A uniform calculus for linear logic is presented. The calculus has the form of a natural deduction system in sequent calculus style with general introduction and elimination rules. General elimination rules are motivated through an inversion principle, the dual form of which gives the general introduction rules. By restricting all the rules to their single-succedent versions, a uniform calculus for intuitionistic linear logic is obtained. The calculus encompasses both natural deduction and sequent calculus that are obtained as special instances from (...) the uniform calculus. Other instances give all the invertibilities and partial invertibilities for the sequent calculus rules of linear logic. The calculus is normalizing and satisfies the subformula property for normal derivations. (shrink)

The introduction of Linear Logic extends the Curry-Howard Isomorphism to intensional aspects of the typed functional programming. In particular, every formula of Linear Logic tells whether the term it is a type for, can be either erased/duplicated or not, during a computation. So, Linear Logic can be seen as a model of a computational environment with an explicit control about the management of resources.This paper introduces a typed functional language ! and a categorical model for it.