Convolution lambda-bar-mu-calculus

Lionel Vaux (1, 2)

1 IML - Institut de mathématiques de Luminy
2 LAMA - Laboratoire de Mathématiques

We define an extension of Herbelin's lambda-bar-mu-calculus, introducing a product operation on contexts (in the sense of lists of arguments, or stacks in environment machines), similar to the convolution product of distributions. This is the computational couterpart of some new semantical constructions, extending models of Ehrhard-Regnier's differential interaction nets, along the lines of Laurent's polarization of linear logic. We demonstrate this correspondence by providing this calculus with a denotational semantics inside a lambda-model in the category of sets and relations.

Mots clés: differential linear logic; classical logic; polarization; lambda-bar-mu-calculus

Domaines: Langage de programmation [cs.PL]; Logique en informatique [cs.LO]; Logique [math.LO]

Lionel Vaux. Convolution lambda-bar-mu-calculus. 8th International Conference onTyped Lambda Calculi and Applications, TLCA 2007, Jun 2007, Paris, France. pp.381-395, ⟨10.1007/978-3-540-73228-0_27⟩. ⟨hal-00387063⟩