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(Solved): Write a BNF description of the Boolean expressions of Java, including the three operators \( \bold ...
Write a BNF description of the Boolean expressions of Java, including the three operators \( \boldsymbol{\&} \boldsymbol{\&}, \| \), and \( ! \) and the relational operators. Use the start symbol for your grammar, the symbol as the left hand side of rules for generating \( \| \) expressions, and the symbol for the left hand side of rules for generating \& \& expressions. You can assume that identifiers can be any of the 1-character symbols A, B, C, D, E, F, G. Remember that logical \&\& has higher precedence than logical |.,. and that! goes in front of identifiers and expressions. Remember that relational operators are \( >,<, !=,==,<= \), and \( >= \). Examples of syntactically correct relational operator expressions include: \( \mathrm{A}>\mathrm{B}, \mathrm{C} !=\mathrm{D} \), and \( \mathrm{F}==\mathrm{G} \). Note that Java does not allow expressions like \( \mathrm{A}>\mathrm{B}>\mathrm{C} \), but we could have an expression like \( (\mathrm{A}>\mathrm{B}) \& \&(\mathrm{~B}>\mathrm{C}) \) This is an involved problem. I recommend you first write a grammar for just \( \boldsymbol{\&} \boldsymbol{\&} \), \( \| \), and !, (use the grammar in the text for correct \( + \) and \( * \) precedence to serve as an inspiration). Then, after that, expand the grammar for the relational expressions.
Expert Answer
::= | ::= ! ::= ("||" )* ::= ("&&" )* ::= ("<" | ">" | "==" | "<=" | ">=" | "!=") ::= ("+" )* ::=