You have to design the syntactic analyzer for language specified by the grammar shown below. We are using the following convention: Terminals (lexical elements) are represented with bold courier font like this.  Non-terminals are represented in the angle brackets .  The character ε (epsilon) represents an empty stream. The non-terminal is the starting symbol of grammar.

Grammar

   ::= *
  ::=  class id {**};
  ::=  program;*
  ::=  id()
  ::=  ;
  ::=  {**}
  ::=  id*;
  ::=  ;
  |  if()thenelse;
  |  while()do;
  |  read();
  |  prepare();
  |  return();
  ::=  {*} | | ε
  ::= |
  ::= |  
  ::=  + | -
  ::= |
  ::=
  |  *id()
  |  num
  |   ()
  |  not
  |
  ::=  *id*
  ::=  id*.
  ::=  []
  ::=  [ int ]
  ::=  integer | real | id
  ::=  id** | ε
  ::=  * | ε
  ::=  ,id*
  ::= ,
Operators and additional lexical conventions
   ::=  =
  ::=  == | <> | < | > | <= | >= 
  ::=  + | - | or 
  ::=  * | / | and
    
id  ::=  follows specification for identifiers found in assignment#1
num  ::=  follows specification for numbers found in assignment#1
int  ::= *
  ::=  1..9
  ::=  | 0
 
For illustration, the non-terminal is a generalization of the addition operators tokens +, - and or. The use of this notation here doesn’t necessarily imply which you have to define a new kind of token in your lexical analyzer. Also, id and num are tokens that refer to the lexical conventions. Note that a new lexical convention for the token int has been added. 
Work to be done

• Analyze the syntactical definition given on the first page (and the additional lexical definition for the token int). Remove all the * notations and replace them by list-generating productions. List in your documentation all the ambiguities and left recursions, or any error you might find in grammar. Modify the productions so that the left recursions and ambiguities are deleting without modifying the language. You must get a set of productions that can be parsed using the top-down predictive parsing method. Include the transformed grammar in your documentation.

• Derive the FIRST and FOLLOW sets for each non-terminal in your transformed grammar and list them in your documentation.

• Implement a predictive parser (recursive descent or table-driven) for your modified set of grammar rules.

• Your parser must optionally output to a file the derivation which derives the source program from the starting symbol.

• The parser must call your lexical analyzer as it needs a new token.

• The parser must properly identify the errors in the input program and print a meaningful message to the user for each error encountered.

The parser must implement an error recover way that permits to report all errors. The error messages must be informative on the nature of the errors, as well as the location of the errors in the input file.

• In this assignment, you only check the syntactic correctness of the program, that is, check whether the source program can be parsed according to the grammar. Don’t check the semantic correctness of the program in this assignment.

• prepare a set of source files that facilitate to test the parser for all syntactical structures involved in the language. Include cases testing for a variety of different errors to demonstrate the accurateness of your error reporting and recovery.