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Syntactically-enriched language models (parsers) constitute a promising component in applications such as machine translation and speech-recognition. To maintain a useful level of accuracy, existing parsers are non-incremental and must span a combinatorially growing space of possible structures as every input word is processed. This prohibits their incorporation into standard linear-time decoders. In this paper, we present an incremental, linear-time dependency parser based on Combinatory Categorial Grammar (CCG) and classification techniques. We devise a deterministic transform of CCG-bank canonical derivations into incremental ones, and train our parser on this data. We discover that a cascaded, incremental version provides an appealing balance between efficiency and accuracy.