fatal error in grammar - piecewise definition - antlr

Question

I am translating a grammar from LALR to ANTLR and I am having trouble with translating this one rule, piecewise expression.
Attached is the sample grammar:
grammar Test;
options {
language = Java;
output = AST;
}
parse : expression ';'
;
expression : binaryExpression
| piecesExpression
;
binaryExpression : addingExpression (('=='|'!='|'<='|'>='|'>'|'<') addingExpression)*
;
addingExpression : multiplyingExpression (('+'|'-') multiplyingExpression)*
;
multiplyingExpression : unaryExpression
(('*'|'/') unaryExpression)*
;
unaryExpression: ('!'|'-')* primitiveElement;
primitiveElement : literalExpression
| id
| '(' expression ')'
;
literalExpression : INT
;
id : IDENTIFIER
;
piecesExpression : 'piecewise' '{' piece expression '}' ('(' expression ',' expression ')')? expression?
;
piece : expression '->' expression ';' (expression '->' expression ';')*
;
// L E X I C A L R U L E S
INT : DIGITS ;
IDENTIFIER : LETTER (LETTER | DIGIT)*;
WS : ( ' '
| '\t'
| '\r'
| '\n'
) {$channel=HIDDEN;}
;
fragment LETTER : ('a'..'z' | 'A'..'Z' | '_') ;
fragment DIGITS: DIGIT+;
fragment DIGIT : '0'..'9';
ANTLR v3.5 is complaining about the piecesExpression rule. It has 2 fatal errors and I would rather not use backtrack option.
Expected results:
piecewise {t -> s; t -> x; 100}
piecewise {t -> s; t -> x; 100} (0, x+1)
piecewise {t -> s; t -> x; 100} (0, x+1) y+5
How can piecesExpression be able to capture the above results?
Thanks in advance!

Answer 1

ANTLR has problems determining which alternatives to take in (at least) 2 cases:
piece starts with a expression but inside the piecewise{...}, it should also end with an expression
piecesExpression ends with '(' expression ... but also has an optional trailing expression (and an primitiveElement also matches '(' expression ... in its turn)
There's no need to use global backtracking, but without rewriting many rules, you do need to add some predicates (the (...)=> in the example below) to fix the two issues outlined above.
Try this:
piecesExpression
: 'piecewise' '{' ((expression '->')=> piece)+ expression '}'
( ('(' expression ',')=> '(' expression ',' expression ')' expression?
| expression
)
;
piece
: expression '->' expression ';'
;