- Uniformity and the Taylor expansion of ordinary lambda-terms doi link

Auteur(s): Ehrhard Thomas, Regnier Laurent

(Article) Publié: -Journal Of Theoretical Computer Science (Tcs), vol. 403 p.347-372 (2008)

Ref HAL: hal-00150275_v1
DOI: 10.1016/j.tcs.2008.06.001
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We define the complete Taylor expansion of an ordinary lambda-term as an infinite linear combination --- with rational coefficients --- of terms of a resource calculus similar to Boudol's resource lambda-calculus. In this calculus, all applications are (multi-)linear in the algebraic sense, i.e. commute with linear combination of the function or the argument. We study the collective behaviour of the beta-reducts of the terms occurring in the Taylor expansion of any ordinary lambda-term, using a uniformity property that they enjoy.