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This paper describes a sound methodology developed at Praxis High Integrity Systems for detecting and exterminating bugs during all stages of a software project. To develop software, the London-based software house uses mathematically based techniques, known as formal methods, which require that programmers begin their work not by writing code but rather by stringing together special symbols that represent the program's logic. Like a mathematical theorem, these symbol strings can be checked to verify that they form logically correct statements. Once the programmer has checked that the program doesn't have logical flaws, it's a relatively simple matter to convert those symbols into programming code. With an average of less than one error in every 10,000 lines of delivered code, Praxis claims a bug rate that is at least 50 times better than the industry standard.