Abstract
We introduce a new cartesian closed category of two-level arenas and innocent strategies to model intersection types that are refinements of simple types. Intuitively a property (respectively computation) on the upper level refines that on the lower level. We prove Subject Expansion—any lower-level computation is closely and canonically tracked by the upper-level computation that lies over it—which is a measure of the robustness of the two-level semantics. The game semantics of the type system is fully complete: every winning strategy is the denotation of some derivation. To demonstrate the relevance of the game model, we use it to construct new semantic proofs of non-trivial algorithmic results in higher-order model checking.
A full version with proofs is available at http://www.cs.ox.ac.uk/people/luke.ong/personal/publications/icalp12.pdf .
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References
Ong, C.H.L.: On model-checking trees generated by higher-order recursion schemes. In: LICS, pp. 81–90. IEEE Computer Society (2006)
Hyland, J.M.E., Ong, C.H.L.: On full abstraction for PCF: I, II, and III. Inf. Comput. 163(2), 285–408 (2000)
Kobayashi, N.: Types and higher-order recursion schemes for verification of higher-order programs. In: Shao, Z., Pierce, B.C. (eds.) POPL, pp. 416–428. ACM (2009)
Salvati, S.: On the membership problem for non-linear abstract categorial grammars. Journal of Logic, Language and Information 19(2), 163–183 (2010)
Kobayashi, N., Ong, C.H.L.: A type system equivalent to the modal mu-calculus model checking of higher-order recursion schemes. In: LICS, pp. 179–188. IEEE Computer Society (2009)
Hague, M., Murawski, A.S., Ong, C.H.L., Serre, O.: Collapsible pushdown automata and recursion schemes. In: LICS, pp. 452–461 (2008)
Salvati, S., Walukiewicz, I.: Krivine Machines and Higher-Order Schemes. In: Aceto, L., Henzinger, M., Sgall, J. (eds.) ICALP 2011, Part II. LNCS, vol. 6756, pp. 162–173. Springer, Heidelberg (2011)
Nielson, F.: Two-level semantics and abstract interpretation. Theor. Comput. Sci. 69(2), 117–242 (1989)
Kobayashi, N.: A Practical Linear Time Algorithm for Trivial Automata Model Checking of Higher-Order Recursion Schemes. In: Hofmann, M. (ed.) FOSSACS 2011. LNCS, vol. 6604, pp. 260–274. Springer, Heidelberg (2011)
Tsukada, T., Kobayashi, N.: Untyped Recursion Schemes and Infinite Intersection Types. In: Ong, L. (ed.) FOSSACS 2010. LNCS, vol. 6014, pp. 343–357. Springer, Heidelberg (2010)
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Ong, C.H.L., Tsukada, T. (2012). Two-Level Game Semantics, Intersection Types, and Recursion Schemes. In: Czumaj, A., Mehlhorn, K., Pitts, A., Wattenhofer, R. (eds) Automata, Languages, and Programming. ICALP 2012. Lecture Notes in Computer Science, vol 7392. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31585-5_31
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DOI: https://doi.org/10.1007/978-3-642-31585-5_31
Publisher Name: Springer, Berlin, Heidelberg
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