Steps Toward Mechanizing Program Transformations Using PVS

PVS is a highly automated framework for speciication and veriication. We show how the language and deduction features of PVS can be used to formalize, mechanize , and apply some useful program transformation techniques. We examine two such examples in detail. The rst is a fusion theorem due to Bird where the composition of a catamorphism (a recursive operation on the structure of a datatype) and an anamorphism (an operation that constructs instances of the datatype) is fused to eliminate the intermediate data structure. The second example is Wand's continuation-based transformation technique for deriving tail-recursive functions from non-tail-recursive ones. These examples illustrate the utility of the language and inference features of PVS in capturing these transformations in a simple, general , and useful form.