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The Differential LambdaCalculus
 Theoretical Computer Science
, 2001
"... We present an extension of the lambdacalculus with differential constructions motivated by a model of linear logic discovered by the first author and presented in [Ehr01]. We state and prove some basic results (confluence, weak normalization in the typed case), and also a theorem relating the usual ..."
Abstract

Cited by 44 (9 self)
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We present an extension of the lambdacalculus with differential constructions motivated by a model of linear logic discovered by the first author and presented in [Ehr01]. We state and prove some basic results (confluence, weak normalization in the typed case), and also a theorem relating the usual Taylor series of analysis to the linear head reduction of lambdacalculus.
Presentation
, 2003
"... We present an extension of the lambdacalculus with di erential constructions. We state and prove some basic results (con uence, strong normalization in the typed case), and also a theorem relating the usual Taylor series of analysis to the linear head reduction of lambdacalculus. Keywords. Lambda ..."
Abstract
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We present an extension of the lambdacalculus with di erential constructions. We state and prove some basic results (con uence, strong normalization in the typed case), and also a theorem relating the usual Taylor series of analysis to the linear head reduction of lambdacalculus. Keywords. Lambdacalculus, linear logic, denotational semantics, linear head reduction. Prerequisites. This paper assumes from the reader some basic knowledge in lambdacalculus and an elementary (but not technical) knowledge of di erential calculus. Notations. Following [Kri93], we denote by (s)t the lambdacalculus application of s to t. The expression (s)t1... tn denotes the term ( · · · (s)t1 · · ·)tn when n ≥ 1, and s when n = 0. Accordingly, if A1,..., An and A are types, both expressions A1,..., An → A and A1 → · · · → An → A denote the type A1 → ( · · · (An → A) · · ·). If a1,..., an are elements of some given set S, we denote by [a1,..., an] the corresponding multiset over S. If x and y are variables, δx,y is equal to 1 if x = y and to 0 otherwise. We denote by N + the set of positive integers {1, 2,...}.