Designing and applying program transformations also fall into the abstraction/instantiation paradigm. The same methodology can be used for this purpose as was used in the previous section for designing and applying program schemata. For example, to design a recursion-elimination transformation (such as in [8, 20, 22, 68]), we could first write, and verify, iterative versions of several recursive programs; then, by abstracting those programs, and their proofs, a general recursion-to-iteration transformation schema may be obtained. As we shall see, very little information is gleaned just by a comparison of output specifications; instead, most of the analogy needs to be derived from the programs themselves.

Consider ...

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