From EBNF to BNF

For building parsers (especially bottom-up) a BNF grammar is often better, than EBNF. But it's easy to convert an EBNF Grammar to BNF:

• Convert every repetition { E } to a fresh non-terminal X and add
  X = $\epsilon$ | X E.
• Convert every option [ E ] to a fresh non-terminal X and add
  X = $\epsilon$ | E.
  (We can convert X = A [ E ] B. to X = A E B | A B.)
• Convert every group ( E ) to a fresh non-terminal X and add
  X = E.
• We can even do away with alternatives by having several productions with the same non-terminal.
  X = E | E'. becomes X = E. X = E'.