Abstract
Application of object-oriented programming techniques to design and implementation of symbolic computation systems is investigated. We show the significance of certain correctness problems, occurring in programming environments based on specialization inheritance, due to use of method redefinition and polymorphism. We propose a solution to these problems, by defining a mechanism of subtyping inheritance and the prototype of an object-oriented programming language for a symbolic computation system. We devise the subtyping inheritance ESI (Enhanced Strict Inheritance) by lifting to programming language constructs a given model of subtyping, which is established by a monotonic (covariant) subtyping rule. Type safeness of language instructions is proved.The adoption of ESI allows to model method and class specialization in a natural way. The ESI mechanism verifies the type correctness of language statements by means of type checking rules and preserves their correctness at run-time by a suitable method lookup algorithm.
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