We give a polymorphic account of the relational algebra. We introduce a formalism of ''type formulas'' specifically tuned for relational algebra expressions, and present an algorithm that computes the ''principal'' type for a given expression. The principal type of an expression is a formula that specifies, in a clear and concise manner, all assignments of types (sets of attributes) to relation names, under which a given relational algebra expression is well-typed, as well as the output type that expression will have under each of these assignments. Topics discussed include complexity and polymorphic expressive power.

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The concept of method schemas is proposed as a simple model for object-oriented programming with features such as classes with methods and inheritance, method name overloading, and late binding. An important issue is to check whether a given method schema can possibly lead to inconsistencies in some interpretations. The consistency problem for method schemas is studied. The problem is shown to be undecidable in 'general. Decidability is obtained for monadic and/or recursionfree method schemas. The effect of covariance is considered. The issues of incremental consistency checking and of a sound algorithm for the general case are briefly discussed.

We present in this paper an approach for XQuery optimization that exploits minimization opportunities raised in composition-style nesting of queries. More precisely, we consider the simplification of XQuery queries in which the intermediate result constructed by a subexpression is queried by another subexpression. Based on a large subset of XQuery, we describe a rule-based algorithm that recursively prunes query expressions, eliminating useless intermediate results. Our algorithm takes as input an XQuery expression that may have navigation within its subexpressions and outputs a simplified, equivalent XQuery expression, and is thus readily usable as an optimization module in any existing XQuery processor. We demonstrate by experiments the impact of our rewriting approach on query evaluation costs and we prove formally its correctness.