The Fine Structure of Game Lambda Models

Authors:
Pietro Di Gianantonio;Gianluca Franco
Affiliations:
-;-
Venue:
FST TCS 2000 Proceedings of the 20th Conference on Foundations of Software Technology and Theoretical Computer Science
Year:
2000

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Abstract

We study models of the untyped lambda calculus in the setting of game semantics. In particular, we show that, in the category of games G, introduced by Abramsky, Jagadeesan and Malacaria, all categorical λ-models can be partitioned in three disjoint classes, and each model in a class induces the same theory (i.e. the set of equations between terms), that are the theory H*, the theory which identifies two terms iff they have the same Böhm tree and the theory which identifies all the terms which have the same LÉvy-Longo tree.