Steedman ( 2020 ) proposes as a formal universal of natural language grammar that grammatical permutations of the kind that have given rise to transformational rules are limited to a class known to mathematicians and computer scientists as the “separable” permutations. This class of permutations is exactly the class that can be expressed in combinatory categorial grammars (CCGs). The excluded non-separable permutations do in fact seem to be absent in a number of studies of crosslinguistic variation in word order in nominal and verbal constructions. The number of permutations that are separable grows in the number n of lexical elements in the construction as the Large Schröder Number S n −1 . Because that number grows much more slowly than the n ! number of all permutations, this generalization is also of considerable practical interest for computational applications such as parsing and machine translation. The present article examines the mathematical and computational origins of this restriction, and the reason it is exactly captured in CCG without the imposition of any further constraints.

This article presents an algorithm for translating the Penn Treebank into a corpus of Combinatory Categorial Grammar (CCG) derivations augmented with local and long-range word-word dependencies. The resulting corpus, CCGbank, includes 99.4% of the sentences in the Penn Treebank. It is available from the Linguistic Data Consortium, and has been used to train wide-coverage statistical parsers that obtain state-of-the-art rates of dependency recovery. In order to obtain linguistically adequate CCG analyses, and to eliminate noise and inconsistencies in the original annotation, an extensive analysis of the constructions and annotations in the Penn Treebank was called for, and a substantial number of changes to the Treebank were necessary. We discuss the implications of our findings for the extraction of other linguistically expressive grammars from the Treebank, and for the design of future treebanks.