Adding the axioms to Axiom Towards a system of automated reasoning in Aldor

A number of combinations of theorem proving 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 modiications 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.