[R-sig-ME] meaning of lmer formula

[Don Cohen]

Fox, John writes:
 > Have you read the vignette on lmer() in the package? 
I guess that's
 https://cran.r-project.org/web/packages/lme4/vignettes/lmer.pdf
and I guess you're referring to section 2.2 and specifically  
table 2 on p.6.
Yes, I had already seen those, but they don't answer my questions.
They provide examples but not a complete specification of the
language.

 > It strikes me that your questions can also be answered by just
 > trying the various formulas that you propose and examining the
 > output.

This would be true if it were obvious how to translate the outputs
to the meanings of formulae that should have those outputs.
I'm working on making that more obvious (to me), but have a long
way to go.
One thing I have found useful is checking to see whether two 
formulae mean the SAME thing by seeing whether they give the SAME
result - I do know how to recognize same results.  I realize that
it's possible to get the same result from two different meanings,
but I view the probability of that as negligible.
I've also tested my understanding by making small changes that
I expect to change the output in very specific ways.