Convolution ¯ λµ-calculus

We define an extension of Herbelin’s ¯ λµ-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.