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.

Consideration of when Right Association works and when it fails lead to a restatement of this parsing principle in terms of the notion of heaviness. A computational investigation of a syntactically annotated corpus provides evidence for this proposal and suggest circumstances when RA is likely to make correct attachment predictions.