Grammar to recognize postfix formulas

Question

I'm trying to create a postfix to infix converter, and I'm unable to create the grammar for postfix formulas. I've been also looking for it for a while without success..

What grammar could I use to recognize valid postfix expressions?

The tokens I need are: number, +, * and ^ (pow).

Answer 1

I would suggest

E ::= number | E E + | E E * | E E ^