Adapting innocent game models for the Böhm tree λ-theory

Authors:
Andrew D. Ker;Hanno Nickau;C.-H. Luke Ong
Affiliations:
Oxford University Computing Laboratory, Parks Road, Oxford, OX1 3QD, UK;Oxford University Computing Laboratory, Parks Road, Oxford, OX1 3QD, UK;Oxford University Computing Laboratory, Parks Road, Oxford, OX1 3QD, UK
Venue:
Theoretical Computer Science
Year:
2003

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Abstract

We present a game model of the untyped λ-calculus, with equational theory equal to the Böhm tree λ-theory B, which is universal (i.e. every element of the model is definable by some term). This answers a question of Di Gianantonio, Franco and Honsell. We build on our earlier work, which uses the methods of innocent game semantics to develop a universal model inducing the maximal consistent sensible theory H*. To our knowledge these are the first syntax-independent universal models of the untyped λ-calculus.