Computational metatheory in Nuprl
This paper describes an implementation within Nuprl of mechanisms that support the use of Nuprl's type theory as a language for constructing theorem-proving procedures. The main component of the implementation is a large library of definitions, theorems and proofs. This library may be regarded as the beginning of a book of formal mathematics; it contains the formal development and explanation of a useful subset of Nuprl's metatheory, and of a mechanism for translating results established about this embedded metatheory to the object level. Nuprl's rich type theory, besides permitting the internal development of this partial reflection mechanism, allows us to make abstractions that drastically reduce the burden of establishing the correctness of new theorem-proving procedures. Our library includes a formally verified term-rewriting system.
Key words and phrasesTheorem proving tactics type theory reflection formal metamathematics constructive mathematics
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