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 |
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| Hlavní autori: | , |
| Médium: | Journal Article |
| Jazyk: | English |
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Elsevier B.V
28.08.2008
Elsevier |
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| ISSN: | 0304-3975, 1879-2294 |
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| Abstract | 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. |
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| AbstractList | 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. 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. |
| Author | Regnier, Laurent Ehrhard, Thomas |
| Author_xml | – sequence: 1 givenname: Thomas surname: Ehrhard fullname: Ehrhard, Thomas email: thomas.ehrhard@pps.jussieu.fr organization: Laboratoire PPS (UMR 7126), Université Paris Diderot–Paris 7, Case 7014, 75205 Paris Cedex 13, France – sequence: 2 givenname: Laurent surname: Regnier fullname: Regnier, Laurent email: regnier@iml.univ-mrs.fr organization: Institut de Mathématiques de Luminy (UMR 6206), Campus de Luminy, Case 907, 13288 Marseille Cedex 9, France |
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| Cites_doi | 10.1016/j.tcs.2007.02.028 10.1016/S0168-0072(00)00056-7 10.1016/S0304-3975(03)00392-X 10.1007/s10990-007-9018-9 10.1016/j.tcs.2006.08.003 10.1017/S096012950100336X 10.1017/S0960129599002893 10.1017/S0960129504004645 10.1007/3-540-57208-2_1 10.1093/logcom/10.3.411 10.1016/0304-3975(86)90044-7 10.1016/0304-3975(87)90045-4 |
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| Keywords | 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 |
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| SubjectTerms | 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 |
| Title | Uniformity and the Taylor expansion of ordinary lambda-terms |
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