Abstract
We generalize the Constructor-based ReWriting Logic CRWL to the setting of the simply typed λ-calculus, where theories are presented by conditional overlapping fully extended pattern rewrite systems. We claim that this logic is useful for higher-order functional-logic programming, and propose a Higher-Order Lazy Narrowing calculus HOLNDT for answering joinability and reducibility queries, in which a variant of Definitional Trees is used to efficiently control the demand-driven narrowing strategy. The calculus HOLNDT is shown to be sound and strongly complete with respect to this higher-order conditional rewriting logic.
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Antoy, S.: Optimal non-deterministic functional logic computations. In: Hanus, M., Heering, J., Meinke, K. (eds.) ALP 1997 and HOA 1997. LNCS, vol. 1298, pp. 16–30. Springer, Heidelberg (1997)
del Vado Vírseda, R.: A demand-driven narrowing calculus with overlapping definitional trees. In: PPDP, pp. 253–263 (2003)
del Vado Vírseda, R.: Declarative constraint programming with definitional trees. In: FroCos, pp. 184–199 (2005)
González-Moreno, J.C., Hortalá-González, M.T., López-Fraguas, F.J., Rodríguez-Artalejo, M.: An approach to declarative programming based on a rewriting logic. J. Log. Program. 40(1), 47–87 (1999)
González-Moreno, J.C., Hortalá-González, M.T., Rodríguez-Artalejo, M.: A higher order rewriting logic for functional logic programming. In: ICLP, pp. 153–167 (1997)
Hamada, M., Ida, T.: Implementation of lazy narrowing calculi in mathematica. Technical report, RISC, Johannes Kepler University, Austria (1997)
Hanus, M., Prehofer, C.: Higher-order narrowing with definitional trees. J. Funct. Program. 9(1), 33–75 (1999)
Hindley, J.R., Seldin, J.P.: Introduction to Combinatorics and λ-Calculus. Cambridge University Press, Cambridge (1986)
Ida, T., Marin, M., Suzuki, T.: Higher-order lazy narrowing calculus: A solver for higher-order equations. In: Moreno-Díaz Jr., R., Buchberger, B., Freire, J.-L. (eds.) EUROCAST 2001. LNCS, vol. 2178, pp. 479–493. Springer, Heidelberg (2001)
Miller, D.: A logic programming language with lambda-abstraction, function variables, and simple unification. J. Log. Comput. 1(4), 497–536 (1991)
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del Vado Vírseda, R. (2007). A Higher-Order Demand-Driven Narrowing Calculus with Definitional Trees. In: Jones, C.B., Liu, Z., Woodcock, J. (eds) Theoretical Aspects of Computing – ICTAC 2007. ICTAC 2007. Lecture Notes in Computer Science, vol 4711. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75292-9_12
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DOI: https://doi.org/10.1007/978-3-540-75292-9_12
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