Grammar for a boolean calculator language

I am writing a grammar for a boolean calculator language. Programmes written in this language will consist of atmost one statement whose result will be boolean.

An example statement of such language is given below:

( A + B >= C ) AND ( D == 4 )

The grammar that I have come up with so far is given below:

E =开发者_StackOverflow中文版> T COP T | EXPR BOP EXPR
T => VAR | EXPR
VAR => A | B | C | D
EXPR => AEXPR | CEXPR
AEXPR => "(" VAR AOP VAR ")"
CEXPR => VAR COP AEXPR | AEXPR COP AEXPR
AOP => + | - | * | / | %
BOP => AND | OR
COP => == | != | < | > | <= | >=

The main thing to consider here is that no two VARs can be joined in a binary operation BOP and that the statement must return a boolean.

I want to know if the above grammar satisfies this criteria or am I missing something?

Any help will be appereciated.

Thanks

The main thing to consider here is that no two VARs can be joined in a binary operation BOP and that the statement must return a boolean.

The above requirement fails in following case:

E = EXPR BOP EXPR
EXPR = AEXPR

=> E = AEXPR BOP AEXPR

I am assuming here that (VAR AOP VAR) yields a VAR.

A more standardized form of your required grammar is given below:

E = T COP T | EXPR BOP EXPR;
T = VAR | AEXPR;
VAR = "A" | "B" | "C" | "D";
AEXPR = "(" VAR AOP VAR ")" | "(" VAR AOP AEXPR ")";
EXPR = VAR COP AEXPR | AEXPR COP AEXPR;
AOP = "+" | "-" | "*" | "/" | "%";
BOP = "AND" | "OR";
COP = "==" | "!=" | "<" | ">" | "<=" | ">=";