Parigot M. (2000) Strong Normalization of Second Order Symmetric λ-Calculus. In: Kapoor S., Prasad S. (eds) FST TCS 2000: Foundations of Software Technology and Theoretical Computer Science. FSTTCS 2000. Lecture Notes in Computer Science, vol 1974. Springer, Berlin, Heidelberg
Typed symmetric α-calculus is a simple computational interpretation of classical logic with an involutive negation. Its main distinguishing feature is to be a true non-confluent computational interpretation of classical logic. Its non-confluence reflects the computational freedom of classical logic (as compared to intuitionistic logic). Barbanera and Berardi proved in , that first order typed symmetric α-calculus enjoys the strong normalization property and showed in  that it can be used to derive symmetric programs.
In this paper we prove strong normalization for second order typed symmetric α-calculus.