[Om3] Om3 Digest, Vol 18, Issue 5
c.a.rowley at open.ac.uk
c.a.rowley at open.ac.uk
Mon Mar 23 14:06:14 CET 2009
This one is really (quite) short!
David wrote --
>> It's not particularly common (and never necessary) to specify both a
>> domain and a condition
And moreover, there is no difference between these since 'being an element
of the domain' is a condition; and the other conditions are merely 'AND'ed
with this condition to describe a new domain.
But hold, I am not sure that I am now again agreeing completely with David.
I do agree with him that there should be no need for things like 'prodcond'
since all BINDS must have a condition (although syntactically it may be
missing since it is assumed or depend on the context or ...)
In particular, it is not clear to me why a 'vector of A's' (or any
collector) is intuitively reasonable just to avoid extending the syntax.
Why must OM remain frozen in this way? Everything in OM could be expressed
in a language as simple as (or even simpler than) NL3 but that might be
less efficient and would certainly make it less understandable to
mathematicians (of coourse, it might help software??).
So it comes back to the question of how close to commonly used non-digital
methods of describing 'mathematical semantics' should OM be?
chris
to a subset of the
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Today's Topics:
1. Re: Summary of the Davenport&Kohlhase Proposal (David Carlisle)
2. Re: Summary of the Davenport&Kohlhase Proposal (Paul Libbrecht)
3. Re: Summary of the Davenport&Kohlhase Proposal (David Carlisle)
----------------------------------------------------------------------
Message: 1
Date: Mon, 23 Mar 2009 10:20:40 GMT
From: David Carlisle <davidc at nag.co.uk>
Subject: Re: [Om3] Summary of the Davenport&Kohlhase Proposal
To: om3 at openmath.org
Message-ID: <200903231020.n2NAKeav022983 at edinburgh.nag.co.uk>
I'm strongly opposed to this. I'm opposed to the change to OpenMath and
if we should as a group decide to change OpenMath in this way, I'd still
argue that MathML would be best advised not to use the new features in
any mapping to its "strict" subset.
This is a breaking change to OpenMath, with a rather thin
justification, which is, in total
> James and I don't like that this has two binds and two unrelated dummy
> variables,
That is, it is introducing a breaking change for purely cosmetic
reasons.
It wouldn't be impossible to consider change if the change was actually
an improvement but I don't think it is, for several reasons.
A binding symbol is currently typeable by viewing
ombind
head
bvar x
f(x)
as syntactic sugar for
apply
head
lambda x. f(x)
A binder with multiple children, as proposed here, can thus be seen as
essentially mapping to the cartesian product of the domains of each of
the children, but uniquely for openmath the vector construct symbol is
being omitted. If it is made explict then no extension is needed, and
only a single child of ombind is needed.
Michael's proposed
bind(O,v_1,...,v_n,A_1,...A_n)
is just a custom syntax for
bind(O,v_1,...,v_n,
apply
vector
(A_1,...A_n)
)
> So we are proposing a liberalization of OpenMath objects: all OpenMath2
> objects are extended Objects and retain their original meanings. But can
> now define more mathematical symbols and represent more objects.
No, actually you can only represent the same set of objects, with the extra
complication that there are more ways to do it, so need extra FMP saying
that they are equivalent, and the extra complication that the new way
breaks all existing OM applications.
> with a new symbol productcond.
Irrespective of whether we extend OMbind, I don't think we should
explode the number of symbols required by introducing symbols like
this.
The example Michael happened to pick on had both a domain [0,k] and a
condition (i !=- j) specified, and the proposed rewrite to a prodcond
symbol that _requires_ both a domain and a condition (as they are given
positionally).
It's not particularly common (and never necessary) to specifiy both a
domain and a condition, so this prodcond symbol would almost always
require dummy conditions being specified (such as ("true" or default
domains being specified, to fill in the relevant slots. Or you have yet
more additional symbols, for product(withdomain) and
product(justwithcondiition)/
In all cases the choice of whether to specify a constraint on a bound
variable as a domain constraint or a condition is entirely arbitrary.
Saying that a bound variable has domain R is the same as saying it is
subject to a condition (x in R) and these two formulations should have
the same openmath encoding, but this proposal arbitrarily distinguishes
them as
ombind
prodcond
bvar x
R
true
f(x)
and
ombind
prodcond
bvar x
some-superset-of-R
apply in x R
f(x)
In general for a more complicated domain you may, at the authors whim,
choose to express part of the constraint as a domain and part as a
condition, so Michael's example
domain: [0,k]
condition: i!=j
could just as easily be expressed as
domain: R
condition: i in [0,k] and i!=j
or
domain: [0,k] \ {j}
condition: true
or any other alternative, the distinction between domain and condition
is entirely arbitrary and it's a feature not of problem of OpenMath that
these are not distinguished.
David
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Message: 2
Date: Mon, 23 Mar 2009 11:39:15 +0100
From: Paul Libbrecht <paul at activemath.org>
Subject: Re: [Om3] Summary of the Davenport&Kohlhase Proposal
To: David Carlisle <davidc at nag.co.uk>
Cc: om3 at openmath.org
Message-ID: <7E732E95-5458-4360-950F-387D14DA4F71 at activemath.org>
Content-Type: text/plain; charset="iso-8859-1"
David,
please explain how much this is breaking.
I only see this as an expansion but I agree this brings yet another
way of writing.
It allows expressions which, earlier, were disallowed by the schema,
to be allowed now.
paul
Le 23-mars-09 ? 11:20, David Carlisle a ?crit :
> This is a breaking change to OpenMath, with a rather thin
> justification,
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Message: 3
Date: Mon, 23 Mar 2009 10:46:16 GMT
From: David Carlisle <davidc at nag.co.uk>
Subject: Re: [Om3] Summary of the Davenport&Kohlhase Proposal
To: om3 at openmath.org
Message-ID: <200903231046.n2NAkGt2023117 at edinburgh.nag.co.uk>
> please explain how much this is breaking.
> I only see this as an expansion but I agree this brings yet another
> way of writing.
Well it's my TeX heritage telling me that any change will break
something. Since one of the main points of OpenMath is communicating
expressions, making a change for cosmetic reasons that results in no
existing systems being able to process the expression seems like
a bad idea, even if you thought the change was an improvement.
So my adjective "breaking" was probably gratuitous, as "breaking change"
and "change" probably mean the same thing here.
> It allows expressions which, earlier, were disallowed by the schema,
> to be allowed now.
In other words, making expressions that were authored previously in
error suddenly aquire an unintended meaning and be no longer flagged as
an error.
David
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