Notes on generalization of proof normalization
Marc Aiguier, Delphine Longuet · 2007
In this paper, we provide a general setting under which results of normalization of proof trees such as, for instance, the logicality result in equational reasoning and the cut-elimination property in sequent or natural deduction calculi, can be unified and generalized. This is achieved by giving simple conditions which are sufficient to ensure that such normalization resultshold, and because syntactical, can be implemented. These conditions are based on basic properties of elementary combinations of inference rules which assure that the induced “global” proof tree transformation processes do terminate.