Abstract
First order conditional rewrite systems R have been extensively studied. If R is confluent and terminating, then narrowing is a sound and complete procedure to compute all solutions of a goal s = t modulo R. Recently there has been developed a satisfactory way to combine higher order terms and unconditional rewriting. In this paper we first show that this approach can be carried over to conditional higher order rewrite systems. Then we study narrowing using higher order rewrite systems. A naive translation of first order narrowing may lead to unsolvable unification problems. So we restrict to ”quasi first order” goals and ”simple” rewrite systems.
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References
P. Aczel: A. general Church-Rosser theorem. Technical report, University of Manchester, 1978.
J. Avenhaus, C. Loría-Sáenz: On conditional rewrite systems with extra variables and deterministic logic programs, to appear in Conf. on Logic Programming and Automated Reasoning (LPAR '94)
J. Avenhaus, K. Madlener: Term rewriting and equational reasoning, 284 in: R.B. Banerji, ed., Formal Techniques in Artifical Intelligence, North Holland, Amsterdam, pp. 1–43, 1990.
V. Breazu-Tannen: Combining algebra and higher order types. In Proc. 3rd IEEE Symp. Logic in Computer Science, 1988, pp. 82–90.
N. Dershowitz: Termination of rewriting. Journal Symbolic Computation, 3:69–116, 1987.
N. Dershowitz and J.-P. Jouannaud: Rewrite systems. In J. van Leeuwen, editor, Formal Models and Semantics, Handbook of Theoretical Computer Science, Vol. B, pp. 243–320. The MIT Press, 1990.
N. Dershowitz, M. Okada: A Rationale for Conditional Equational Programming. Theoretical Computer Science, 75:111–138, 1990
J. Hindley, J. Seldin: Introduction to Combinators and λ-Calculus. Cambridge University Press, 1986.
S. Hölldobler: Foundations of Equational Logic Programming, volume 353 of Lectures Notes in Artificial Intelligence. Springer, 1989.
S. Kaplan: Simplifying conditional term rewriting systems: Unification termination and confluence, JSC, 1987, pp. 295–334.
J. Klop: Combinatory reduction systems. Mathematical Centre Tracts 127. Mathematisch Centrum, Amsterdam, 1980.
C. Loría-Sáenz, J. Steinbach: Termintion of combined (rewrite systems and lambda-calculus) systems. In M. Rusinowitch and J.L. Remy, editors, Conditional Term Rewriting Systems, pp. 143–147, LNCS 656, 1992.
C. Loría-Síenz: A theoretical framework for reasoning about program construction based on extensions of rewrite systems, Dissertation, Univ. Kaiserslautern, 1993.
D. Miller: A logic programming language with lambda-abstraction, function variables, and simple unification. In P. Schroeder-Heister, editor, Extensions of Logic Programming, pp. 253–281, LNCS 475, 1991.
A. Middeldorp, E. Hamoen: Counterexamples to completeness results for basic narrowing. In H. Kirchner, G. Levi, editors, Algebraic and Logic Programming, pp. 244–258, LNCS 632.
T. Nipkow: Higher-order critical pairs. Symposium on Logic in Computer Science, pp. 342–349, 1991.
C. Prehofer: Higher-order narrowing. To appear in: Logic in Computer Science, 1994.
D.A. Wolfram: The clausal theory of types, Cambridge University Press, Cambridge Tracts in Theoretical Computer Science, Vol. 21, 1993.
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© 1994 Springer-Verlag Berlin Heidelberg
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Avenhaus, J., Loría-Sáenz, C. (1994). Higher order conditional rewriting and narrowing. In: Jouannaud, JP. (eds) Constraints in Computational Logics. CCL 1994. Lecture Notes in Computer Science, vol 845. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0016859
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DOI: https://doi.org/10.1007/BFb0016859
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