Why the usual candidates of reducibility do not work for the symmetric $\lambda\mu$-calculus

Abstract

The symmetric $\lambda mu$-calculus is the $\lambda\mu$-calculus introduced by Parigot in which the reduction rule $\mu'$, which is the symmetric of $\mu$, is added. We give examples explaining why the technique using the usual candidates of reducibility does not work. We also prove a standardization theorem for this calculus.