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grammarcompiler-theorylanguage-theory

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 could I use to recognize valid postfix expressions?

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


Solution

  • I would suggest

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