I'm on your side, but single | usually doesn't mean norm, rather absolute value, so it would be fine to do it twice. Though as you said it's contrived.
My point is that abs∘abs=abs and mathematicians will simplify when they can. Double-| is norm and you definitely cannot do that twice, because:
‖.‖ : V → ℝ
...where V is a vector space. I guess technically the reals fulfil the definition of a vector space, but I'd imagine that would grate against most people!
I suppose one could read ||c||a|b| as norm(c).a.abs(b), but usually the sets involved and typesetting would distinguish this. (i.e., It's only ambiguous in ASCII!)
I know what you meant and I agree, i just read you as (alao) saying that he single lines could be norm. There are situations where you wouldn’t simplify, like if this expression was the result of some function applications and then in the next step you simplify it.
R can definitely be seen as a vector space, just like R^3 for example, but then you wouldn’t also have absolute valley.
It wouldn’t be ambiguous in ASCII either because c would be defined earlier, you’d know what it is.
