Higher-Order Matching in the Linear Lambda Calculus in the Absence of Constants Is NP-Complete
A lambda term is linear if every bound variable occurs exactly once. The same constant may occur more than once in a linear term. It is known that higher-order matching in the linear lambda calculus is NP-complete (de Groote 2000), even if each unknown occurs exactly once (Salvati and de Groote 2003). Salvati and de Groote (2003) also claim that the interpolation problem, a more restricted kind of matching problem which has just one occurrence of just one unknown, is NP-complete in the linear lambda calculus. In this paper, we correct a flaw in Salvati and de Groote’s (2003) proof of this claim, and prove that NP-hardness still holds if we exclude constants from problem instances. Thus, multiple occurrences of constants do not play an essential role for NP-hardness of higher-order matching in the linear lambda calculus.
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- 2.de Groote, P.: Towards abstract categorial grammars. In: Association for Computational Linguistics, 39th Annual Meeting and 10th Conference of the European Chapter, Proceedings of the Conference, pp. 148–155 (2001)Google Scholar
- 8.Levy, J.: Linear second-order unification. In: Ganzinger, H. (ed.) RTA 1996. LNCS, vol. 1103, pp. 332–346. Springer, Heidelberg (1996)Google Scholar
- 11.Pogodalla, S.: Using and extending ACG technology: Endowing categorial grammars with an underspecified semantic representation. In: Proceedings of Categorial Grammars 2004, Montpellier, June 2004, pp. 197–209 (2004)Google Scholar