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This paper presents the ideas underlying a computer program that takes as input a schematic of a mechanical or hydraulic power transmission system, plus specifications and a utility function, and returns catalog numbers from predefined catalogs for the optimal selection of components implementing the design. Unlike programs for designing single components or systems, this program provides the designer with a high level 'language' in which to compose new designs. It then performs some of the detailed design process for him. The process of 'compilation', or transformation from a high to a low level description, is based on a formalization of quantitative inferences about hierarchically organized sets of artifacts and operating conditions. This allows compilation without the exhaustive enumeration of alternatives. The paper introduces the formalism, illustrating its use with examples. It then outlines some differences from previous work, and summarizes early tests and conclusions. Keywords: Computer aided design; Computer programs; Mechanical design; Quantitative inference; Qualitative reasoning; Constraint propagation.