Categorial accounts of cross-serial dependencies initially made use of a syntactic rule of composition . Recognizing the lexical nature of the process, more recent proposals have used either a lexical rule of composition  or a lexical rule of `division' . Division is a rule which enables a functor to inherit the arguments of its argument:
To generate cross-serial dependencies, a `disharmonic' version of this rule is needed:
Hoeksema proposes that verbs which trigger cross-serial word order are subject to (8):
In a framework using recursive constraints, generalized disharmonic division can be implemented as a recursive constraint connecting the initial category of such verbs with a derived category:
Only verbs that trigger the cross-serial order are subject to the division constraint. This accounts immediately for the fact that cross-serial orders do not arise with all verbs selecting infinitival complements.