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Journal of Logic and Computation Advance Access originally published online on April 23, 2008
Journal of Logic and Computation 2008 18(6):849-883; doi:10.1093/logcom/exn007
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© The Author, 2008. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Original Articles

The Expansion Problem in Lambda Calculi with Explicit Substitution

Ariel Arbiser

Department of Computer Science, University of Buenos Aires, Pabellón I - Ciudad Universitaria (1428) Buenos Aires, Argentina.
E-mail: arbiser{at}dc.uba.ar

Received 30 January 2006.


  Abstract

In this article, we address the problem of expansion with respect to rules of a calculus with explicit substitution. Mainly, we analyse the {lambda}{upsilon}– and {lambda}s–calculi sets of terms having the property of expansion to pure terms, as minimal sets of terms for these calculi. We prove that, contrarily to what happens in the {lambda}x–calculus in which this set is trivial, for {lambda}{upsilon} and {lambda}s they are proper and non-recursive, so a calculus based on a minimal set of terms has a syntax which is not context-free and hence cannot be presented in the usual way.

Keywords: Context-free; expansion; explicit substitution; lambda calculus; lambda s; lambda upsilon; recursiv set


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