A confluent lambda-calculus with a catch/throw mechanism

Abstract

We derive a confluent λ-calculus with a catch/throw mechanism (called λ ct -calculus) from Parigot's λμ-calculus. We also present several translations from one calculus into the other which are morphisms for the reduction. We use them to show that the λ ct -calculus is a retract of λμ-calculus (these calculi are isomorphic if we consider only convertibility). As a by-product, we obtain the subject reduction property for the λ ct -calculus, as well as the strong normalization for λ ct -terms typable in the second order classical natural deduction.