Abstract
This paper extends Curry-Howard interpretations of Intuitionistic Logic and Intuitionistic Linear Logic rules for recursion. The resulting term languages, the λrec-calculus and the linear λrec-calculus respectively, are given sound categorical interpretations. The embedding of proofs of Intuitionistic Logic into proofs of Intuitionistic Linear Logic given by the Girard Translation is extended with the rules for recursion such that an embedding of terms of the λrec-calculus into terms of the linear λrec-calculus is induced via the extended Curry-Howard isomorphisms. This embedding is shown to be sound with respect to the categorical interpretations.
A full version of this paper is available as Technical Report BRICS-RS-95-13.
Basic Research in Computer Science, Centre of the Danish National Research Foundation.
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© 1995 Springer-Verlag Berlin Heidelberg
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Braüner, T. (1995). The Girard Translation extended with recursion. In: Pacholski, L., Tiuryn, J. (eds) Computer Science Logic. CSL 1994. Lecture Notes in Computer Science, vol 933. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0022245
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DOI: https://doi.org/10.1007/BFb0022245
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