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A classical linear λ-calculus

✍ Scribed by G.M. Bierman

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
215 KB
Volume
227
Category
Article
ISSN
0304-3975

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✦ Synopsis

This paper proposes and studies a particular typed -calculus for classical linear logic. I shall give an explanation of a natural deduction formulation of classical logic due to Parigot and compare it to more traditional treatments by Prawitz and others. I shall use Parigot's method to devise a natural deduction formulation of classical linear logic. This formulation is compared in detail to the sequent calculus formulation.

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We show that any λ-model gives rise to a λµ-model, in the sense that if we have M = λµ N in the equational theory of type free λµ-calculus then ] holds true for some structure [[-]], D induced from a λ-model. The construction of λµ-models can be given by the use of a fixed point operator and the Gö