On Thursday, April 2, 2015 at 2:33:17 PM UTC-7, Thomas 'PointedEars' Lahn wrote: > Ian Kelly wrote: > > > […] Thomas 'PointedEars' Lahn […] wrote: > >> Ian Kelly wrote: > >>> Within a grammar, the question of "is an X a Y" is nonsensical in > >>> isolation. It can only be answered in relation to a parse tree. > >>> Consider the simple grammar: > >>> > >>> S -> A | B > >>> A -> x > >>> B -> x > >>> > >>> Is x an A? It depends. > >> > >> No, by the definition 2 below, that we all accepted implicitly up to this > >> point, x is *definitely* an A. > > > > What gives you the impression that I ever accepted it? > > ,-<news:mailman.181.1427346636.10327.python-l...@python.org> > | > | What the grammar that you quoted from shows is that STRING+ is an > | expression. > > There is *no way* for you to make that statement if you did not accept > definition (2). > > >> (2) Let the statement “x is an A” be true if x can be produced in a > >> production chain starting with or including the non-terminal A > >> left-hand side – > >> > >> x ∈ A ↔ ∃A (… ⇒ A ⇒ … ⇒ x). > > > > Sorry, but this definition just seems entirely arbitrary to me. > > It is just the formalization of the definition that we all have agreed to, > including you. > > > Mathematically, it looks nonsensical; A is a symbol, not a set. > > “A” is the goal symbol of a production, so it can be interpreted as the > superset of all set of terminals that can be produced from it, through the > goal symbols that can be produced from it. And all of us implicitly did > that when we said “STRING(+) (literals) is/are (not) (an) expression(s)”. > > > This question of whether "x is an A" is informal and not a topic of formal > > language theory so far as I'm aware. Can you cite some source for it? > > No, because I was formalizing the ad-hoc definition by Chris Angelico in > <news:mailman.51.1426995416.10327.python-l...@python.org>. > > >> Now, according to these definitions, in the offered grammar x is *both* > >> an A and a B. Because what matters is _not_ the practical result of > >> production chains (the actual parse tree), but the certainty of the > >> theoretical possibility of it. > > > > This strikes me as being a lot like arguing, "some kites are toys, and > > some kites are birds; therefore, all kites are both toys and birds." > > False analogy again. We are discussing *in theory* a *formal* grammar. Its > goal symbols have *no meaning* except what can be produced from them. > > > As noted above, the inaccuracy that Gregory pointed out has no bearing > > on my argument. > > But it does. > > > You're really going to make me spell it out, aren't you? Fine, here you > > go. > > > > single_input -> […] -> expr -> […] -> atom -> STRING STRING > > > > Note: the derivation contains exactly one expr node, which indirectly > > produces both STRINGs. Neither STRING in this derivation is > > individually produced from the expr. > > So you have proven that which nobody ever doubted nor requested, but I > pointed out already. What you have still not proven is what you claimed: > the parse tree. > > I am sorry that you cannot see that your argument is strewn with gaping > defects in logic, but I think I will stop trying to convince you of that > now. > > -- > PointedEars > > Twitter: @PointedEars2 > Please do not cc me. / Bitte keine Kopien per E-Mail.
*sigh* https://xkcd.com/386/ -- https://mail.python.org/mailman/listinfo/python-list