Semantic Foundations for Embedding HOL in Nuprl

We give a new semantics for Nuprl's constructive type theory that justiies a useful embedding of the logic of the HOL theorem prover inside Nuprl. The embedding gives Nuprl eeective access to most of the large body of formalized mathematics that the HOL community has amassed over the last decade. The new semantics is dramatically simpler than the old, and gives a novel and general way of adding set-theoretic equivalence classes to untyped functional programming languages.