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A proof rule for the procedure call is derived for procedures with value, result and value-result parameters. It is extended to procedures with unrestricted global variables and to recursive procedures. Like D. Gries's proof rule, it is based on the substitution rule for assignment. However, it is more general and much simpler to apply. Assume that {U} S {V} has been proved about the procedure body S. The proof rule for determining whether a call establishes predicate E is based on finding an “adaptation” A satisfying A?V ? E', where E' is derived from E by some substitution of parameters.

A general proof rule for procedures in predicate transformer semantics