Well-Definedness and Semantic Type-Checking in the Nested Relational   Calculus and XQuery
  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. 
Jan Van den Bussche, Dirk Van Gucht, Stijn Vansummeren