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On the Logical Content of Computational Type Theory: A Solution to Curry’s Problem

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Types for Proofs and Programs (TYPES 2000)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2277))

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Abstract

In this paper we relate the lax modality Ο to Intuitionistic Propositional Logic (IPL) and give a complete characterisation of inhabitation in Computational Type Theory (CTT) as a logic of constraint contexts. This solves a problem open since the 1940’s, when Curry was the first to suggest a formal syntactic interpretation of Ο in terms of contexts.

This work is supported by EPSRC grants GR/L86180 and GR/M99637, by the EU Types Working Group IST-EU-29001 and by the British Council.

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Fairtlough, M., Mendler, M. (2002). On the Logical Content of Computational Type Theory: A Solution to Curry’s Problem. In: Callaghan, P., Luo, Z., McKinna, J., Pollack, R., Pollack, R. (eds) Types for Proofs and Programs. TYPES 2000. Lecture Notes in Computer Science, vol 2277. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45842-5_5

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  • DOI: https://doi.org/10.1007/3-540-45842-5_5

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  • Print ISBN: 978-3-540-43287-6

  • Online ISBN: 978-3-540-45842-5

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