Linear λμ is CP (more or less)

Abstract

In this paper we compare Wadler’s CP calculus for classical linear processes to a linear version of Parigot’s λμ calculus for classical logic. We conclude that linear λμ is “more or less” CP, in that it equationally corresponds to a polarized version of CP. The comparison is made by extending a technique from Melliès and Tabareau’s tensor logic that correlates negation with polarization. The polarized CP, which is written CP± and pronounced “CP more or less,” is an interesting bridge in the landscape of Curry-Howard interpretations of logic.