Paul B. Jackson. Exploring Abstract Algebra in Constructive Type Theory. In A. Bundy, editor, 12th International Conference on Automated Deduction, Lecture Notes in Artifical Intelligence. Springer Verlag, June 1994.

I describe my implementation of computational abstract algebra in the Nuprl system. I focus on my development of multivariate polynomials. I show how I use Nuprl's expressive type theory to define classes of free abelian monoids and free monoid algebras. These classes are combined to create a class of all implementations of polynomials.

I discuss the issues of subtyping and computational content that came up in designing the class definitions. I give examples of relevant theory developments, tactics and proofs. I consider how Nuprl could act as an algebraic `oracle' for a computer algebra system and the relevance of this work for abstract functional programming.

Last Modified Sep 18th, 1996