Istituto per La Ricerca Scientifica E Tecnologica Specification and Integration of Theo- Rem Provers and Computer Algebra Sys- Tems Speciication and Integration of Theorem Provers and Computer Algebra Systems

limited distribution notice This report has been submitted for publication outside of ITC and will probably be copyrighted if accepted for publication. It has been issued as a Technical Report for early dissemination of its contents. In view of thetransfer of copyright to the outside publisher, its distribution outside of ITC prior to publication should be limited to peer communications and speciic requests. After outside publication, requests should be lled only by reprints or legally obtained copies of the article. Abstract. Computer algebra systems (CASs) and automated theorem provers (ATPs) exhibit complementary abilities. CASs focus on ee-ciently solving domain-speciic problems. ATPs are designed to allow for the formalization and solution of wide classes of problems within some logical framework. Integrating CASs and ATPs allows for the solution of problems of a higher complexity than those confronted by each class alone. However, most experiments conducted so far followed an ad-hoc approach, resulting in tailored solutions to speciic problems. A struc-tured and principled approach is necessary to allow for the sound integration of systems in a modular way. The Open Mechanized Reasoning Systems (OMRS) framework was introduced for the speciication and implementation of mechanized reasoning systems, e.g. ATPs. The approach was recasted to the domain of computer algebra systems. In this paper, we introduce a generalization of OMRS, named OMSCS (Open Mechanized Symbolic Computation Systems). We show how OMSCS can be used to soundly express CASs, ATPs, and their integration, by formalizing a combination between the Isabelle prover and the Maple algebra system. We show how the integrated system solves a problem which could not be tackled by each single system alone.