  Considering the speed in which humans resolve syntactic ambiguity, and the
overwhelming evidence that syntactic ambiguity is resolved through selection of
the analysis whose interpretation is the most `sensible', one comes to the
conclusion that interpretation, hence parsing take place incrementally, just
about every word. Considerations of parsimony in the theory of the syntactic
processor lead one to explore the simplest of parsers: one which represents
only analyses as defined by the grammar and no other information.
  Toward this aim of a simple, incremental parser I explore the proposal that
the competence grammar is a Combinatory Categorial Grammar (CCG). I address the
problem of the proliferating analyses that stem from CCG's associativity of
derivation. My solution involves maintaining only the maximally incremental
analysis and, when necessary, computing the maximally right-branching analysis.
I use results from the study of rewrite systems to show that this computation
is efficient.
