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Seibel: Peter van der Linden in his book Expert C Programming has a sort of dismissive chapter about proofs in which he shows a proof of something, but then, ha ha, this proof has a bug in it Steele: Yes, indeed Proofs can also have bugs Seibel: Are they at least less likely to have a bug than the code which they are proving Steele: I think so, because you come at it in a different way and you use different tools You use proofs for the same reason you use data types, or for the same reason that mountain climbers use ropes If all is well, you don t need them But they increase the chance of catching it if something does go wrong Seibel: I suppose the really bad case would be if you had a bug in your program and then a compensating bug in your proof.

Any detective work that you re forced to do will pay off handsomely by deepening you knowledge and understanding of where you work If you are looking for a technical solution to finding databases, there are a handful of ways to get the job done One of the simplest ways is to use the SQLCMD utility with the L parameter to return a list of database servers that are broadcasting on the network Since it is possible that some servers may not be found with that tool, you would be wise to still ask around when putting together your list And where do you keep such a list I like to keep a lot of notes written down in a notebook When I say notebook, I m not talking about a computer I m talking about a physical, paper book that I can hold in my hands.

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Hopefully that would be rare Steele: That can happen I m not even sure it s necessarily rare, because you tend to construct the proof to match the structure of the code Or conversely, if you ve got a proof in mind as you re writing the code, that tends to guide your construction of the program So you really can t say the code and the proof are totally independent, in the probabilistic sense But you can bring different tools and different modes of thought to bear..

// Addition of two complex numbers. // Could also be defined as a member operator. static Complex operator+(Complex c1, Complex c2) { return Complex(c1.re + c2.re, c1.im + c2.im); } // This cannot be a member operator, since a double is on the left. static Complex operator+(double d, Complex c) { return Complex(c.re + d, c.im); } // If Complex is the first argument, this could also be // a member operator. static Complex operator+(Complex c, double d) { return Complex(c.re + d, c.im); } // etc. };

Guy Steele In particular, the details of the programming tend to take a local point of view and the invariants tend to focus on the global point of view It s in doing the proof that you cause those two things to interact You look at how the local steps of the program affect the global invariant you re trying to maintain One of the most interesting exercises in my career was the time I was asked to review a paper for CACM by David Gries on proving a garbagecollector algorithm correct, a parallel garbage collector Susan Owicki was a student of Gries s and she developed some tools for proving parallel programs correct, and he decided to apply these techniques to a version of a parallel garbage collector that had been developed by Dijkstra The whole piece of code fit on, I think, a half a page.

And then the entire rest of the paper was the proof of correctness I cranked through the proof and tried to verify every step for myself And what makes it tricky is, in effect, every statement in the program has the potential to violate any invariant because it s a parallel program So the Owicki technique involves cross-checking these at all points And it took me about 25 hours to go through, and in the process I found a couple of steps I couldn t push through So I reported this and it turned out they did represent bugs in the algorithm Seibel: So they were bugs in the algorithm which the proof missed since the result of the proof was, QED this thing works Steele: Yes, the proof presented was a faulty proof Because something had been overlooked somewhere.

As you know, in classic C++ you can define type conversion operators to enable automatic conversions between your type and another type. You can do this in managed types as well as in C++/CLI. The additional option you have in C++/CLI is to specify whether the conversion requires an explicit cast, or not. You do this with the explicit keyword. While the explicit keyword is also used in classic C++, in classic C++ it is used only on constructors, to prevent the constructor from being used to define an implicit conversion. In C++/CLI, the situation is different. Constructors for managed types are never used for implicit conversions, whether or not the explicit keyword is used on them, so using the keyword would be redundant. However, the keyword is used on conversion operators. Without the keyword, the conversion operator is assumed to be implicit, as it is in classic C++. With the keyword, the conversion operator is only invoked with an explicit cast (see Listing 7-23). Listing 7-23. Using explicit with a Conversion Operator // explicit_conversion.cpp using namespace System; value class BigIntExplicit { __int64 m_i;

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