Strong normalization proofs by CPS-translations

In this paper, we propose a new proof method for strong normalization of calculi with control operators, and, by this method, we prove strong normalization of the system λμ→∧∨⊥ , which is introduced in [3] by de Groote and corresponds to the classical natural deduction with disjunctions and permutative conversions by the Curry-Howard isomorphism. For our method, we introduce a new CPS-translation, continuation and garbage passing style translation (CGPS-translation). Our method by CGPS-translations is applicable to not only λμ→∧∨⊥ but many other calculi with control operators such as Parigot’s λμ-calculus and its call-by-value variant, and de Groote’s calculus λexn for ML-like exception handling. We also show that our method by CGPS-translations gives much simpler proof than any other strong normalization proofs.