An exercise in formal program verification
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Verifying Launch Interceptor Routines with the Asymptotic Method Using Penelope This report describes the results of an exercise in formal program verification conducted at ORA. In this exercise, we started with code written by students at Syracuse University as part of work conducted by Professor Amrit Goel on program development methods. The code was an implementation of the routines of the Launch Interceptor Program (LIP), a specification of a protocol for launching an interceptor missile. The exercise consisted of specifying the routines using the asymptotic method and verifying a number of them using Penelope. The asymptotic method is a relatively simple approach to specification and verification of numerical programs that takes account of numerical error without quantifying it. It is important to take account of numerical error, even if it is small, because even a small error can change the result of a numerical program if it is a discontinuous function of the input. All non-constant discrete-valued (integer or Boolean) functions of real number arguments are discontinuous, and many real-valued functions appearing in geometry are discontinuous at certain degenerate configurations. When a specification, like the LIP specification, does not say anything quantitative about permissible error, the asymptotic method is the appropriate way to formalize that specification. The asymptotic method exposes problems of this kind, without requiring any more work than is necessary for that purpose. Classical error analysis will expose similar problems and give quantitative measures of how bad they are, but also requires more effort and expertise. This verification exercise had the following results. 1. A number of weaknesses in the specification were found regarding the treatment of near-degenerate geometrical situations. We adopted what seemed to be a reasonable solution to these problems and adapted the programs accordingly. 2. Some problems were found with the programs in that they used discontinuous formulas to compute continuous quantities, creating problems dealing with exceptions and permitting unpredictable results near singularities. 3. A few other errors were found in the programs. In particular, in one place an incorrect formula was used and in another uninitialized variables were read. 4. Considering the effect of error cast doubt on the method that Knight and Leveson used to test programs for faults, and on their evaluation of some program variants as faulty. 5. We outlined a development method for numerical programs that would appear to address the problems exposed by this verification exercise.
STARS-AC-A023/006/00 1 June 94 Initial release to the PAL
Approved for public release; Distribution unlimited
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