I did my dissertation on an aspect of Combinatory Categorial Grammar, as mentioned in the article as a byproduct of Schönfinkel's work. One of the interesting

I did my dissertation on an aspect of Combinatory Categorial Grammar, as mentioned in the article as a byproduct of Schönfinkel's work. One of the interesting byproducts of considering sequences of words in a natural language sentence as functions, is a solution to analysing a phenomenon in syntax called right node raising: "I washed and you dried the dishes." In context-free grammars of English, "I washed" and "you dried" do not form constituents (unlike "washed the dishes" or "dried the dishes", which are VPs — verb phrases). However, in Combinatory Categorial Grammar, this is no problem, as "I washed" is simply a function looking rightward for a noun phrase (NP), and returning a sentence (S). In CCG terms, this function would be notated S/NP, corresponding to an interpretation function of type NP -> S.