Abstract
We prove that the inhabitation problem for rank two intersection types is decidable, but (contrary to a common belief) EXPTIME-hard. The exponential time hardness is shown by reduction from the in-place acceptance problem for alternating Turing machines.
Partly suported by the Polish government grant 3 T11C 002 27.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Alessi, F., Barbanera, F., Dezani-Ciancanglini, M.: Intersection types and lambda models. Theoretical Computer Science 355(2), 108–126 (2006)
Kurata, T., Takahashi, M.: Decidable properties of intersection type systems. In: Dezani-Ciancaglini, M., Plotkin, G. (eds.) TLCA 1995. LNCS, vol. 902, pp. 297–311. Springer, Heidelberg (1995)
Leivant, D.: Polymorphic type inference. In: Proceedings of the 10th ACM Symposium on Principles of Programing Languages, Austin, Texas, pp. 88–98. ACM Press, New York (1983)
Lopez-Escobar, E.G.K.: Proof-Functional Connectives. In: Proof-Functional Connectives. LNCS, vol. 1130, pp. 208–221. Springer, Heidelberg (1985)
Mints, G.: The Completeness of Provable Realizability. Notre Dame Journal of Formal Logic 30, 420–441 (1989)
Papadimitriou, C.H.: Computational Complexity. Addison-Wesley Publishing Company, Reading, MA (1995)
Statman, R.: Intuitionistic propositional logic is polynomial-space complete. TCS 9, 67–72 (1979)
Urzyczyn, P.: The emptiness problem for intersection types. Journal of Symbolic Logic 64(3), 1195–1215 (1999)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer Berlin Heidelberg
About this paper
Cite this paper
Kuśmierek, D. (2007). The Inhabitation Problem for Rank Two Intersection Types. In: Della Rocca, S.R. (eds) Typed Lambda Calculi and Applications. TLCA 2007. Lecture Notes in Computer Science, vol 4583. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73228-0_18
Download citation
DOI: https://doi.org/10.1007/978-3-540-73228-0_18
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-73227-3
Online ISBN: 978-3-540-73228-0
eBook Packages: Computer ScienceComputer Science (R0)