  Designers of statistical machine translation (SMT) systems have begun to
employ tree-structured translation models. Systems involving tree-structured
translation models tend to be complex. This article aims to reduce the
conceptual complexity of such systems, in order to make them easier to design,
implement, debug, use, study, understand, explain, modify, and improve. In
service of this goal, the article extends the theory of semiring parsing to
arrive at a novel abstract parsing algorithm with five functional parameters: a
logic, a grammar, a semiring, a search strategy, and a termination condition.
The article then shows that all the common algorithms that revolve around
tree-structured translation models, including hierarchical alignment, inference
for parameter estimation, translation, and structured evaluation, can be
derived by generalizing two of these parameters -- the grammar and the logic.
The article culminates with a recipe for using such generalized parsers to
train, apply, and evaluate an SMT system that is driven by tree-structured
translation models.
