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Strong functors and interleaving fixpoints in game semantics∗
Published online by Cambridge University Press: 10 January 2013
Abstract
We describe a sequent calculus μLJ with primitives for inductive and coinductive datatypes and equip it with reduction rules allowing a sound translation of Gödel’s system T. We introduce the notion of a μ-closed category, relying on a uniform interpretation of open μLJ formulas as strong functors. We show that any μ-closed category is a sound model for μLJ. We then turn to the construction of a concrete μ-closed category based on Hyland-Ong game semantics. The model relies on three main ingredients: the construction of a general class of strong functors called open functors acting on the category of games and strategies, the solution of recursive arena equations by exploiting cycles in arenas, and the adaptation of the winning conditions of parity games to build initial algebras and terminal coalgebras for many open functors. We also prove a weak completeness result for this model, yielding a normalisation proof for μLJ.
Keywords
- Type
- Research Article
- Information
- RAIRO - Theoretical Informatics and Applications , Volume 47 , Issue 1: 6th Workshop on Fixed Points in Computer Science (FICS'09) , January 2013 , pp. 25 - 68
- Copyright
- © EDP Sciences 2013
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