Why is the Minus Sign Not Overloaded Like the Plus Sign?

coding-standardshistoryoperatorsoverload

The plus sign + is used for addition and for string concatenation, but its companion: the minus sign, -, is generally not seen for trimming of strings or some other case other than subtraction. What could be the reason or limitations for that?

Consider the following example in JavaScript:

var a = "abcdefg";
var b = "efg";

a-b == NaN
// but
a+b == "abcdefgefg"

Best Answer

In short, there aren’t any particularly useful subtraction-like operations on strings that people have wanted to write algorithms with.

The + operator generally denotes the operation of an additive monoid, that is, an associative operation with an identity element:

  • A + (B + C) = (A + B) + C
  • A + 0 = 0 + A = A

It makes sense to use this operator for things like integer addition, string concatenation, and set union because they all have the same algebraic structure:

1 + (2 + 3) == (1 + 2) + 3
1 + 0 == 0 + 1 == 1

"a" + ("b" + "c") == ("a" + "b") + "c"
"a" + "" == "" + "a" == "a"

And we can use it to write handy algorithms like a concat function that works on a sequence of any “concatenable” things, e.g.:

def concat(sequence):
    return sequence.reduce(+, 0)

When subtraction - gets involved, you usually talk about the structure of a group, which adds an inverse −A for every element A, so that:

  • A + −A = −A + A = 0

And while this makes sense for things like integer and floating-point subtraction, or even set difference, it doesn’t make so much sense for strings and lists. What is the inverse of "foo"?

There is a structure called a cancellative monoid, which doesn’t have inverses, but does have the cancellation property, so that:

  • A − A = 0
  • A − 0 = A
  • (A + B) − B = A

This is the structure you describe, where "ab" - "b" == "a", but "ab" - "c" is not defined. It’s just that we don’t have many useful algorithms that use this structure. I guess if you think of concatenation as serialisation, then subtraction could be used for some kind of parsing.

Related Topic