The past decade has seen a burgeoning interest in functional programming languages such as Haskell or, in the Microsoft world, F#. Though still on the periphery of mainstream programming, functional programming concepts are gradually seeping into the imperative C# language (for example, Lambda expressions have their root in functional programming).

One of the more interesting concepts from functional programming languages is the use of formal methods, the lofty ideal behind which is bug-free software. The idea is that we write a specification that describes exactly how our function (say) should behave. We then prove that our function conforms to it, and in doing so have proved beyond any doubt that it is free from bugs.

All programmers already use one form of specification, specifically their programming language's type system. If a value has a specific type then, in a type-safe language, the compiler guarantees that value cannot be an instance of a different type. Many extensions to existing type systems, such as generics in Java and .NET, extend the range of programs that can be type-checked.

Unfortunately, type systems can only prevent some bugs. To take a classic problem of retrieving an index value from an array, since the type system doesn't specify the length of the array, the compiler has no way of knowing that a request for the "value of index 4" from an array of only two elements is "unsafe". We restore safety via exception handling, but the ideal type system will prevent us from doing anything that is unsafe in the first place and this is where we start to borrow ideas from a language such as Haskell, with its concept of "dependent types". If the type of an array includes its length, we can ensure that any index accesses into the array are valid. The problem is that we now need to carry around the length of arrays and the values of indices throughout our code so that it can be type-checked.

In general, writing the specification to prove a positive property, even for a problem very amenable to specification, such as a simple sorting algorithm, turns out to be very hard and the specification will be different for every program. Extend this to writing a specification for, say, Microsoft Word and we can see that the specification would end up being no simpler, and therefore no less buggy, than the implementation.

Fortunately, it is easier to write a specification that proves that a program doesn't have certain, specific and undesirable properties, such as infinite loops or accesses to the wrong bit of memory. If we can write the specifications to prove that a program is immune to such problems, we could reuse them in many places. The problem is the lack of specification "provers" that can do this without a lot of manual intervention (i.e. hints from the programmer).

All this might feel a very long way off, but computing power and our understanding of the theory of "provers" advances quickly, and Microsoft is doing some of it already. Via their Terminator research project they have started to prove that their device drivers will always terminate, and in so doing have suddenly eliminated a vast range of possible bugs. This is a huge step forward from saying, "we've tested it lots and it seems fine".

What do you think? What might be good targets for specification and verification? SQL could be one: the cost of a bug in SQL Server is quite high given how many important systems rely on it, so there's a good incentive to eliminate bugs, even at high initial cost.

[Many thanks to Mike Williamson for guidance and useful conversations during the writing of this piece]

Cheers,

Tony.