Explicit substitutions for the - calculus ?

The-calculus is a-calculus with a control-like operator whose reduction rules are closely related to normalisation procedures in classical logic. We introduce exp, an explicit substitution calculus for , and study its properties. In particular, we show that exp preserves strong normalisation, which provides us with the rst example {moreover a very natural one indeed{ of explicit substitution calculus which is not structure-preserving and has the preservation of strong normalisation property. One particular application of this result is to prove that the simply typed version of exp is strongly nor-malising. In addition, we show that Plotkin's call-by-name continuation-passing style translation may be extended to exp and that the extended translation preserves typing. This seems to be the rst study of CPS translations for calculi of explicit substitutions.