Definition versus equality testing
In standard mathematical notation, the = symbol can be used in
at least two distinct (yet related) contexts:
To define things, as in, “Let \(x = 3y + 2\), and consider…” In this example sentence, \(x = 3y + 2\) defines the variable
xas standing for the expression3y + 2.As a relation which can hold, or not, as in, “If \(x = 3y + 2\), then … but otherwise …”. In this example sentence, \(x\) and \(y\) must already be defined, and \(x = 3y + 2\) is something that is either true or false.
Notice how the exact same expression \(x = 3y + 2\) is used in
both examples, but means two very different things depending on the
context—which is defined entirely by the English words surrounding
the symbols! Disco does not have the luxury of using English words to
figure out what we mean; instead, Disco must use two different
symbols. The = symbol is used to express definitions, as in the first example; whereas the == symbol
tests whether two things are equal, as in the second
example.