Interfaces for Refining Recursion and Procedures
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This paper presents novel definitions of interfaced recursion blocks, interfaced procedures, and interfaced recursive procedures for the Refinement Calculus. These definitions allow step-wise refinement rules to be formally stated and proved for these constructs. An interface is associated with a (recursive) call by preceding the body of the implementation by an assertion statement which says that the interface refines to the implementation. An interface will typically be a specification statement, but in principle can be any command. The theory and rules presented in this paper have been mechanised in the theorem prover Isabelle/ZF.
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