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3.2.3 Precedence and grouping

At school most of us are taught that multiplications must be done before additions in a sum. In E it's different--there is no operator precedence, and the normal order in which the operations are performed is left-to-right, just like the expression is written. This means that expressions like 1+3*3 do not give the results a mathematician might expect. In fact, 1+3*3 represents the number 12 in E. This is because the addition, 1+3, is done before the multiplication, since it occurs before the multiplication. If the multiplication were written before the addition it would be done first (like we would normally expect). Therefore, 3*3+1 represents the number 10 in E and in school mathematics.

To overcome this difference we can use parentheses to group the expression. If we'd written 1+(3*3) the result would be 10. This is because we've forced E to do the multiplication first. Although this may seem troublesome to begin with, it's actually a lot better than learning a lot of rules for deciding which operator is done first (in C this can be a real pain, and you usually end up writing the brackets in just to be sure!).

The logic examples above contained the expression:

  (2<1) AND (-1=0)

This expression was false. If we'd left the parentheses out, it would have been:

  2<1 AND -1=0

This is actually interpreted the same as:

  ((2<1) AND -1) = 0

Now the number -1 shouldn't really be used to represent a truth value with AND, but we do know that TRUE is the number -1, so E will make sense of this and the E compiler won't complain. We will soon see how AND and OR really work (see 10.4.3 Bitwise AND and OR), but for now we'll just work out what E would calculate for this expression:

  1. Two is not less than one so 2<1 can be replaced by FALSE.
      (FALSE AND -1) = 0
    
  2. TRUE is -1 so we can replace -1 by TRUE.
      (FALSE AND TRUE) = 0
    
  3. FALSE AND TRUE is FALSE.
      (FALSE) = 0
    
  4. FALSE is really the number zero, so we can replace it with zero.
      0 = 0
    
  5. Zero is equal to zero, so the expression is TRUE.
      TRUE
    

So E calculates the expression to be true. But the original expression (with parentheses) was false. Bracketing is therefore very important! It is also very easy to do correctly.


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