> What interpreters such as GNU APL does is to first evaluate b+c, resulting in a new array, and then add that result to a.

Is this really what most implementations would do? I'd assume it would parse the expression `a+b+c` into a tree like

     +
    / \
   a   +
      / \
     b   c

But then run a pass on the tree to identify expressions like this that could be fused together without creating intermediate results. I know that most APL implementations have more efficient implementations of certain idioms (commonly-used sequences of operators/functions), so I figured they must be doing something like this to be able to identify those idioms.

This is just conjecture though, I'd love to know more about how this actually works in practice.