Grammar to recognize postfix formulas

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开发者_运维知识库 could I use to recognize valid postfix expressions?

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

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I would suggest

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

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Valid in what sense? Resulting in one value?

B ::= number | B B O
O ::= + | * | ^