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Term Assignment for Intuitionistic Linear Logic (1992)
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| Citations: | 61 - 11 self |
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@TECHREPORT{Benton92termassignment,
author = {Nick Benton and Gavin Bierman and Valeria Paiva and Martin Hyland},
title = {Term Assignment for Intuitionistic Linear Logic},
institution = {},
year = {1992}
}
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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) 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 define a simple (but more general than previous proposals) categorical model for Intuitionistic Linear Logic and show how this can be used to derive the term assignment system. We also consider term reduction arising from cut-elimination in the sequent calculus and normalisation in natural deduction. We explore the relationship between these, as well as with the equations which follow from our categorical model.
Keyphrases
intuitionistic linear logic term assignment categorical model sequent calculus term assignment system valid deduction previous proposal important property subject reduction previous calculus term reduction system differs substitution property natural deduction proof system natural deduction
