Auto-Active Proof of Red-Black Trees in SPARK.

Formal program verification can guarantee that a program is free from broad classes of errors (like reads of uninitialized data and run-time errors) and that it complies with its specification. Tools such as SPARK make it cost effective to target the former in an industrial context, but the latter is much less common in industry, owing to the cost of specifying the behavior of programs and even more the cost of achieving proof of such specifications. We have chosen in SPARK to rely on the techniques of auto-active verification for providing cost effective formal verification of functional properties. These techniques consist in providing annotations in the source code that will be used by automatic provers to complete the proof. To demonstrate the potential of this approach, we have chosen to formally specify a library of red-black trees in SPARK, and to prove its functionality using auto-active verification. To the best of our knowledge, this is the most complex use of auto-active verification so far.