Böhm trees, krivine's machine and the taylor expansion of lambda-terms

Authors:
Thomas Ehrhard;Laurent Regnier
Affiliations:
Preuves, Programmes et Systèmes (UMR 7126);Institut de Mathématiques de Luminy (UMR 6206)
Venue:
CiE'06 Proceedings of the Second conference on Computability in Europe: logical Approaches to Computational Barriers
Year:
2006

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Abstract

We introduce and study a version of Krivine's machine which provides a precise information about how much of its argument is needed for performing a computation. This information is expressed as a term of a resource lambda-calculus introduced by the authors in a recent article; this calculus can be seen as a fragment of the differential lambda-calculus. We use this machine to show that Taylor expansion of lambda-terms (an operation mapping lambda-terms to generally infinite linear combinations of resource lambda-terms) commutes with Böhm tree computation.