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The design of programs which are both correct and robust is investigated. It is argued that the notion of an exception is a valuable tool for structuring the specification, design, verification, and modification of such programs. The syntax and semantics of a language with procedures and exception handling are presented. A deductive system is proposed for proving total correctness and robustness properties of programs written in this language. The system is both sound and complete. It supports proof modularization, in that it allows one to reason separately about fault-free and fault-tolerant system properties. Since the programming languages considered closely resembles CLU or Ada, the presented deductive system is easily adaptable for verifying total correctness and robustness properties of programs written in these, or similar, languages.