Böhm trees, Krivine machine and the Taylor expansion of ordinary lambda-terms
Résumé
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 Boehm tree computation.