Hajek and Pudlak Metamathematics of First-Order Arithmetic use the Ackermann encoding of hereditarily finite sets, but they use no notation for codes. They let the reader see from context when a number is functioning as a code. Alberto Policriti http://www.dmi.unict.it/~cilc2013/submissions/cilc20130_submission_24.pdf writes $\mathbb{N}_A(x)$ for the Ackermann code for the hereditarily finite set $x$.
I would like to use some notation more explicit than the first and lighter than the second. Say $\ulcorner x\urcorner$ or $\overline{x}$. But I want something reasonably standard. Is the corner quote notation usually used only for Godel numbering of terms and formulas? Would overline be confused with some other concept?