Abstract
We prove that higher-order matching in the linear λ-calculus with pairing is decidable. We also establish its NP-completeness under the assumption that the right-hand side of the equation to be solved is given in normal form.
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References
Comon, H.: Completion of rewrite systems with membership constraints. Part I: Deduction rules. Journal of Symbolic Computation 25(4), 397–419 (1998)
Comon, H.: Completion of rewrite systems with membership constraints. Part II: Constraint solving. Journal of Symbolic Computation 25(4), 421–453 (1998)
Cook, S.A.: The complexity of theorem proving procedures. In: Proceedings of the 3rd annual ACM Symposium on Theory of Computing, pp. 151–158 (1971)
Dougherty, D., Wierzbicki, T.: A decidable variant of higher order matching. In: Tison, S. (ed.) RTA 2002. LNCS, vol. 2378, pp. 340–351. Springer, Heidelberg (2002)
Dowek, G.: Third order matching is decidable. Annals of Pure and Applied Logic 69(2–3), 135–155 (1994)
Dowek, G.: Higher-order unification and matching. In: Robinson, A., Voronkov, A. (eds.) Handbook of Automated Reasoning, pp. 1009–1062. Elsevier, Amsterdam (2001)
Girard, J.Y.: Linear logic. Theoritical Computer Science 50, 1–102 (1987)
Goldfarb, W.D.: The undecidability of the second-order unification problem. Theoretical Computer Science 13(2), 225–230 (1981)
de Groote, P.h.: Higher-order linear matching is NP-complete. In: Bachmair, L. (ed.) RTA 2000. LNCS, vol. 1833, pp. 127–140. Springer, Heidelberg (2000)
de Groote, P.h., Salvati, S.: On the complexity of higher-order matching in the linear. In: Nieuwenhuis, R. (ed.) RTA 2003. LNCS, vol. 2706, pp. 234–245. Springer, Heidelberg (2003)
Huet, G.: The undecidability of unification in third order logic. Information and Control 22(3), 257–267 (1973)
Huet, G.: R´esolution d’´equations dans les langages d’ordre 1, 2,..., ω. Thèse de Doctorat d’Etat, Université Paris 7 (1976)
Levy, J.: Linear second-order unification. In: Ganzinger, H. (ed.) RTA 1996. LNCS, vol. 1103, pp. 332–346. Springer, Heidelberg (1996)
Loader, R.: Higher order β matching is undecidable. Logic Journal of the IGPL 11(1), 51–68 (2002)
Mairson, H., Terui, K.: On the Computational Complexity of Cut-Elimination in Linear Logic. In: Blundo, C., Laneve, C. (eds.) ICTCS 2003. LNCS, vol. 2841, pp. 23–36. Springer, Heidelberg (2003)
Padovani, V.: Filtrage d’ordre sup´erieure. Thèse de Doctorat, Université de Paris 7 (1996)
Schmidt-Schauß, M., Stuber, J.: On the complexity of linear and stratified context matching problems. Rapport de recherche A01-R-411, LORIA (December 2001)
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de Groote, P., Salvati, S. (2004). Higher-Order Matching in the Linear λ-calculus with Pairing. In: Marcinkowski, J., Tarlecki, A. (eds) Computer Science Logic. CSL 2004. Lecture Notes in Computer Science, vol 3210. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30124-0_19
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DOI: https://doi.org/10.1007/978-3-540-30124-0_19
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