Duality of computation and sequent calculus: a few more remarks

A succession of works have contributed to the understanding of the computational content of Gentzen-style classical sequent calculus. Especially, it has been shown that the left-right duality of sequent calculus expresses a syntactic duality between programs and their evaluation contexts and that sequent calculus has two dual syntactic restrictions that respectively correspond to callby-name evaluation and call-by-value evaluation. We propose here an interpretation of the unrestricted syntax of sequent calculus, which, thanks to the use of laziness operators, validates eta-equalities and for which the call-by-name and call-by-value subsystems are obtained by restrictions at the semantic level only. Also, to reason with connectives in sequent calculus, we introduce a purely computational and generic approach of the notion of logical connective.