Ken Q. Pu
ABSTRACT
We present a framework for functionally modeling query languages and data models. Data and queries are uniformly represented by first-order functions, and query-language constructs by polymorphic higher-order functions. The functions are typed by a database-oriented type system that supports polymorphism and nesting of types, thus one can perform static type-checking and type-inferencing of query-expressions. The query language can be freely extended by introducing new querying constructs as polymorphic higher-order functions.While type information gives the input-output description of the functions, the semantic information is captured by equational specifications. Knowledge about the functions is represented as equalities of functional expressions in the form of equations. By equational axiomatization of the query language, database problems of query equivalence and answering-query with views can be posed as equational word-problems and equational matching.
- F. Baader and T. Nipknow. Term Rewriting and All That. Cambridge University Press, 1998. Google Scholar
Digital Library
- F. Baader and W. Snyder. Unification theory. Handbook of automated reasoning, pages 445--532, 2001.Google Scholar
- P. Buneman and R. E. Frankel. FQL -- a functional query language. In SIGMOD, pages 52--58, 1979. Google ScholarDigital Library
- P. Buneman and A. Ohori. Polymorphism and type inference in database programming. ACM Transactions on Database Systems, 21(1):30--76, March 1996. Google ScholarDigital Library
- Y. Kaji, T. Fujiwara, and T. Kasami. Solving a unification problem under constrained substitutions using tree automata. J. Symb. Comput., 23(1):79--117, 1997. Google ScholarDigital Library
- A. Ohori, P. Buneman, and V. Tannen. Database programming in Machiavelli -- a polymorphic language with static type inference. In SIGMOD, pages 46--57, 1989. Google ScholarDigital Library
- D. Rémy. Type inference for records in a natural extension of ML. In TACS, volume 789 of Lecture Notes in Computer Science. Springer, 1994.Google Scholar
- D. W. Shipman. The functional data model and the data languages DAPLEX. ACM Transactions on Database Systems, 6(1):140--173, March 1981. Google ScholarDigital Library
- M. Wand. Complete type inference for simple objects. In LICS, pages 37--44, 1987.Google Scholar
Index Terms
- Typed functional query languages with equational specifications
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