Explicit substitutions for control operators ?

The-calculus is a-calculus with a local operator closely related to normal-isation procedures in classical logic and control operators in functional programming. We introduce exp, an explicit substitution calculus for , show it preserves strong normali-sation and that its simply typed version is strongly normalising. Interestingly, exp is the rst example for which the decency method of showing preservation of strong normalisation (PSN) works whereas the structure preserving method which is based on the decency method does not. In particular, exp is a very simple calculus yet is not structure preserving. This shows that the structure preserving notion intended to give a general description of calculi of explicit substitution that satisfy PSN, is restrictive. To our knowledge, exp is the rst calculus of explicit substitution that is not structure preserving. 5