Proof Rules for Recursive Procedures

Four proof rules for recursive procedures in a Pascal-like language are presented. The main rule deals with total correctness and is based on results of Gries and Martin. The rule is easier to apply than Martin's. It is introduced as an extension of a specification format for Pascal-procedures, with its associated correctness and invocation rules. It uses well-founded recursion and is proved under the postulate that a procedure is semantically equal to its body. This rule for total correctness is compared with Hoare's rule for partial correctness of recursive procedures, in which no well-founded relation is needed. Both rules serve to prove correctness, i.e. sufficiency of certain preconditions. There are also two rules for proving necessity of preconditions. These rules can be used to give formal proofs of nontermination and refinement. They seem to be completely new.