Monadic translation of classical sequent calculus

We study monadic translations of the call-by-name (cbn) and the call-by-value (cbv) fragments of the classical sequent calculus λμμ̃ by Curien and Herbelin and give modular and syntactic proofs of strong normalization. The target of the translations is a new meta-language for classical logic, named monadic λμ. It is a monadic reworking of Parigot’s λμ-calculus, where the monadic binding is confined to commands, thus integrating the monad with the classical features. Also its μ-reduction rule is replaced by one expressing the interaction between monadic binding and μ-abstraction.