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Object Algebras: What Is Wrong?

Conceptual flaws (crippled conception) Explicit and implicit limitations of data structures to be processed Explicit and implicit limitations of universality of query operators

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Object Algebras: What Is Wrong?

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  1. Conceptual flaws (crippled conception) Explicit and implicit limitations of data structures to be processed Explicit and implicit limitations of universality of query operators No clean semantics of object-oriented concepts (complex objects, links among objects, encapsulation, classes, overriding, methods, polymorphism,...) The “closure” of the algebra over “objects” is a total conceptual nonsense. Mathematical flaws (bad, totally inadequate mathematics) Lack of many definitions Inadequate mix of the language and meta-language mathematical levels An attempt to treat quantifiers and other non-algebraic operators as algebraic ones Ignoring the vital concept of database/program state (and the corresponding assumption that the semantics of a query is a mapping from states into query results) Object Algebras: What Is Wrong? by Kazimierz Subieta

  2. Pragmatic flaws (wishful thinking) Doubts concerning the possibility to develop formal mappings from practical languages (SQL-99, OQL, XQuery...) to any matematical model, including algebraic models No proof that the query execution model based on an algebra is practically feasible Bad mathematics makes it impossible to prove query equivalence theorems (necessary for optimization) Algebraic methods are able to deal with limited optimizations (query rewriting only) Other formalisms (denotational, operational) have at least the same potential Object Algebras: What Is Wrong? (con.) Conclusion 1. All object algebras that I am aware of present pseudo-scientific rubbish not worth reading, referencing and even mentioning. Conclusion 2. If you are motivated to understand correct and efficient formal methods behind object-oriented query languages, try to learn and understand the Stack-Based Approach.

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