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fix a typo: obeection -> objection #12

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fix a typo: obeection -> objection #12

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Expand Up @@ -147,7 +147,7 @@ <h3 id="22-conventions-for-linearizing-trees">2.2 Conventions for Linearizing Tr

<p>One way to resolve the issue is simply to announce the outcome in advance for each pair <code>A</code> and <code>B</code>, 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 <code>E</code> 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.</p>

<p>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.</p>
<p>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.</p>

<p>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 <code>print</code>), 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 <code>Strings &lt; References</code>, etc.</p>

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