2mo40

This is a nice comparison. I particularly like the images :) and drawing the comparisons setting aside historical accidents.

A few comments that came to mind as I was reading:

Perform an interchange intervention on the treeification of L such that the corresponding intervention in the treeification of H would not change any values.

As far as I saw, you don’t mention how causal scrubbing specifies selecting the interchange intervention (the answer is: preserving the distribution of inputs to nodes in H, see e.g. the Appendix post). I think ...

12mo

Thanks! Mostly agree with your comments.
I think any combination of {rewriting, using some canonical form} and
{treeification, no treeification} is at least possible, and they all seem sort
of reasonable. Do you mean the relation is that both rewriting and treeification
give you more expressiveness/more precise hypotheses? If so, I agree for
treeification, not sure for rewriting. If we allow literally arbitrary
extensional rewrites, then that does increase the number of different hypotheses
we can make, but these hypotheses can't be understood as making precise claims
about the original computation anymore. I could even see an argument that
allowing rewrites in some sense always makes hypotheses less precise, but I feel
pretty confused about what rewrites even are given that there might be no
canonical topology for the original computation.

Not sure if I'm fully responding to your q but...

This sounds right to me, and overall I mostly think of treeification as just a kind of extensional rewrite (plus adding more inputs).

I think of the underlying graph as providing some combination of 1) causal relationships, and 2) smaller pieces to help with search/reasoning, rather than being an object we inherently care about. (It's possibly use... (read more)