Ableitungen

Expression = Term . Expression = Term "+" Expression . Expression = Term "-" Expression . Term = Factor . Term = Factor "*" Term . Term = Factor "/" Term . Factor = "(" Expression ")" . Factor = "+" Factor . Factor = "-" Factor . Factor = Constant . Constant = "0" . Constant = "1" . ... Constant = "9" .

Wenn eine Grammatik vorgegeben ist, lassen sich leicht entsprechend der Produktionsregeln zulässige Sätze bilden:

Expression Startsymbol

Term "+" Expression Expression = Term "+" Expression

Factor "+" Expression Term = Factor

Constant "+" Expression Factor = Constant

"1" "+" Expression Constant = "1"

"1" "+" Term Expression = Term

"1" "+" Factor "*" Term Term = Factor "*" Term

"1" "+" Constant "*" Term Factor = Constant

"1" "+" "2" "*" Term Constant = "2"

"1" "+" "2" "*" Factor Term = Factor

"1" "+" "2" "*" Constant Factor = Constant

"1" "+" "2" "*" "3" Constant = "3"

`Expression`	Startsymbol
`Term "+" Expression`	`Expression = Term "+" Expression`
`Factor "+" Expression`	`Term = Factor`
`Constant "+" Expression`	`Factor = Constant`
`"1" "+" Expression`	`Constant = "1"`
`"1" "+" Term`	`Expression = Term`
`"1" "+" Factor "*" Term`	`Term = Factor "*" Term`
`"1" "+" Constant "*" Term`	`Factor = Constant`
`"1" "+" "2" "*" Term`	`Constant = "2"`
`"1" "+" "2" "*" Factor`	`Term = Factor`
`"1" "+" "2" "*" Constant`	`Factor = Constant`
`"1" "+" "2" "*" "3"`	`Constant = "3"`