Self-redefinition as a program manipulation strategy

This is an exploration of a constructive strategy for program improvement and synthesis. A first part recalls unfolding-folding style of manipulations initiated by BURSTALL and DARLINGTON with an application to proofs of equivalence of certain function compositions. Second part, in a more abstract way, presents three basic “forms” and their associated “transforms” constructed with this strategy in a hierarchical order ; they may serve as goals of transformations. Last part associates self-redefinition to mixed strategies for program composition: symbolic macro replacement, logarithmic speed up, resolution of formal recurrences. Each situation, where technique and method apply, is depicted on examples and open problems are evoked.