Geometry of resource interaction and Taylor–Ehrhard–Regnier expansion: a minimalist approach

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.

Uniformity and the Taylor expansion of ordinary lambda-terms

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...

Taylor Expansion, β-Reduction and Normalization

We introduce a notion of reduction on resource vectors, i.e. infinite linear combinations of resource λ-terms. The latter form the multilinear fragment of the differential λ-calculus introduced by Ehrhard and Regnier, and resource vectors are the target of the Taylor expansion of λ-terms. We show that the reduction of resource vectors contains the image, through Taylor expansion, of β-reduction...

A characterization of the Taylor expansion of λ-terms∗

The Taylor expansion of λ-terms, as introduced by Ehrhard and Regnier, expresses a λ-term as a series of multi-linear terms, called simple terms, which capture bounded computations. Normal forms of Taylor expansions give a notion of infinitary normal forms, refining the notion of Böhm trees in a quantitative setting. We give the algebraic conditions over a set of normal simple terms which chara...