The differential lambda-calculus

Thomas Ehrhard (1) , Laurent Regnier (1)

1 IML - Institut de mathématiques de Luminy

We present an extension of the lambda-calculus with differential constructions. We state and prove some basic results (confluence, strong normalization in the typed case), and also a theorem relating the usual Taylor series of analysis to the linear head reduction of lambda-calculus.

Mots clés: Lambda-calculus; Linear logic; Denotational semantics; Linear head reduction

Domaines: Logique en informatique [cs.LO]

Thomas Ehrhard, Laurent Regnier. The differential lambda-calculus. Theoretical Computer Science, 2003, 309 (1-3), pp.1-41. ⟨10.1016/S0304-3975(03)00392-X⟩. ⟨hal-00150572⟩