tmpUI | JavaScript framework written on es6 | Style Language library

As @sepp2k pointed out, | expression expression will correct your issue.

ANTLR defaults to left associativity., but you were overriding that with the (expression)+ in trying to gather all the expressions.

Of course, this will give you a parse tree of (expr (expr (expr f) (expr "a")) (expr "b"))

but this is probably more in keeping with a Haskell approach to function application than just a list of expressions.

BTW, precedence only comes into play when operators are involved. Having StringLiteral before LSquareParen his no effect on precedence since there's no ambiguity in determining the correct parse tree to derive. You may find that your OperatorApplicationExpresion alternative gives "surprising" results as it will evaluate all operators left-to-right, so a + b * c will be evaluated as "(a + b) * c" and this violates arithmetic norms (maybe it's what you want however).