what is the difference between the below functions? $$\lambda x.\lambda y.f(x, y)$$ $$\lambda y.\lambda x.f(x, y)$$
And it appears that there is a $\texttt{reverse operation}$ in lambda calculus which can reverse the order of the arguments. So does the order actually matter?
I am asking this question because I am reading this paper, in which the author reverse the argument order in the 5th page: $$ [\![ R[b]]\!] = \lambda y.\lambda x.[\![b]\!](x, y) $$ Here $R$ is the ${reverse}$ $operator$. I am not sure why the author did this. And why it matters to change the order in which the arguments are taken.