Intuitionistic dual-intuitionistic nets

Abstract

The intuitionistic sequent calculus (at most one formula on the right-hand side of sequents) comes with a natural dual system: the dual-intuitionistic sequent calculus (at most one formula on the left-hand side). We explain how the duality between these two systems exactly corresponds to the intensively studied duality between call-by-value systems and call-by-name systems for classical logic. Relying on the uniqueness of the computational behaviour underlying these four logics (intuitionistic, dual-intuitionistic, call-by-value classical and call-by-name classical), we define a generic syntax of nets which can be used for any of these logics. © The Author, 2009. Published by Oxford University Press. All rights reserved.