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We have two main purposes in this paper. First, we clarify and extend known results about computation of recursive programs, emphasizing the difference between the theoretical and practical approaches. Secondly, we present and examine various known methods for proving properties of recursive programs. We discuss in detail two powerful inductive methods, computational induction and structural induction, illustrating their applications by various examples. We also briefly discuss some other related methods.
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Manna et al. (1972) studied this question.