Homework 4

Eliminate left recursion from the following grammar:

P in Program
K in Block
D in Declaration
C in Command
E in Arithmetic Expression
B in Boolean Expresion
I in Identifier
N in Number

P ::= K.
K ::= begin D; C end
D ::= D ; D | const I = N | var I
C ::= C ; C | I := E | if B then C else C | while B do C | K
B ::= true | false | E = E | not B
E ::= E + E | I | N
I ::= x | y | z | u | v
N ::= 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9

Program the resulting grammar as a Definite Clause Grammar.
Your grammar should produce parse trees for the input programs.

An example input program:

begin
   const  x  =  8;
   var  y;
   var  z;
   z  :=  0;
   if  x  =  y + 2 then  z  :=  5 else  z  :=  3;
   while  not  x  =  z  do
   z  :=  z  +  2
end.