Grammar for Additive Expressions

_auxiliary Ï  E stands for Expression

^symbols Ó  V stands for Variable

Quoted symbols are literal

Grammar Rules

V Þ 'a' | 'b' | 'c'  (say)

E Þ V

E Þ V '+' E

 

a + b + c

not a V

V + E

if b+c is an E

   þ

  V+E

  b+V

Unlike programs, grammars are generative  (non-deterministic)

The rules generate  all possible expressions:

     a

     b

     c

    a+a

    a+b

    a+c

    b+a

     :

    c+c

    a+a+a

    a+a+b

      :