Well-definedness and semantic type-checking in the nested relational calculus and xquery

The well-definedness problem for a programming language consists of checking, given an expression and an input type, whether the semantics of the expression is defined for all inputs adhering to the input type. A related problem is the semantic type-checking problem which consists of checking, given an expression, an input type, and an output type whether the expression always returns outputs adhering to the output type on inputs adhering to the input type. Both problems are undecidable for general-purpose programming languages. In this paper we study these problems for the Nested Relational Calculus, a specific-purpose database query language. We also investigate how these problems behave in the presence of programming language features such as singleton coercion and type tests.

Well-definedness and semantic type-checking in the nested relational calculus and xquery

Abstract. Two natural decision problems regarding the XML query language XQuery are well-definedness and semantic type-checking. We study these problems in the setting of a relational fragment of XQuery. We show that well-definedness and semantic type-checking are undecidable, even in the positive-existential case. Nevertheless, for a “pure” variant of XQuery, in which no identification is made between an item and the singleton containing that item, the problems become decidable. We also consider the analogous problems in the setting of the nested relational calculus.