将BNF语法的形式转换为g4语法

Question

I'm trying to covert this BNF grammar for validating boolean expression which is currently being used in Swift. Now want to implement similar parser in Java. I came across Antlr4 lib and want to use it to generate parser for the same grammar. I'm not very familiar with antlr4. Can someone please provide me some guidance? This is what I have so far.

Expr                ::= <ConcatenationExpr>;
NonInfixExpr        ::= <BracketExpr>
                      | <Function>
                      | <Literal>
                      | <Accessor>;
BracketExpr         ::= '(' <Expr> ')';
Accessor            ::= ('$' <AccessorComponent> | <AccessorComponent>) ('.' <AccessorComponent> )*;
AccessorComponent   ::= 'Identifier' ':' 'Identifier' | 'Identifier';
Function            ::= 'Identifier' '(' ')' | ('Identifier' '(' <Expr> (',' <Expr>)* ')');
Literal             ::= 'True'
                     | 'False'
                     | 'Null'
                     | 'Number'
                     | 'Text';
ConcatenationExpr   ::= <AndExpr>
                     | <ConcatenationExpr> '&' <AndExpr>;
AndExpr             ::= <OrExpr>
                     | <AndExpr> '&&' <OrExpr>;
OrExpr              ::= <EqualityExpr>
                     | <OrExpr> '||' <EqualityExpr>;
EqualityExpr        ::= <ComparisonExpr>
                     | <EqualityExpr> ('==' | '=' | '!=' | '<>') <ComparisonExpr>;
ComparisonExpr      ::= <AddExpr>
                     | <AddExpr> ('<' | '<=' | '>' | '>=') <AddExpr>;
AddExpr             ::= <ExponentialExpr>
                     | <AddExpr> ('+' | '-') <ExponentialExpr>;
ExponentialExpr     ::= <MultExpr>
                     | <ExponentialExpr> '^' <MultExpr>;
MultExpr            ::= <NonInfixExpr>
                     | <MultExpr> ('*' | '/') <NonInfixExpr>;

I tried to convert to g4 and this is what it looks like.

grammar VALIDATE;

Expr
    : ConcatenationExpr ';'
    ;

NonInfixExpr
    : BracketExpr 
    | Function 
    | Literal 
    | Accessor
    ;

BracketExpr 
    : '(' Expr ')'
    ;

Accessor
    : ('$' AccessorComponent | AccessorComponent ) ('.' AccessorComponent )*
    ;

AccessorComponent
    : 'Identifier' ':' 'Identifier' | 'Identifier'
    ;

Function
    : 'Identifier' '(' ')' | ('Identifier' '(' Expr (',' Expr)* ')')
    ;

Literal
    : 'True' | 'False' | 'Null' | 'Number' | 'Text'
    ;

ConcatenationExpr
    : AndExpr 
    | ConcatenationExpr '&&' AndExpr
    ;

AndExpr
    : OrExpr | AndExpr '&&' OrExpr
    ;

OrExpr
    : EqualityExpr | OrExpr '||' EqualityExpr
    ;

EqualityExpr
    : ComparisonExpr | EqualityExpr ('==' | '=' | '!=' | '<>') ComparisonExpr
    ;

ComparisonExpr
    : AddExpr | AddExpr ('<' | '<=' | '>' | '>=') AddExpr
    ;

AddExpr
    : ExponentialExpr | AddExpr ('+' | '-') ExponentialExpr
    ;

ExponentialExpr
    : MultExpr | ExponentialExpr '^' MultExpr
    ;

MultExpr
    : NonInfixExpr | MultExpr ('*' | '/') NonInfixExpr
    ;

I'm stuck at antlr4 VALIDATE.g4 step. I'm not sure I did the conversion right.

error(119): VALIDATE.g4::: The following sets of rules are mutually left-recursive [MultExpr] and [ExponentialExpr] and [AddExpr] and [EqualityExpr] and [OrExpr] and [AndExpr] and [ConcatenationExpr]
error(99): VALIDATE.g4::: grammar VALIDATE has no rules

Answer 1

The original grammar has no mutual left recursion - that was only introduced in the converted version by using && in ConcatenationExpr where it should have read & . Once that is fixed, the grammar has only direct left recursion which ANTLR 4 should be able to cope with.

You could even completely remove left recursion by rewriting recursive rules, such that eg ConcatenationExpr would become

ConcatenationExpr
     ::= AndExpr ( '&' AndExpr )*

If this is done for all recursive rules, the resulting grammar is LL(2).