Abstract
Abstract Real number theorem proving has many uses, particularly for verification of safety critical systems and systems for which design errors may be costly. We discuss a chain of developments building on real number theorem proving in PVS. This leads from the verification of aspects of an air traffic control system, through work on the integration of computer algebra and automated theorem proving to a new tool, NRV, first presented here that builds on the capabilities of Maple and PVS to provide a verified and automatic analysis of Nichols plots. This automates a standard technique used by control engineers and greatly improves assurance compared with the traditional method of visual inspection of the Nichols plots.
Highlights
The purpose of this paper is to highlight a trajectory in the development of real number theorem proving, with applications to real world problems in engineering and design verification in mind
Nichols plot Requirements Verifier (NRV) exploits the symbolic computation provided by the computer algebra system Maple, the formal techniques provided by PVS and the quantifier elimination routines provided by QEPCAD
The work on Small Aircraft Transportation System (SATS) showed the practical utility of real number theorem proving in verifying safety-critical systems
Summary
The purpose of this paper is to highlight a trajectory in the development of real number theorem proving, with applications to real world problems in engineering and design verification in mind. Our line of enquiry has led us to develop theories in PVS, and to use them in verifying safety-critical systems using the theorem prover directly. By real number theorem proving we mean the machine verification in a computational logic system of results about real valued functions, typically equalities, inequalities, and properties such as continuity or differentiability, over elementary functions (combinations of powers, cos, sin, exp, log) and subject to constraints on the variables. A function is strictly convex (or strictly concave) if the inequality is strict. A function that is linear in all variables is both convex and concave but neither strictly convex nor strictly concave
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