Reasoning About the Reals: the marriage of HOL and Maple

. Computer algebra systems are extremely powerful and flexible, but often give results which require careful interpretation or are downright incorrect. By contrast, theorem provers are very reliable but lack the powerful specialized decision procedures and heuristics of computer algebra systems. In this paper we try to get the best of both worlds by careful exploitation of a link between a theorem prover and a computer algebra system. 1 Motivation In the HOL theorem prover[5], a theory of real numbers has been developed, using a rigorous definition in terms of Dedekind cuts [8]. It is therefore possible to apply HOL to areas traditionally within the purview of Computer Algebra Systems (CASs). This offers two main benefits. Firstly, theorem provers are designed to manipulate proofs and theorems in a coherent and structured way, with all concepts clearly defined. By contrast, most CASs have no concept of `logic' as such -- they usually take an algebraic expression and return another pur..