Re: Fwd: Latest Draft of ISO/IEC 15909 for comment

[Jonathan <jbil@crosswinds.net>]

Dear Nisse,

Many thanks for your comments
Will get back to you soon - hopefully today.

Cheers - Jonathan

On 21/11/00 09:13, Nisse Husberg (nhu@saturn.tcs.hut.fi) wrote:

>
>
>On Sat, 18 Nov 2000, Jonathan wrote:
>
>> As yet, I have not had comment on the draft from
>> Tad Murata (USA), Jean Berube (Canada), Nisse Huisberg (Finland) or any 
>> one from France or Italy.
>
>Sorry, I've been terribly busy. We do not have any serious comments, but a
>few small details I could mention (many from Kimmo Varpaaniemi):
>
>1.
>
>I'm personally not very happy with the definition of the multisets. It is
>the usual one, yes, but it is not very good. Already in 1987 G.P. Monro
>(Zeitschrift f. math. Logik und Grundlagen d. Math. 33) pointed out the
>problem, i.e. B: A -> N and C: D -> N are different even if they have the
>same elements because D may have an element not in A and this element is
>mapped to zero. If the multiset is {a,a,b} then C: {a,b} -> N: a mapsto 2
>and b mapsto 1 is different from D: {a,b,c} -> N: a mapsto 2, b mapsto 1
>and c mapsto 0.
>
>The solution (acording to Monro) is to see a multiset as a partition of a
>"normal" set or as a surjective mapping M: I -> S where I is an index set. 
>
>We really see a multiset as an equivalence class where all non-zero
>mappings are the same. I have a discussion about these problems in my
>thesis.
>
>2.
>
>Together with Kimmo we wondered why the multiset must have a *non-empty*
>basis set. Any special reason ? Also the place set must be non-empty. A
>net with a non-empty place set is not very useful, but are there any
>mathematical problems ?
>
>3. 
>
>Is there a definition of "capacity" ?
>
>4. 
>
>It seems that you have chosen the pair: "net" <-> "net graph" instead of
>"(net) system" <-> "net" for a net with resp. without initial marking.
>Well, no problems.
>
>5.
>
>Kimmo who has been working with unfoldings wondered if it is a good idea
>to restrict P/T nets to finite ones. It is not stated explicitly, but the
>only net graph defined has a finite set of places and a finite
>set of transitions. 
>
>6. 
>
>There is a small problem with the fonts on page 27 where (sigma) and s are
>of different size. A LaTeX problem maybe ?
>
>
>7.
>
>The operator *Dot (should be bullet+Dot) is difficult. It would not hurt
>to use another bullet in the signature than in the algebra. Or perhaps
>another font. I have been working for many years with many-sorted algebras
>and I had difficulties with the notations. 
>
>I am working with category theory and the algebra is just the Hom-functor
>on the algebraic theory generated by the signature. It is mapping the
>sorts to the morphism sets with the sort as target, i.e. Dot = {*} (in the
>algebra)  and I do not see why a new sort name "dot" should be introduced?
>If the algebra is not initial then the sort is just mapped to the
>Hom-functor for (a certain object, i.e. sort string) w instead of the
>empty sort string (which gives us the initial algebra). The sort string w
>defines the sorts (and number) of the variables in the algebra. And the
>morphism set from w to the sort gives us all the terms of that sort.
>
>It is all in my thesis. I used some time to figure it out although you can
>find the basic work in the ADJ papers. 
>
>8.
>
>Kimmo was not very happy with the notation 2`1c (p. 34) because he thinks
>it is not very readable. I know it is used in Design/CPN but it was
>perhaps introduced for syntactical reasons (implementation related) and
>not for readability. Why not use 2*1c or something ?
>
>` is dangerous because it is so close to ' and ´ (and very small).
>
>
>
>These comments are from reading through the draft. It is of course a
>different thing when we really start working with the standard, but at
>this point it seems quite nice to me. I am especially pleased that you
>have got the many-sorted approach into the standard. I would personally
>like to have operators also to target *strings* - not only to one-sorted
>targets, but I realise that it may be too difficult and perhaps a bit out
>of scope. My reason is that a Petri net transition is equivalent to an
>operator with many-sorted target as well as many-sorted source.
>
>OK, that was our comments.
>
>Nisse
>
>__________________________________________________
>Nisse Husberg, D.Sc.(Tech.), Prof.
>Computer Science Theory Laboratory
>Technical University Helsinki
>FIN-02150 Esbo
>Finland
>Tel: +358- 9-451 3254 (job),
>     +358-19-614 056 (home),
>     +358-40-769 0402 (mobile)
>Email: Nisse.Husberg@hut.fi
>
>
>
>
>
>
>
>-- pnx
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