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The next point is that there s obviously a big logical difference between values and variables: Variables are updatable, values aren t. To elaborate: Values are nonupdatable by definition, as we ve already seen. As for variables, to say that something s a variable is precisely to say it s updatable, no more and no less! That s what variable means the current value changes over time. Furthermore, the way to effect those changes (the only way) is by updating the variable in question. Note: For simplicity, I m ignoring here the case of a variable that s never actually updated. This simplification doesn t materially affect the discussion, of course. Just as an aside, I ve always thought the term variable as used in mathematics (at least in some contexts) was a little bit of a misnomer. Certainly variables in the sense I have in mind don t have values that vary over time, as variables in the computer science sense do. For example, consider the equation x + 3 = 5 Mathematicians would call x a variable here, but it obviously has the constant value 2. Perhaps unknown would be a better term; solving a set of equations is the activity of determining the values the unknowns in those equations stand for. Of course, it s true that the set of equations might not have a unique solution, as in the case of, e.g., the set consisting of the single equation x + y = 0. In such a case, referring to the unknowns as variables is perhaps more reasonable. But it s still the case that those variables don t vary over time; rather, they vary over some prescribed range. Back to values vs. variables in the computing sense. The fact that there s a logical difference between these concepts accounts in turn for another logical difference: namely, that between read-only and update operators. Read-only operators operate on values; in particular, they operate, harmlessly, on those values that happen to be the current values of variables. Update operators, by contrast, operate on variables I m speaking just a trifle loosely here and they have the effect of replacing the current values of such variables by other values, probably different ones.
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CHAPTER 6 ON THE LOGICAL DIFFERENCES BETWEEN TYPES, VALUES, AND VARIABLES
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And talking of update operators, let me now point out that, logically speaking, only one such operator is needed: namely, the assignment operator. All other update operators are really just shorthand for some assignment. (I ll spell this point out in detail in connection with the relational update operators in particular in the section Relation Values and Variables, later.) Since we already know that to say something s a variable is to say it s updatable, no more and no less, it follows that to say something s a variable is to say it s assignable to, no more and no less. In other words, to say that V is a variable is to say, precisely, that the following assignment is legal: V := v ; (where v is a value of the same type as V). Of course, v can be denoted by an arbitrary expression of the appropriate type; thus, the assignment operation takes the general syntactic form LHS := RHS ; where LHS is a variable reference, denoting some variable V of some type T, and RHS is an arbitrary expression of that same type T denoting a value v also of that type T. Note: Actually the syntactic form just shown for the assignment operator is not the most general. In The Third Manifesto, Hugh Darwen and I require support for a more general form that we call multiple assignment, which allows several variables to be updated at the same time (I m speaking pretty loosely here!). Multiple assignment is discussed in detail in 11; for the remainder of the present chapter, I ll limit my attention to assignments of the simple (or single ) form already discussed.
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