Combinatory Categorial Grammar (CCG).  The CCG framework (see Steedman 2000 for a comprehensive presentation) takes its name from the Combinatory Logic of Curry and Feys.  Whereas the design of typelogical grammars follows a logical agenda (sequent calculus, soundness, completeness, etc), grammars in the CCG tradition are presented as finite sets of rules for type change and type combination.  This rule inventory will typically include function application schemata, type lifting, and functional composition, both of the kind valid within associative L (composing implicational types with the same directionality), and of the mixed kind (composing functors with different directionality).