Abstract
Lattice-based algebraic structures containing semantics of production-logic inference on a type hierarchy in an object-oriented system with an additional relation are introduced. Specific features of these structures, such as closedness, possibility of equivalent transformations, existence of logical reduction, are studied. It is shown how to apply the model developed to verification and optimization of type hierarchies. An important direction of the optimization is automatic elimination of code duplication by "pulling up" common attributes in the type hierarchy. Implementation issues are briefly discussed.
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