Kestrel Institute, 3260 Hillview Avenue, Palo Alto
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California 94304, USA
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This paper addresses the problem of how to construct refinements of specifications formally and incrementally. The key idea is to use a taxonomy of abstract design concepts, each represented by a design theory. An abstract design concept is applied by constructing a specification morphism from its design theory to a requirement specification. Procedures for propagating constraints, computing colimits, and constructing specification morphisms provide computational support for this approach. Although we conjecture that classification generally applies to the incremental application of knowledge represented in a taxonomy of design theories, this paper mainly focuses on algorithm design theories and presents several examples of design by classification.