Strong normalizability of the non-deterministic catch/throw calculi

The catch/throw mechanism in Common Lisp provides a simple control mechanism for non-local exit. We study typed calculi by Nakano and Sato which formalize the catch/throw mechanism. These calculi correspond to classical logic through the Curry-Howard isomorphism, and one of their characteristic points is that they have nondeterministic reduction rules. These calculi can represent various computational meaning of classical proofs. This paper is mainly concerned with the strong normalizability of these calculi. Namely, we prove the strong normalizability of these calculi, which was an open problem. We rst formulate a non-deterministic variant of Parigot's -calculus, and show it is strongly normalizing. We then translate the catch/throw calculi to this variant. Since the translation preserves typing and reduction, we obtain the strong normalization of the catch/throw calculi. We also brie y consider second-order extension of the catch/throw calculi.