Re: How is ambiguity defined?

> On 6,Jan2022, at 8:39 AM, C. M. Sperberg-McQueen <cmsmcq@blackmesatech.com> wrote:
> 
> 
> 
>> On 6,Jan2022, at 3:40 AM, Tomos Hillman <yamahito@gmail.com> wrote:
>> 
>> I'm not sure I understand approach B, or how it avoids ambiguity within the non-terminal definition: there may be only one parse tree, but surely the fact that it contains a choice means that it is itself ambiguous in some way?
> 
> Define “ambiguity”.

To put it another way:  I think you may be appealing here to
an intuitive but hazy notion that there are two different ways
to derive the empty string from the right-hand side ‘a’*; ‘b’*.

I think that if you attempt to make that notion explicit and
clear, you will discover that you have just undertaken to
reinvent parsing theory with a new definition of what it means
to derive a string of terminals from a start symbol using a
grammar.

The two ‘derivations' S => ‘a’*; ‘b’* => ‘a’* => ‘’ and S => ‘a’*; ‘b’* 
=> ‘b’* => ‘’ I offered as a way of making more explicit the
intuition I think you are working from are not, of course,
derivations at all.  In the usual account, a derivation is a sequence
of sentential forms beginning with the start symbol and 
ending with a sequence of terminal symbols, in which each
sentential form replaces one nonterminal symbol in the
preceding form with a right-hand side for that symbol. 

But sentential forms are sequences of terminal and nonterminal
symbols.  The expression ‘a’*; ‘b’* is not a sentential form and
cannot appear as a step in a derivation, as that term is normally
defined.  Since derivation as normally defined requires the right-hand
side which replaces a nonterminal in a sentential form to be a 
sequence of symbols, it can apply only to BNF, not to EBNF.

So if in this discussion anyone wants to appeal to any intuitive 
notion of ‘ambiguity’ in ixml, I am increasingly likely to point out
that I do not know what you mean, since in the context of ixml, 
‘ambiguity’ is not defined.  

To put it a third way:  what do you mean by “ambiguous in
some way”?

Michael

Received on Thursday, 6 January 2022 16:25:08 UTC