Uniformity and the Taylor expansion of ordinary lambda-terms

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 lambda-calculus with multiplicities (or with resources). In our resource calculus, all applications are (multi)linear in...

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Vydané v:	Theoretical computer science Ročník 403; číslo 2; s. 347 - 372
Hlavní autori:	Ehrhard, Thomas, Regnier, Laurent
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Amsterdam Elsevier B.V 28.08.2008 Elsevier
Predmet:	Algebra Applied sciences Commutative rings and algebras Computer Science Computer science; control theory; systems Denotational semantics Differential lambda-calculus Exact sciences and technology General logic Lambda-calculus Lambda-calculus with multiplicities Lambda-calculus with resources Linear logic Logic and foundations Logic in Computer Science Mathematical logic, foundations, set theory Mathematics Miscellaneous Programming theory Sciences and techniques of general use Theoretical computing Differential lambda-calculus Linear logic Lambda-calculus with resources Denotational semantics Lambda-calculus Lambda-calculus with multiplicities Linear combination Computer theory Semantics Lambda calculus Multiplicity Proof Resource Tree Application Expansion Uniformity Lambda-calculus;Linear logic;Differential lambda-calculus;Lambda-calculus with resources;Lambda-calculus with multiplicities;Denotational semantics lambda-calculus differential lambda-calculus
ISSN:	0304-3975, 1879-2294
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Popis
Shrnutí:	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 lambda-calculus with multiplicities (or with resources). In our resource calculus, all applications are (multi)linear in the algebraic sense, i.e. commute with linear combinations 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, in a surprisingly crucial way, a uniformity property that they enjoy. As a corollary, we obtain (the main part of) a proof that this Taylor expansion commutes with Böhm tree computation, syntactically.
ISSN:	0304-3975 1879-2294
DOI:	10.1016/j.tcs.2008.06.001