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The infinitary lambda calculus of the infinite eta Böhm trees

Published online by Cambridge University Press:  17 August 2015

PAULA SEVERI  and
FER-JAN DE VRIES
PAULA SEVERI
Affiliation:
Department of Computer Science, University of Leicester, Leicester, U.K. Email: pgs11@le.ac.uk, fdv1@mcs.le.ac.uk
FER-JAN DE VRIES
Affiliation:
Department of Computer Science, University of Leicester, Leicester, U.K. Email: pgs11@le.ac.uk, fdv1@mcs.le.ac.uk
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Abstract

In this paper, we introduce a strong form of eta reduction called etabang that we use to construct a confluent and normalising infinitary lambda calculus, of which the normal forms correspond to Barendregt's infinite eta Böhm trees. This new infinitary perspective on the set of infinite eta Böhm trees allows us to prove that the set of infinite eta Böhm trees is a model of the lambda calculus. The model is of interest because it has the same local structure as Scott's D∞-models, i.e. two finite lambda terms are equal in the infinite eta Böhm model if and only if they have the same interpretation in Scott's D∞-models.

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 27 , Special Issue 5: Computing with Lambda-terms. A Special Issue Dedicated to Corrado Böhm for his 90th Birthday , June 2017 , pp. 681 - 733
Copyright
Copyright © Cambridge University Press 2015 

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