Abstract
In this paper we consider the problem of deriving a term assignment system for Girard's Intuitionistic Linear Logic for both the sequent calculus and natural deduction proof systems. Our system differs from previous calculi (e.g. that of Abramsky [1]) and has two important properties which they lack. These are the substitution property (the set of valid deductions is closed under substitution) and subject reduction (reduction on terms is well-typed). We also consider term reduction arising from cut-elimination in the sequent calculus and normalisation in natural deduction. We explore the relationship between these and consider their computational content.
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References
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© 1993 Springer-Verlag Berlin Heidelberg
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Benton, N., Bierman, G., de Paiva, V., Hyland, M. (1993). A term calculus for Intuitionistic Linear Logic. In: Bezem, M., Groote, J.F. (eds) Typed Lambda Calculi and Applications. TLCA 1993. Lecture Notes in Computer Science, vol 664. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0037099
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DOI: https://doi.org/10.1007/BFb0037099
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