Typed functional query languages with equational specifications

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.