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)


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.


Model Check Intersection Type Winning Strategy Type Environment Recursion Scheme 
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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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