ghfick wrote:David and Phil provide clarity here.

How does Phil provide clarity if his rule set is both incomplete and redundant, as I pointed out? Or was I wrong? Just asking Edit: I think I was indeed wrong

I am now a solid proponent of the Eureka notation for chains. David's writings have convinced me.

I don't know what David has written about them, but at least I didn't need any convincing. I only know three sudoku notations: generic implication chains (like eleven's), Nice Loop notation, and Eureka. I learned them in that order, because the first one is self-explanatory and the Nice Loop notation is pushed by every strategy site. Eureka I learned here. Of those three the Nice Loop notation is the worst in every way, so that leaves two practical choices. Of them the implication chains are the simplest to write and understand without any prior knowledge, which is a major benefit. On the other hand, Eureka is the most expressive one. When properly written it's often easy to follow Eureka chains without even seeing the grid. Most importantly, it's the de facto standard here, and I like standards because they help communication. So my vote is for Eureka, but I don't mind seeing implication chains either. I'd be quite happy to see the Nice Loop notation die out, though. Too bad Hodoku etc keep using it.

Phil's solver shows that ALS-XZ and ALS-XY moves can be very nicely written as chains using Eureka.

Of course they can. They are chains, and to me it's the simplest way to see and use them. No need to understand their RCCs and elimination rules as long as you understand how generic chains work. Otherwise I still wouldn't even be able to use them, as I have no interest in memorizing every single pattern there is, as long as it's covered by some generic rule. Seen as chains ALS patterns are pretty straightforward to me, while as ALS patterns they're not intuitive at all.