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

Jérôme Rocheteau (1)

1 PPS - Preuves, Programmes et Systèmes

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.

Mots clés: Lambda Mu Calculus; Natural Deduction; Lambda Bar Mu Mu Tilde Calculus; Sequent Calculus; Call-by-Name; Call-by-Value; Simulation.; Simulation

Domaines: Logique [math.LO]

Jérôme Rocheteau. Lambda Mu Calculus and Duality: Call-by-Name and Call-by-Value. Rewriting Techniques and Applications, Apr 2005, Nara, Japan. pp.204-218. ⟨hal-00153935⟩