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Two-Level Game Semantics, Intersection Types, and Recursion Schemes

  • C. -H. Luke Ong
  • Takeshi Tsukada
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7392)

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.

Keywords

Model Check Intersection Type Winning Strategy Type Environment Recursion Scheme 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • C. -H. Luke Ong
    • 1
  • Takeshi Tsukada
    • 2
    • 3
  1. 1.Department of Computer ScienceUniversity of OxfordUK
  2. 2.Graduate School of Information ScienceTohoku UniversityJapan
  3. 3.JSPSJapan

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