> Practice, experience and good heuristics help, though. And if they don't, then you redesign the formal system until they do.
I'm not sure anyone really understands the cognitive processes behind doing math. But maybe?
> The desired invariants (see below) and complexity bounds for your code will tell you what data structures might be more convenient than others.
I rarely write code where I even need to think about complexity bounds! I'd be surprised if that was a dominating concern for even a significant fraction of programmers (systems HPC programmers, for sure, but...UI programmers?).
> Only if I can't see what the invariants are, then I might use some examples to generate plausible candidates, but the job isn't done until I have found and confirmed the invariants themselves. In other words, I don't conflate “works for these few examples” with “works in general”.
We don't. But you need to start somewhere. Don't underestimate the value of a few good examples in the problem solving process.
> I'm not sure anyone really understands the cognitive processes behind doing math.
As long as we all play by the rules of the symbolic game, I don't really need to understand what's going on inside anyone else's (or even my own) head.
> I rarely write code where I even need to think about complexity bounds! I'd be surprised if that was a dominating concern for even a significant fraction of programmers (systems HPC programmers, for sure, but...UI programmers?).
Invariants still remain, e.g., “the textboxes Red, Green, Blue, Hue, Saturation and Brightness must contain each a number between 0 and 255 inclusive; additionally, these numbers must satisfy the following equations (...)”.
> We don't. But you need to start somewhere. Don't underestimate the value of a few good examples in the problem solving process.
Oh, sure, examples can be a useful tool for finding the general rule, as I mentioned in my previous comment. But they don't replace the general rule.
I'm not sure anyone really understands the cognitive processes behind doing math. But maybe?
> The desired invariants (see below) and complexity bounds for your code will tell you what data structures might be more convenient than others.
I rarely write code where I even need to think about complexity bounds! I'd be surprised if that was a dominating concern for even a significant fraction of programmers (systems HPC programmers, for sure, but...UI programmers?).
> Only if I can't see what the invariants are, then I might use some examples to generate plausible candidates, but the job isn't done until I have found and confirmed the invariants themselves. In other words, I don't conflate “works for these few examples” with “works in general”.
We don't. But you need to start somewhere. Don't underestimate the value of a few good examples in the problem solving process.