Abstract. Dimensional safety policy checking is an old topic in software analysis concerned with ensuring that programs do not violate basic principles of units of measurement. Scientific and/or navigation software is routinely dimensional and violations of measurement unit safety policies can hide significant domain-specific errors which are hard or impossible to find otherwise. Dimensional analysis of programs written in conventional programming languages is addressed in this paper. We draw general design principles for dimensional analysis tools and then discuss our prototypes, implemented by rewriting, which include both dynamic and static checkers. Our approach is based on assume/assert annotations of code which are properly interpreted by our tools and ignored by standard programming language compilers/interpreters. The output of our prototypes consists of warnings that list those expressions violating the unit safety policy. These prototypes are implemented in the rewriting system Maude, using more than 2,000 rewriting rules. This paper presents a non-trivial application of rewriting techniques to software analysis.
The theme of this paper is certifying software for state estimation of dynamic systems, which is an important problem found in spacecraft, aircraft, geophysical, and in many other applications. The common way to solve state estimation problems is to use Kalman filters, i.e., stochastic, recursive algorithms providing statistically optimal state estimates based on noisy sensor measurements. We present an optimality certifier for Kalman filter programs, which is a system taking a program claiming to implement a given formally specified Kalman filter, as well as a formal certificate in the form of assertions and proof scripts merged within the program via annotations, and tells whether the code correctly implements the specified state estimation problem. Kalman filter specifications and certificates can be either produced manually by expert users or can be generated automatically: we also present our first steps in merging our certifying technology with AutoFilter, a NASA Ames state estimation program synthesis system, the idea being that AutoFilter synthesizes proof certificates together with the code.
Formal certification is based on the idea that a mathematical proof of some property of a piece of software can be regarded as a certificate of correctness which, in principle, can be subjected to external scrutiny. In practice, however, proofs themselves are unlikely to be of much interest to engineers. Nevertheless, it is possible to use the information obtained from a mathematical analysis of software to produce a detailed textual justification of correctness. In this paper, we describe an approach to generating textual explanations from automaticdy generated proofs of program safety, where the proofs are of compliance with an explicit safety policy that can be varied. Key to this is tracing proof obligations back to the program, and we describe a tool which implements this to certify code auto-generated by AutoBayes and AutoFilter, program synthesis systems under development at the NASA Ames Research Center. Our approach is a step towards combining formal certification with traditional certification methods.
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