Identity of Proofs Based on Normalization and Generality

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In general proof theory there are two approaches to the question of identity criteria for proofs. The first approach, which stems from Prawitz, Kreisel and Lambek, and is based on normalization of proofs, gives good results in intuitionistic, but not in classical logic. The second approach, which stems from Lambek, Mac Lane and Kelly, and is inspired by the generality of proofs, seems to be more promissing in classical logic.