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This paper studies a particular variant of Generic Programming, called Adaptive Programming (AP).W e explain the approach taken by Adaptive Programming to attain the goals set for Generic Programming.Within the formalism of AP, we explore the important problem of refinement: given two generic programs, does one express a subset of the programs expressed by the other? We show that two natural definitions of refinement coincide, but the corresponding decision problem is computationally intractable (co-NP-complete).W e proceed to define a more restricted notion of refinement, which arises frequently in the practice of AP, and give an efficient algorithm for deciding it.