Implementing constructive real analysis (preliminary report)
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).
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