Why is the argument on the right? 
In most of Mathematics in English, the argument $x$ of a function (or partial map) $f$ with value $y$ is written $y=f(x)$ instead of, at least in Semigroup Theory and Formal Languages & Automata, $xf=y$. Why?

Thoughts:
A function $f$ is a subset of the Cartesian product of its domain $D$ and its codomain $C$ (i.e., $f\subseteq D\times C$) such that for each $d$ in $D$, $\lvert\{(d, c)\mid c\in C\}\rvert=1$. We write either $y=f(x)$ or $xf=y$ for $(x, y)\in f$.
The $xf=y$ notation has its strengths: composition of functions is usually taken left-to-right with this notation, as read in English, instead of right-to-left, with the argument $x$ first, as, I suppose, one usually has when evaluating $y$; one can read it as "$x$ through $f$ is $y$" instead of, say, "$y$ is $f$ at $x$"; and the left-to-right order respects that of going from the domain to the codomain.
Let me know if you can think of any strengths & weaknesses of the $xf=y$ notation.
I think history might have gotten the better of convention, that's all.


Hint:  According to A History of Mathematical Notations by F. Cajori this notation was  introduced by Johann Bernoulli  in  1718  . See this MSE post for a complete citation of the relevant section in the book.

