Section: New Results
Proof normalization in sequent calculus
Participant : Stéphane Lengrand.
One way of obtaining cut-free proofs is to normalize a proof that contains cuts. Stéphane Lengrand has studied the termination of normalization procedures in sequent calculi.
The methodology uses proof-terms and rewrite systems on these objects, which have to be proved terminating.
Lengrand and Kikuchi in  have designed such a cut-elimination system for one of the simplest, and non-focused, sequent calculus for intuitionistic logic. Yet it provides a computation model that simulates the -calculus in a strong sense. Thus, termination of the system is at least as strong as that of the (simply-typed) -calculus.
The proof term approach could provide a systematic method to obtain cut-elimination results in focused sequent calculi such as LJF and LKF  .