  We reduce phrase-representation parsing to dependency parsing. Our reduction
is grounded on a new intermediate representation, "head-ordered dependency
trees", shown to be isomorphic to constituent trees. By encoding order
information in the dependency labels, we show that any off-the-shelf, trainable
dependency parser can be used to produce constituents. When this parser is
non-projective, we can perform discontinuous parsing in a very natural manner.
Despite the simplicity of our approach, experiments show that the resulting
parsers are on par with strong baselines, such as the Berkeley parser for
English and the best single system in the SPMRL-2014 shared task. Results are
particularly striking for discontinuous parsing of German, where we surpass the
current state of the art by a wide margin.
