## A Classical Set-Theoretic Model of Polymorphic Extensional Type Theory (1997)

Citations: | 5 - 1 self |

### BibTeX

@TECHREPORT{Howe97aclassical,

author = {Douglas J. Howe},

title = {A Classical Set-Theoretic Model of Polymorphic Extensional Type Theory},

institution = {},

year = {1997}

}

### OpenURL

### Abstract

. We give a new semantic foundation for type theories in the lineage of Martin-Lof's "polymorphic extensional" type theory, and use it to give a model of the constructive type theory of the interactive theorem proving system Nuprl. These type theories are based on an operational semantics of an untyped programming language. We show how to integrate classical set-theoretic objects, such as functions-as-graphs and equivalence classes, into this operational framework. The new semantics is dramatically simpler than the previous ones, and enables direct reasoning about classical mathematics. A practical consequence is that it justifies a useful embedding of the logic of the HOL theorem prover that gives Nuprl effective access to most of the large body of formalized mathematics that the HOL community has amassed over the years. 1 Introduction The so-called "polymorphic extensional" type theory of Martin-Lof (Martin-Lof, 1982) has two features that set it apart from other constructive type t...