consider the grammar of expressions provided in file `grammar.txt`. Write a parser for the given grammar.

The parser will use the scanner to process a file and return true or false, depending on whether the input is syntactically correct according to the given grammar

`grammar.txt`

Program = "begin" Body "end" . Body = [ Declarations ] Statements . Declarations = Declaration { Declaration } . Declaration = [ "bool | "int" ] Identifier ';' . Statements = Statement { ";" Statement } . Statement = AssignmentStatement | ConditionalStatement | IterativeStatement | PrintStatement . AssignmentStatement = Identifier ":=" Expression . ConditionalStatement = "if" Expression "then" Body [ "else" Body ] "fi" . IterativeStatement = "while" Expression "do" Body "od" . PrintStatement = "print" Expression . Expression = BooleanExpression . BooleanExpression = BooleanTerm { "or" BooleanTerm } . BooleanTerm = BooleanFactor { "and" BooleanFactor } . BooleanFactor = [ "not" ] ArithmeticExpression [ ( "=" | "<") ArithmeticExpression) ] . ArithmeticExpression = Term { ("+" | "-") Term } . Term = Factor { ("*" | "/") Factor } . Factor = Literal | Identifier | "(" Expression ")" . Literal = BooleanLiteral | IntegerLiteral . BooleanLiteral = "false" | "true" . IntegerLiteral = Digit { Digit } . Identifier = Letter { Letter | Digit | "_" }. Digit = "0" | "1" | "2" | "3" | "4" | "5" | "6" | "7" | "8" | "9" . Letter = "a" | "b" | "c" | "d" | "e" | "f" | "g" | "h" | "i" | "j" | "k" | "l" | "m" | "n" | "o" | "p" | "q" | "u" | "r" | "s" | "t" | "u" | "v" | "w" | "x" | "y" | "z" | "A" | "B" | "C" | "D" | "E" | "F" | "G" | "H" | "I" | "J" | "K" | "L" | "M" | "N" | "O" | "P" | "Q" | "U" | "R" | "S" | "T" | "U" | "V" | "W" | "X" | "Y" | "Z" .