Yeah, makes sense. Dynamic breadth first search has been a thing for a while; it seems like they&#x27;re just introducing it with a new name. The automatic part seems cool though!

Where did you learn how it worked? Was it just through his other blog posts?

How would writing f using combinators yield the ability to derive g?

Incremental. I think the problem is this: you have an input that you want to change a bunch of times<pre><code> input = ...;
 input += d1;
 input += d2;
 input += d3;
</code></pre>
and you have some output that depends on the input. Whenever the input changes, the output needs to be recomputed, like this<pre><code> input = ...; output = f(input);
 input += d1; output = f(input);
 input += d2; output = f(input);
 input += d3; output = f(input);
</code></pre>
The idea here is to, instead of recomputing the output every time from scratch, find a function g that will compute the output-difference from the input-difference<pre><code> input = ...; output = f(input);
 input += d1; output += g(d1);
 input += d2; output += g(d2);
 input += d3; output += g(d3);
</code></pre>
And I think if you write f using the combinators from the differential dataflow framework it will be able to find g automatically for you.

Wow thanks a ton, looks like I have some more reading to do! :)

The main distinction that led to a different name is that (unlike most instances of dynamic or incremental algorithms) differential dataflow allows you to move through a partial order of updates, rather than a sequence of updates. This is important for automatically updating iterative computations, if you want to do multi-temporal streaming computation, and a few other reasons.It appeared at the time analogous to multivariate calculus, though the better analogy appears to be to Moebius inversion (roughly: integration and differentiation on partial orders). Read more here: <a href="https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Möbius_inversion_formula" rel="nofollow">https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Möbius_inversion_formula</a>&quot;Moebius dataflow&quot; would have been a pretty bad-ass name, I think we can all agree. And it might have done a better job of preparing the reader for what was about to happen to their brain.

Is differential a synonym for &quot;dynamic&quot; (or &quot;incremental&quot;) here?

Differential Dataflow but at what cost? (2017)