Stabilization — An Alternative to Double-Negation Translation for Classical Natural Deduction

@inproceedings{Matthes2004StabilizationA,
title={Stabilization — An Alternative to Double-Negation Translation for Classical Natural Deduction},
author={Ralph Matthes},
year={2004}
}

A new proof of strong normalization of Parigot’s second-order λμ-calculus is given by a reduction-preserving embedding into system F (second-order polymorphic λ-calculus). The main idea is to use the least stable supertype for any type. These non-strictly positive inductive types and their associated iteration principle are available in system F, and allow to give a translation vaguely related to CPS translations (corresponding to Kolmogorov’s double-negation embedding of classical logic into… CONTINUE READING