An essential difference between the categorial approaches and the glue approach is their relation to syntax. Categorial approaches describe syntactic rules, starting from the point of view of how meanings will functionally compose, and using types. The glue approach doesn't try to describe syntactic rules, but rather connects to a separate grammar, and says how to assemble meanings of sentences that have been analyzed by the grammar. It focuses on mediating the differences between the compositional structure of the grammar and the compositional structure of meaning assembly, differences such as occur with quantifier scoping.
A historical difference between the categorial approach and the glue approach has stemmed from the former's use of lambda expressions to manipulate meanings, compared to the latter's use of quantification. This has meant that the actual composition of meanings in the categorial approach is clearly separated from the syntactic types. The original formulation of the glue approach, in contrast, intermixed syntactic information and meanings.
This paper shows that a significant fragment of the glue approach can be reformulated to separate out the meaning composition in a way that is very similar to that of the categorial approaches. Specifically, we show the following: