Integrating Computer Algebra and Reasoning through the Type System of Aldor (2000)
BibTeX
@MISC{Poll00integratingcomputer,
author = {Erik Poll and Simon Thompson},
title = {Integrating Computer Algebra and Reasoning through the Type System of Aldor},
year = {2000}
}
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Abstract
. A number of combinations of reasoning and computer algebra systems have been proposed; in this paper we describe another, namely a way to incorporate a logic in the computer algebra system Axiom. We examine the type system of Aldor { the Axiom Library Compiler { and show that with some modications we can use the dependent types of the system to model a logic, under the Curry-Howard isomorphism. We give a number of example applications of the logic we construct and explain a prototype implementation of a modied type-checking system written in Haskell. 1 Introduction Symbolic mathematical { or computer algebra { systems, such as Axiom [13], Maple and Mathematica, are in everyday use by scientists, engineers and indeed mathematicians, because they provide a user with techniques of, say, integration which far exceed those of the person themselves, and make routine many calculations which would have been impossible some years ago. These systems are, moreover, taught as standar...
