Domain-Independent Queries on Databases with External Functions

We investigate queries in the presence of external functions with arbitrary inputs and outputs (atomic values, sets, nested sets etc). We propose a new notion of domain independence for queries with external functions which, in contrast to previous work, can also be applied to query languages with fixpoints or other kinds of iterators. Next, we define two new notions of computable queries with external functions, and prove that they are equivalent, under the assumption that the external functions are total. Thus, our definition of computable queries with external functions is robust. Finally, based on the equivalence result, we give examples of complete query languages with external functions. A byproduct of the equivalence result is the fact that Relational Machines are complete for complex objects: it was known that they are not complete over flat relations.

[1]  Desmond Fearnley-Sander,et al.  Universal Algebra , 1982 .

[2]  Serge Abiteboul,et al.  An Extensible Rule-Based Language with Complex Objects and data-Functions , 1989, DBPL.

[3]  Serge Abiteboul,et al.  Fixpoint logics, relational machines, and computational complexity , 1992, [1992] Proceedings of the Seventh Annual Structure in Complexity Theory Conference.

[4]  Limsoon Wong,et al.  Naturally Embedded Query Languages , 1992, ICDT.

[5]  C. H. Papadimitriou,et al.  The Power of Re ective Relational MachinesS , 1994 .

[6]  Victor Vianu,et al.  Expressiveness and Complexity of Restricted Languages for Complex Objects , 1991, DBPL.

[7]  Val Tannen,et al.  Logical and Computational Aspects of Programming with Sets/Bags/Lists , 1991, ICALP.

[8]  Pierre-Louis Curien,et al.  Categorical Combinators , 1986, Inf. Control..

[9]  Dan Suciu,et al.  Fixpoints and Bounded Fixpoints for Complex Objects , 1993 .

[10]  Serge Abiteboul,et al.  Fixpoint logics, relational machines, and computational complexity , 1997, JACM.

[11]  Dan Suciu,et al.  On Two Forms of Structural Recursion , 1995, ICDT.

[12]  Serge Abiteboul,et al.  Object identity as a query language primitive , 1989, SIGMOD '89.

[13]  Dan Suciu,et al.  A query language for NC , 1994, PODS '94.

[14]  O. Deux,et al.  The Story of O2 , 1990, IEEE Trans. Knowl. Data Eng..

[15]  Marc Gyssens,et al.  The Powerset Algebra as a Natural Tool to Handle Nested Database Relations , 1992, J. Comput. Syst. Sci..

[16]  O. Deux,et al.  The story of O 2 , 1992 .

[17]  Serge Abiteboul,et al.  The power of reflective relational machines , 1994, Proceedings Ninth Annual IEEE Symposium on Logic in Computer Science.

[18]  Richard Hull,et al.  Safety and translation of calculus queries with scalar functions , 1993, PODS.

[19]  D. C. Cooper,et al.  Theory of Recursive Functions and Effective Computability , 1969, The Mathematical Gazette.

[20]  Jr. Hartley Rogers.  Theory of Recursive Functions and Effective Computability , 1969 .

[21]  Marc Gyssens,et al.  A Comparison between Algebraic Query Languages for Flat and Nested Databases , 1991, Theor. Comput. Sci..

[22]  Jianwen Su,et al.  Untyped sets, invention, and computable queries , 1989, PODS '89.

[23]  Serge Abiteboul,et al.  Generic Computation and its complexity , 1991, STOC '91.

[24]  Rodney W. Topor,et al.  Domain-Independent Formulas and Databases , 1987, Theor. Comput. Sci..

[25]  David Harel,et al.  Computable Queries for Relational Data Bases , 1980, J. Comput. Syst. Sci..

[26]  Dan Suciu.  Bounded Fixpoints for Complex Objects , 1993 .

[27]  Carl A. Gunter.  Semantics of programming languages: structures and techniques , 1993, Choice Reviews Online.

[28]  Robert L. Constable,et al.  Type two computational complexity , 1973, STOC.

[29]  Dan Suciu,et al.  A Query Language for NC , 1994, LCC.

[30]  Pierre-Louis Curien.  Categorical Combinators, Sequential Algorithms, and Functional Programming , 1993, Progress in Theoretical Computer Science.

[31]  Catriel Beeri,et al.  On the power of languages for manipulation of complex objects , 1987, VLDB 1987.