  In our paper "Uniformity and the Taylor expansion of ordinary lambda-terms"
(with Laurent Regnier), we studied a translation of lambda-terms as infinite
linear combinations of resource lambda-terms, from a calculus similar to
Boudol's lambda-calculus with resources and based on ideas coming from
differential linear logic and differential lambda-calculus. The good properties
of this translation wrt. beta-reduction were guaranteed by a coherence relation
on resource terms: normalization is "linear and stable" (in the sense of the
coherence space semantics of linear logic) wrt. this coherence relation. Such
coherence properties are lost when one considers non-deterministic or algebraic
extensions of the lambda-calculus (the algebraic lambda-calculus is an
extension of the lambda-calculus where terms can be linearly combined). We
introduce a "finiteness structure" on resource terms which induces a linearly
topologized vector space structure on terms and prevents the appearance of
infinite coefficients during reduction, in typed settings.
