Two-level game semantics, intersection types, and recursion schemes

Authors:
C.-H. Luke Ong;Takeshi Tsukada
Affiliations:
Department of Computer Science, University of Oxford, UK;Graduate School of Information Science, Tohoku University, Japan, JSPS, Japan
Venue:
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part II
Year:
2012

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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.