Object-oriented data as prefix rewriting systems.(English)Zbl 1463.68032

Summary: A deterministic longest-prefix rewriting system is a rewriting system such that there are no rewriting rules $$X\to Y$$, $$X\to Z$$ with $$Y\ne Z$$, and only longest prefixes of words are subject to rewriting. Given such a system, analogs are defined and examined of some concepts related to object-oriented data systems: inheritance of classes and objects, instances of classes, class and instance attributes, conceptual dependence and consistency, conceptual scheme, types and subtypes, etc. A special attention is paid to the effective verification of various properties of the rewriting systems under consideration. In particular, algorithms are presented for answering the following questions: Are all words finitely rewritable? Do there exist recurrent words? Is the system conceptually consistent? Given two words $$X$$ and $$Y$$, does $$X$$ conceptually depend on $$Y$$? Does the type of $$X$$ coincide with that of $$Y$$? Is the type of $$X$$ a subtype of that of $$Y$$?

MSC:

 68Q42 Grammars and rewriting systems 68N19 Other programming paradigms (object-oriented, sequential, concurrent, automatic, etc.) 68P05 Data structures 68T30 Knowledge representation
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References:

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