One way to resolve the issue is simply to announce the outcome in advance for each pair A and B, basing the choices on some reasonable heuristics. Floyd [1963] suggested this approach, called operator precedence. The outcome was stored in a table. Floyd also suggested a way of encoding this table that would work in a small number of cases, namely that a number should be associated with each argument position by means of precedence functions over tokens; these numbers are sometimes called "binding powers". Then E is associated with the argument position having the higher number. Ties need never occur if the numbers are assigned carefully; alternatively, ties may be broken by associating to the left, say. Floyd showed that Algol 60 could be so treated.
One objection to this approach is that there seems to be little guarantee that one will always be able to find a set of numbers consistent with one's needs. Another obeection is that the programmer has to learn as many numbers as there are argument positions, which for a respectable language may be the order of a hundred. We present an approach to language design which simultaneously solves both these problems, without unduly restricting normal usage, yet allows us to retain the numeric approach to operator precedence.
+One objection to this approach is that there seems to be little guarantee that one will always be able to find a set of numbers consistent with one's needs. Another objection is that the programmer has to learn as many numbers as there are argument positions, which for a respectable language may be the order of a hundred. We present an approach to language design which simultaneously solves both these problems, without unduly restricting normal usage, yet allows us to retain the numeric approach to operator precedence.
The idea is to assign data types to classes and then to totally order the classes. An example might be, in ascending order, Outcomes (e.g., the pseudo-result of print), Booleans, Graphs (e.g. trees, lists, plexes), Strings, Algebraics (e.g. integers, complex nos, polynomials, real arrays) and References (as on the left side of an assignment.) We write Strings < References, etc.