# * Exploring Abstract Algebra in Constructive Type Theory *

## by Paul B. Jackson

1994

Proceedings of 12th Conference on Automated Deduction

**Abstract**

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.

**bibTex ref: Jac94a**

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