A confluent lambda-calculus with a catch/throw mechanism
Résumé
We derive a confluent lambda-calculus with a catch/throw mechanism (called lambda-ct-calculus) from M. Parigot's lambda-mu-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 lambda-ct-calculus is a retract of lambda-mu-calculus (these calculi are isomorphic if we consider only convertibility). As a by-product, we obtain the subject reduction property for the lambda-ct-calculus, as well as the strong normalization for lambda-ct-terms typable in the second order classical natural deduction.