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Uniformity , Interpolation and Modulespeci cation in a Development

Interpolation and Schematic Reasoning are shown to underlie critical and somewhat complementary aspects of designing and (syntactically) manipulating speciication modules. In addition, the presence of a Uniform presentation of interpolants facilitates the speciication of modules. Also, the ability to encapsulate and manipulate Uniform Schemata may assist us in reasoning with (abstractions of) hidden data. Unfortunately, most formalisms that have been used in fundamental approaches to software engineering lack uniform interpolation and do not directly support schematic reasoning. This paper reveals the critical role of uniform interpolants and uniform schemata from the perspective of modularity, and quotes a general construction indicating that a potentially large class of calculi can be extended conservatively so that a uniform presentation of the critical interpolants becomes available and the manipulation of uniform schemata is supported.