1991. Springer-Verlag.
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Leuschel, M. (1998). On the Power of Homeomorphic Embedding for Online Termination. In: Levi, G. (eds) Static Analysis. SAS 1998. Lecture Notes in Computer Science, vol 1503. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-49727-7_14
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DOI: https://doi.org/10.1007/3-540-49727-7_14
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