Here is a complete grammar that evaluates expressions containing +, -, * and variable assignments. A simple hash table is used to store variable values.

The tutorial requires the current depot version of ANTLR 3.0, i.e. the version must be later than 3.0 beta 5.

grammar Expr;

@header {
import java.util.HashMap;
}

@members {
/** Map variable name to Integer object holding value */
HashMap memory = new HashMap();
}

prog:   stat+ ;
                
stat:   expr NEWLINE {System.out.println($expr.value);}
    |   ID '=' expr NEWLINE
        {memory.put($ID.text, new Integer($expr.value));}
    |   NEWLINE
    ;

expr returns [int value]
    :   e=multExpr {$value = $e.value;}
        (   '+' e=multExpr {$value += $e.value;}
        |   '-' e=multExpr {$value -= $e.value;}
        )*
    ;

multExpr returns [int value]
    :   e=atom {$value = $e.value;} ('*' e=atom {$value *= $e.value;})*
    ; 

atom returns [int value]
    :   INT {$value = Integer.parseInt($INT.text);}
    |   ID
        {
        Integer v = (Integer)memory.get($ID.text);
        if ( v!=null ) $value = v.intValue();
        else System.err.println("undefined variable "+$ID.text);
        }
    |   '(' expr ')' {$value = $expr.value;}
    ;

ID  :   ('a'..'z'|'A'..'Z')+ ;
INT :   '0'..'9'+ ;
NEWLINE:'\r'? '\n' ;
WS  :   (' '|'\t')+ {skip();} ;

And here is the main program to execute the parser:

import org.antlr.runtime.*;

public class Test {
    public static void main(String[] args) throws Exception {
        ANTLRInputStream input = new ANTLRInputStream(System.in);
        ExprLexer lexer = new ExprLexer(input);
        CommonTokenStream tokens = new CommonTokenStream(lexer);
        ExprParser parser = new ExprParser(tokens);
        parser.prog();
    }
}

Run ANTLR on the grammar and compile:

java org.antlr.Tool Expr.g
javac Test.java ExprLexer.java ExprParser.java

Here is a sample run:

$java Test
x=1
y=2
3*(x+y)
<EOF>
9
$

What if you want to build trees instead? Here is a grammar that builds trees instead of evaluating the expressions:

grammar Expr;
options {
    output=AST;
    ASTLabelType=CommonTree; // type of $stat.tree ref etc...
}

prog:   ( stat {System.out.println($stat.tree.toStringTree());} )+ ;

stat:   expr NEWLINE        -> expr
    |   ID '=' expr NEWLINE -> ^('=' ID expr)
    |   NEWLINE             ->
    ;

expr:   multExpr (('+'^|'-'^) multExpr)*
    ; 

multExpr
    :   atom ('*'^ atom)*
    ; 

atom:   INT 
    |   ID
    |   '('! expr ')'!
    ;

ID  :   ('a'..'z'|'A'..'Z')+ ;
INT :   '0'..'9'+ ;
NEWLINE:'\r'? '\n' ;
WS  :   (' '|'\t')+ {skip();} ;

And here is the tree grammar that will read the trees and evaluate the expressions.

tree grammar Eval;

options {
    tokenVocab=Expr;
    ASTLabelType=CommonTree;
}

@header {
import java.util.HashMap;
}

@members {
/** Map variable name to Integer object holding value */
HashMap memory = new HashMap();
}

prog:   stat+ ;

stat:   expr
        {System.out.println($expr.value);}
    |   ^('=' ID expr)
        {memory.put($ID.text, new Integer($expr.value));}
    ;

expr returns [int value]
    :   ^('+' a=expr b=expr)  {$value = a+b;}
    |   ^('-' a=expr b=expr)  {$value = a-b;}   
    |   ^('*' a=expr b=expr)  {$value = a*b;}
    |   ID 
        {
        Integer v = (Integer)memory.get($ID.text);
        if ( v!=null ) $value = v.intValue();
        else System.err.println("undefined variable "+$ID.text);
        }
    |   INT                   {$value = Integer.parseInt($INT.text);}
    ;

Here is the main program:

import org.antlr.runtime.*;
import org.antlr.runtime.tree.*;

public class Test {
    public static void main(String[] args) throws Exception {
        ANTLRInputStream input = new ANTLRInputStream(System.in);
        ExprLexer lexer = new ExprLexer(input);
        CommonTokenStream tokens = new CommonTokenStream(lexer);
        ExprParser parser = new ExprParser(tokens);
        ExprParser.prog_return r = parser.prog();

        // walk resulting tree
        CommonTree t = (CommonTree)r.getTree();
        CommonTreeNodeStream nodes = new CommonTreeNodeStream(t);
        Eval walker = new Eval(nodes);
        walker.prog();
    }
}

and a sample run:

$ java Test
x=1
y=2
3*(x+y)
<EOF>
(= x 1)
(= y 2)
(* 3 (+ x y))
9
$