# Functional Application in LaTeX

This month’s Guess the code shows an example of Functional Application which is an operation in compositional semantics. As you all know, in mathematics and in programming a function takes an input argument from some specified domain and yields an output value. Applying a function f to an argument x yields the value for that argument, which can be written as f(x). In beginner semantics, this same procedure is what happens when verb takes its object.

verb(object) ~ function(argument)

The only mystery in this example is the denotation double brackets which indicate that it is the denotation, not the orthographic word, which is being operated upon. The code also gives us two trees to show that in English functional application applies to the right, and in Turkish it applies to the left.

In (41) we simplify things and pretend that “hug” is a function, which takes “Mary” as its object.” In reality, in most languages “hug” is a complex predicate, itself the return value of a Functional Application between a function (we call it “little v”) and its object, a root. Sound like Javascript anyone?

 \begin{example}Typical example of Functional Appilcation (FA)\\ \label{typicalFA} \begin{tabular}{ll} \Tree[-1]{ \K{(a) English}\\ & VP_{}\Below{$_\textsc{fa}$}\B{dl}\B{dr} && =\denote{hug}(\denote{NP})\\ {V}_{>}\Below{\denote{hug}} && NP_e\Below{\denote{Mary}}\\ }& \Tree[-1]{ \K{(b) Turkish} \\ & VP_{}\Below{$_\textsc{fa}$}\B{dl}\B{dr} && \hspace{-.2in} =(\denote{NP e})\denote{sardil-di}\\ NP_e\Below{\denote{Mary-e}} && {V}_{>}\Below{\denote{sarid-di}}\\ } \end{tabular} \end{example} 