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We propose a new approach for the efficient evaluation of XPath expressions. This is important, since XPath is not only used as a simple, stand-alone query language, but is also an essential ingredient of XQuery and XSLT. The main idea of our approach is to translate XPath into algebraic expressions parameterized with programs. These programs are mainly built from navigational primitives like accessing the first child or the next sibling. The goals of the approach are: 1) to enable pipelined evaluation, 2) to avoid producing duplicate (intermediate) result nodes, 3) to visit as few document nodes as possible, and 4) to avoid visiting nodes more than once. This improves the existing approaches, because our method is highly efficient.