Computer Algebra Meets Automated Theorem Proving: Integrating Maple and PVS

We describe an interface between version 6 of the Maple computer algebra system with the PVS automated theorem prover. The interface is designed to allow Maple users access to the robust and checkable proof environment of PVS. We also extend this environment by the provision of a library of proof strategies for use in real analysis. We demonstrate examples using the interface and the real analysis library. These examples provide proofs which are both illustrative and applicable to genuine symbolic computation problems.

[1]  Hanne Gottliebsen,et al.  Transcendental Functions and Continuity Checking in PVS , 2000, TPHOLs.

[2]  Bruce W. Char,et al.  Maple V Language Reference Manual , 1993, Springer US.

[3]  John Harrison,et al.  Reasoning About the Reals: The Marriage of HOL and Maple , 1993, LPAR.

[4]  Thomas Sturm,et al.  REDLOG: computer algebra meets computer logic , 1997, SIGS.

[5]  Paul B. Jackson.  Enhancing the NUPRL Proof Development System and Applying it to Computational Abstract Algebra , 1995 .

[6]  Piergiorgio Bertoli,et al.  Specification and Integration of Theorem Provers and Computer Algebra Systems , 1998, Fundam. Informaticae.

[7]  Jacques Calmet,et al.  Theorems and algorithms: an interface between Isabelle and Maple , 1995, ISSAC '95.

[8]  Keith O. Geddes,et al.  Maple 6 Programming Guide , 2000 .

[9]  John Harrison,et al.  Theorem proving in higher order logics : 13th International Conference, TPHOLs 2000, Portland, OR, USA, August 14-18, 2000 : proceedings , 2000 .

[10]  John Rushby,et al.  User guide for the pvs specification and verification system (beta release) , 1991 .

[11]  Bruno Buchberger,et al.  A survey of the Theorema project , 1997, ISSAC.

[12]  Andreas Strotmann,et al.  Objectives of Openmath , 1995 .

[13]  Piergiorgio Bertoli,et al.  Specification and Integration of Theorem Provers and Computer Algebra Systems , 1998, AISC.

[14]  E. Poll,et al.  Adding the axioms to Axiom: Towards a system of automated reasoning in Aldor , 1998 .

[15]  Bruno Buchberger.  Symbolic Computation: Computer Algebra and Logic , 1996, FroCoS.

[16]  Richard D. Jenks,et al.  AXIOM: the scientific computation system , 1992 .

[17]  Steve Linton,et al.  Automated theorem proving in support of computer algebra: symbolic definite integration as a case study , 1999, ISSAC '99.

[18]  Paul S. Wang,et al.  MP: a protocol for efficient exchange of mathematical expressions , 1994, ISSAC '94.

[19]  G. Latta,et al.  Ordinary differential equations and their solutions , 1960 .

[20]  Jacques Calmet,et al.  Classification of Communication and Cooperation Mechanisms for Logical and Symbolic Computation Systems , 1996, FroCoS.

[21]  Bruno Dutertre,et al.  Elements of Mathematical Analysis in PVS , 1996, TPHOLs.

[22]  Mike Dewar.  OpenMath: an overview , 2000, SIGS.

[23]  Richard J. Boulton,et al.  The PROSPER Toolkit , 2000, TACAS.