CONTINUATION-PASSING STYLE AND STRONG NORMALISATION FOR INTUITIONISTIC SEQUENT CALCULI
The intuitionistic fragment of the call-by-name version of Curien and Herbelin's (lambda) over bar mu(mu) over tilde -calculus is isolated and proved strongly normalising by means of an embedding into the simply-typed lambda-calculus. Our embedding is a continuation-and-garbagepassing style translation, the inspiring idea coming from Ikeda and Nakazawa's translation of Parigot's lambda mu-calculus. The embedding strictly simulates reductions while usual continuation-passing-style transformations erase permutative reduction steps. For our intuitionistic sequent calculus, we even only need "units of garbage" to be passed. We apply the same method to other calculi, namely successive extensions of the simply-typed lambda-calculus leading to our intuitionistic system, and already for the simplest extension we consider (lambda-calculus with generalised application), this yields the first proof of strong normalisation through a reduction-preserving embedding. The results obtained extend to second and higher-order calculi.
continuation-passing style strong normalisation intuitionistic sequent calculus garbage passing strict simulation curry-howard isomorphism