converting precedence to productions

I am trying to convert an operator precedence grammar to an
unambiguous grammar without precedence rules. This is usually easy
(e.g. expressions with normal precedence rules), but my grammar has a
low-precedence postfix operator.


The grammar looks something like this:


    S ::= n | S and S | S or S | S post | ( S )


with left associativity, and precedence decreasing to the left.


Clearly, "A and B or C" must be parsed as "(A and B) or C".


It is less clear how "A or B post and C" should be parsed; it might
reasonably be "((A or B) post) and C" or "A or ((B post) and C)".
Assuming the former is intended, how can this grammar be transformed to
an unambiguous grammar without precedence rules?


A naive approach defines precedence numbers, and results in


  S ::= S1 | S post


  S1 ::= S2 | S1 "or" S2


  S2 ::= S3 | S2 "and" S3


  S3 ::= n | ( S )


which does not work at all here; "A post or B" is rejected.
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