Let $f^{\circ n}$ denote the $n$-fold composition of function $f$. As an example, $f^{\circ 3}x$ is short-hand for $f(f(fx))$.
Is there another form of composition to denote $((ff)f)x$?
Would one be “left-composition” and the other be “right-composition”? Or maybe “pre-composition” and “post-composition”? And if so, which is which?
These come in handy for Church numbers. E.g. $\lambda fx.f^{\circ 3}x$ denotes $\bar 3$.