Uniformity and the Taylor expansion of ordinary lambda-terms

Uniformity and the Taylor expansion of ordinary lambda-terms

Böhm trees, Krivine machine and the Taylor expansion of ordinary lambda-terms

We show that, given an ordinary lambda-term and a normal resource lambda-term which appears in the normal form of its Taylor expansion, the unique resource term of the Taylor expansion of the ordinary lambda-term reducing to this normal resource term can be obtained by running a version of the Krivine abstract machine.

Böhm Trees, Krivine's Machine and the Taylor Expansion of Lambda-Terms

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 e...

Normalizing the Taylor expansion of non-deterministic {\lambda}-terms, via parallel reduction of resource vectors

It has been known since Ehrhard and Regnier’s seminal work on the Taylor expansion of λ-terms that this operation commutes with normalization: the expansion of a λ-term is always normalizable and its normal form is the expansion of the Böhm tree of the term. We generalize this result to the non-uniform setting of the algebraic λ-calculus, i.e., λ-calculus extended with linear combinations of te...

Strong Normalizability as a Finiteness Structure via the Taylor Expansion of \lambda λ -terms

In the folklore of linear logic, a common intuition is that the structure of finiteness spaces, introduced by Ehrhard, semantically reflects the strong normalization property of cut-elimination. We make this intuition formal in the context of the non-deterministic λ-calculus by introducing a finiteness structure on resource terms, which is such that a λ-term is strongly normalizing iff the supp...