A finiteness structure on resource terms

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 ...

• Type: Journal
• Year: 2010
• Where: CORR
• Authors: Thomas Ehrhard
• Keywords: Coherence Relation, CORR 2010, Education, Lambda-calculus, Linear Logic