Lambda Mu Calculus and Duality: Call-by-Name and Call-by-Value

Under the extension of Curry-Howard’s correspondence to classical logic, Gentzen’s NK and LK systems can be seen as syntax-directed systems of simple types respectively for Parigot’s Lambda Mu Calculus and Curien-Herbelin’s Lambda Bar Mu Mu Tidle Calculus. We aim at showing their computational equivalence. We define translations between these calculi. We prove simulation theorems for an undirected evaluation as well as for call-by-name and call-by-value evaluations.