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.
Supported by NASA GSRP Fellowship NGT-50786 and ONR Grant N00014-92J-1764
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Jackson, P. (1994). Exploring abstract algebra in constructive type theory. In: Bundy, A. (eds) Automated Deduction — CADE-12. CADE 1994. Lecture Notes in Computer Science, vol 814. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58156-1_43
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DOI: https://doi.org/10.1007/3-540-58156-1_43
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