  XML database query languages such as XQuery employ regular expression types
with structural subtyping. Subtyping systems typically have two presentations,
which should be equivalent: a declarative version in which the subsumption rule
may be used anywhere, and an algorithmic version in which the use of
subsumption is limited in order to make typechecking syntax-directed and
decidable. However, the XQuery standard type system circumvents this issue by
using imprecise typing rules for iteration constructs and defining only
algorithmic typechecking, and another extant proposal provides more precise
types for iteration constructs but ignores subtyping. In this paper, we
consider a core XQuery-like language with a subsumption rule and prove the
completeness of algorithmic typechecking; this is straightforward for XQuery
proper but requires some care in the presence of more precise iteration typing
disciplines. We extend this result to an XML update language we have introduced
in earlier work.
