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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Bibliographic Details
Published in:Theoretical computer science Vol. 403; no. 2; pp. 347 - 372
Main Authors: Ehrhard, Thomas, Regnier, Laurent
Format: Journal Article
Language:English
Published: Amsterdam Elsevier B.V 28.08.2008
Elsevier
Subjects:
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
Online Access:Get full text
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Summary: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