Computer Algebra Meets Automated Theorem Proving: Integrating Maple and PVS

Abstract

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.

An Extensible Ad Hoc Interface between Lean and Mathematica

“…We can use these tools to, e.g., define a tactic lu_decomp which computes and verifies the LU decomposition of a matrix. example : ∃ l u, is_lower_triangular l ∧ is_upper_triangular u ∧ l ** u = [ [1,2,3], [1,4,9], [1,8,27]] := by lu_decomp…”

An Interpreter for Quantum Circuits

“…It may be more useful, however, to invoke a computer algebra system from ACL2(r) in order to simplify such expressions. Combinations of theorem provers and computer algebra systems have already been done, e.g., [1,5]. We believe such an integration would be quite useful for ACL2(r) as well.…”

Automated deduction for verification

“…The PVS framework is open so that new inference tools can be plugged into the system. PVS has been used as a back-end inference framework in a number of tools including TLV [Pnueli and Shahar 1996], Why [Filliâtre and Marché 2007], LOOP [van den Berg and Jacobs 2001], Bandera [Corbett et al 2000], PVS-Maple [Adams et al 2001], TAME [Archer and Heitmeyer 1996], and InVeSt [Bensalem et al 1998]. PVS has also been applied in a number of significant verification exercises covering distributed algorithms [Miner et al 2004], hardware verification [Rueß et al 1996], air-traffic control [Carreño and Muñoz 2000], and computer security [Millen and Rueß 2000].…”