The Girard Translation Extended with Recursion
نویسنده
چکیده
This paper extends Curry-Howard interpretations of Intuitionistic Logic (IL) and Intuitionistic Linear Logic (ILL) with rules for recursion. The resulting term languages, the λ-calculus and the linear λ-calculus respectively, are given sound categorical interpretations. The embedding of proofs of IL into proofs of ILL given by the Girard Translation is extended with the rules for recursion, such that an embedding of terms of the λ-calculus into terms of the linear λ-calculus is induced via the extended Curry-Howard isomorphisms. This embedding is shown to be sound with respect to the categorical interpretations. ∗Full version of paper to appear in Proceedings of CSL ’94, LNCS 933, 1995. †Basic Research in Computer Science, Centre of the Danish National Research Foundation.
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