An algebraic treatment of procedure refinement to support mechanical verification

We introduce a new algebraic model for program variables, suitable for reasoning about recursive procedures with parameters and local variables in a mechanical verification setting. We give a predicate transformer semantics to recursive procedures and prove refinement rules for introducing recursive procedure calls, procedure parameters, and local variables. We also prove, based on the refinement rules, Hoare total correctness rules for recursive procedures, and parameters. We introduce a special form of Hoare specification statement which alone is enough to fully specify a procedure. Moreover, we prove that this Hoare specification statement is equivalent to a refinement specification. We implemented this theory in the PVS theorem prover.