Right, I realize it isn't a "pure" function in the direct sense, but at the abstract level it can and often is presented as such. In programming this is trivial to simply return a new one that is diced. (Consider the typical "cons" example, where the trick is to actually return a new list, not modify the existing one. Something that is not exactly intuitive for most folks.)

And, I do strongly believe that declarative works best to start. This is mirrored in the physical world where people say to focus on easily specified goals for tasks. (And why my examples started high level.) Similarly, I suspect once you get down to the nitty gritty, it is again nice to be in the declarative realm. It seems that "somewhere between" these layers is where the imperative really belongs. I just don't know where that is.

I will probably take a while to digest your post. Thanks for sharing it!