David Harel. Recursion in Logics of Programs. In Barry K. Rosen, Alfred V. Aho, Stephen N. Zilles , editors, Proceedings of the 6th ACM SIGACT-SIGPLAN symposium on Principles of programming language. pages 81-92, ACM, 1979. [doi]
The problem of reasoning about recursive programs is considered. Utilizing a simple analogy between iterative and recursive programs viewed as unfinite unions of finite terms, we carry out an investigation analogous to that carried out recently for iterative programs. The main results are the arithmetical completeness of axiom systems for (1) context-free dynamic logic and (2) its extension for dealing with infinite computations. Having the power of expression of these logics in mind, these results can be seen to supply (as corollaries) complete proof methods for the various kinds of correctness of recursive programs.