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The well-definedness problem for a database query language consists of checking, given an expression and an input type, that the expression never yields a runtime error on any input adhering to the input type. In this article, we study the well-definedness problem for query languages on trees that are built from a finite set of partially defined base operations by adding variables, constants, conditionals, let bindings, and iteration. We identify properties of base operations that can make the problem undecidable and give restrictions that are sufficient to ensure decidability. As a direct result, we obtain a large fragment of XQuery for which well-definedness is decidable.