Strong normalization of [formula omitted] via a calculus of coercions

Abstract

ML F is a type system extending ML with first-class polymorphism as in system F . The main goal of the present paper is to show that ML F enjoys strong normalization, i.e., it has no infinite reduction paths. The proof of this result is achieved in several steps. We first focus on xML F , the Church-style version of ML F , and show that it can be translated into a calculus of coercions: terms are mapped into terms and instantiations into coercions. This coercion calculus can be seen as a decorated version of system F , so that the simulation result entails strong normalization of xML F through the same property of system F . We then transfer the result to all other versions of ML F using the fact that they can be compiled into xML F and showing there is a bisimulation between the two. We conclude by discussing what results and issues are encountered when using the candidates of reducibility approach to the same problem.