Re: *which* alternative that matches nothing? (was Re: repetition)

Thanks Michael (and Norm) for your patience.

On Thu, 16 Dec 2021 at 16:47, C. M. Sperberg-McQueen
<cmsmcq@blackmesatech.com> wrote:
>
>
>
> > On 16,Dec2021, at 8:30 AM, Dave Pawson <dave.pawson@gmail.com> wrote:

> I can try to explain.  Please bear with me.

> Why does the expression []? denote the language consisting
> of the empty sequence?
>
> Empty brackets are a character inclusion with no members.
> The meaning of a character inclusion is that at least one of the
> members of the inclusion must match the current input
> character (I hope people know what I mean by ’the current
> input character', because I am not in a position to offer a simple
> clear definition).  An empty inclusion cannot satisfy that condition,
> so no sequence of input symbols can match an empty inclusion.

Grates, but accepted.



> So the language recognized by [] is the empty set.  In the
> set notation I learned in school:  {} or ∅.
>
> Adding a question mark to [] so as to form []? gives us an
> expression recognizing a different and larger language.  In general,
> for any expression E, the expression E? recognizes a language
> which contains (a) all the sentences of the language of E,
> plus (b) the empty sequence of symbols.  As an operation on
> sets of sentences, the operation ‘?’ adds the empty sequence
> (often written ε) to the set.

Which is quite different from DTD's, regex etc (my prior exposure).


>
> Since [] denotes the set ∅, the expression []? denotes the
> union of {} and {ε}.  Now, it’s a theorem of set theory that
> the union of any set S with {} is S itself.  The union of {} and
> {ε} is {ε}, the set containing only the empty sequence.

Accepted.

>
> That is why I say that []? is a way of writing the empty sequence.
> It recognizes a set of input sequences that contains the empty
> sequence and no other sequences.

How to avoid having this discussion a thousand times over in the future?
Is it feasible to extract 'implementer' notes (with this inclusion) and
a simpler (glossed) term for users? Perhaps 'glossed over' more accurately.
 Estimate: For each MSM there are 10^n DP's | those not exposed to set theory.
<grin/>


regards



-- 
Dave Pawson
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Received on Thursday, 16 December 2021 17:31:29 UTC