Paramatricity and possible worlds

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Representation independence is of primary importance in modern programming methodology: it is at the heart of the specification/implementation distinction for such linguistic features as modules, abstract data types, classes, and application-programmer interfaces. However we still lack a completely satisfactory  *theoretical* foundation for this fundamental concept.A notion of relational parametricity introduced by J. C. Reynolds in 1981 is clearly relevant and we will attempt in this project to find a rigorous general formulation of parametricity using concepts of category theory, a branch of abstract mathematics. We expect this to lead to significant advances in our abilities to analyze programs and to verify system correctness.