How to write notation for this function?

Question

Say $X=(x_1,x_2,x_3,..,x_n)$, and there is a function of $X$, which is $f(X)=g(h(c,X))$ where $c$ is constant.

Now in my case, given a $X_0$,there will be a function $i_1(x_1)$, which takes $x_1$ in $X_0$ as variable while other $x$ are fixed. I try $i_1(x_1)=g_1(h(c,x_1;X_0))$. It is kind of ugly.

So, is there any better way to write the $i_1(x_1)$? Any way people usually do? Or is this kind of notation allowed at all?

Thank you.

Answer 1

You need the $\lambda$ (lambda) calculus. There are lots of textbooks and websites about it.