Abstract
Hyland and Ong [HO93] recently showed that given an arbitrary (right-absorptive) conditionally partial combinatory algebra (Cpca), there is a systematic way to construct a Kreisel-style modified realizability topos which has more than sufficient completeness properties to provide a categorical semantics for a wide range of higher type theories. Based on the topos generated from the C-pca of an appropriate quotient of the strongly normalising untyped λ*-terms (where * is just a formal constant), they obtained a “generic” strong normalization argument. This argument reduces the strong normalization property of a class of higher type theories (up to F ω) to the validity of two “stripping arguments” which are reasonably easy to verify. This paper reports work which carries the same programme a step further. We illustrate the general applicability and simplicity of the argument by bringing it to bear on the demanding test case of Coquand and Huets' Calculus of Constructions.
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Ong, C.H.L., Ritter, E. (1994). A generic strong normalization argument: Application to the Calculus of Constructions. In: Börger, E., Gurevich, Y., Meinke, K. (eds) Computer Science Logic. CSL 1993. Lecture Notes in Computer Science, vol 832. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0049336
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DOI: https://doi.org/10.1007/BFb0049336
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