Abstract
In this paper we present the results of an investigation into the use of the Nuprl proof development system to implement higher constructive mathematics. As a first step in exploring the issues involved, we have developed a basis for formalizing substantial parts of real analysis. More specifically, we have: developed type-theoretic representations of concepts from Bishop's treatment of constructive mathematics that allow reasonably direct formalizations; used Nuprl's facility for sound extension of its inference system to implement automated reasoners for analysis; and tested these ideas in a formalization of rational and real arithmetic and of a proof of the completeness theorem for the reals (every Cauchy sequence converges).
Both authors were supported, in part, by ONR contract N00014-88-K-0409 and NSF grant CCR-8616552.
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© 1992 Springer-Verlag Berlin Heidelberg
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Chirimar, J., Howe, D.J. (1992). Implementing constructive real analysis (preliminary report). In: Myers, J.P., O'Donnell, M.J. (eds) Constructivity in Computer Science. Constructivity in CS 1991. Lecture Notes in Computer Science, vol 613. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0021090
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DOI: https://doi.org/10.1007/BFb0021090
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