Typed Lambda Calculi and Applications

Volume 902 of the series Lecture Notes in Computer Science pp 78-93


What is a categorical model of Intuitionistic Linear Logic?

  • G. M. BiermanAffiliated withUniversity of Cambridge Computer Laboratory

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This paper re-addresses the old problem of providing a categorical model for Intuitionistic Linear Logic (ILL). In particular we compare the now standard model proposed by Seely to the lesser known one proposed by Benton, Bierman, Hyland and de Paiva. Surprisingly we find that Seely's model is unsound in that it does not preserve equality of proofs. We shall propose how to adapt Seely's definition so as to correct this problem and consider how this compares with the model due to Benton et al.