In this paper we propose a new set of rules for a judgement calculus, i.e. a typed lambda calculus, based In Intuitionistic Linear Logic; these rules ease the problem of defining a suitable mathematical semantics. A proof of the canonical form theorem for this new system is given: it assures, beside the consistency of the calculus, the termination of the evaluation process of every well-typed element. The definition of the mathematical semantics and a completeness theorem, that turns out to be a representation theorem, follow. This semantics is the basis to obtain a semantics for the evaluation process of every well-typed program.
The judgement calculus for Intuitionistic Linear Logic: proof theory and semantics
VALENTINI, SILVIO
1992
Abstract
In this paper we propose a new set of rules for a judgement calculus, i.e. a typed lambda calculus, based In Intuitionistic Linear Logic; these rules ease the problem of defining a suitable mathematical semantics. A proof of the canonical form theorem for this new system is given: it assures, beside the consistency of the calculus, the termination of the evaluation process of every well-typed element. The definition of the mathematical semantics and a completeness theorem, that turns out to be a representation theorem, follow. This semantics is the basis to obtain a semantics for the evaluation process of every well-typed program.File in questo prodotto:
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