Is there such a thing as short circuit multiplication?

Question

We all know about short circuiting in logical expressions, i.e. when

if ( False AND myFunc(a) ) then
...

doesn't bother executing myFunc() because there's no way the if condition can be true.

I was curious as to whether there is an equivalent for your everyday algebraic equation, say

result = C*x/y + z

If C=0 there is no point in evaluating the first term. It wouldn't matter much performance-wise if x and y were scalars, but if we pretend they are large matrices and the operations are costly (and applicable to matrices) then surely it would make a difference. Of course you could avoid such an extreme case by throwing in an if C!=0 statement.

So my question is whether such a feature exists and if it is useful. I'm not much of a programmer so it probably does under some name that I haven't come across; if so please enlighten me :)

Answer 1

The concept you are talking about goes under different names: lazy evaluation, non-strict evaluation, call by need, to name a few and is actually much more powerful than just avoiding a multiplication here and there.

There are programming languages like Haskell or Frege whose evaluation model is non-strict. There it would be quite easy to write your "short circuiting" multiplication operator, for example you could write something like:

infixl 7 `*?`        -- tell compiler that ?* is a left associative infix operator
                     -- with precedence 7 (like the normal *)

0 *? x = 0           -- do not evaluate x
y *? x = y * x       -- fall back to standard multiplication