[Om] Named functions in OpenMath

[Wenzel, Ken]

I could also have done something like:
_:expr a :Application ; :operator _:someOp ; :arguments (_:x 2) .
_:someOp a :Reference ; :target <http://www.openmath.org/cd/arith1#power> .
...

This makes clear that _:someOp (which is a blank node in RDF) is a reference to
an object named <http://www.openmath.org/cd/arith1#power>.

Or I could also have:

_:expr a :Application ; :operator _:someOp ; :arguments (_:x 2) .
_:someOp a :Symbol ; :name <http://www.openmath.org/cd/arith1#power> .
...

This makes clear that _:someOp should be regarded as a Symbol in this context.

These notations are comparable to <OMR> and <OMS> elements in OpenMath.
Both elements give explicit typing information to the referenced object at the point where they are used.
This means that a user of <OMR> or <OMS> must know beforehand if he wants to refer to another object or to a symbol.

Now the question is if it would be desirable (and possible) to have a unified mechanism that allows to reference
symbols or other OpenMath objects with one element (like <OMR>).

Then the decision if the referenced object is a symbol or another OpenMath object is made at the time
when the OpenMath object is interpreted and not at the time of writing.
This also simplifies the representation in RDF to:

 _:expr a :Application ; :operator <http://www.openmath.org/cd/arith1#power> ; :arguments (_:x 2) .

Now <http://www.openmath.org/cd/arith1#power> can be described as

<http://www.openmath.org/cd/arith1#power> a :Symbol .

or 

<http://www.openmath.org/cd/arith1#power> a :Application ; :operator [...] .

somewhere on the web.

Best regards,
Ken

________________________________________
Von: David Carlisle [davidc at nag.co.uk]
Gesendet: Freitag, 8. Mai 2015 11:55
An: Wenzel, Ken; Paul Libbrecht; om at openmath.org
Betreff: Re: AW: [Om] Named functions in OpenMath

On 08/05/2015 09:43, Wenzel, Ken wrote:
> Thank you for your suggestions.
>
> I have one last question regarding symbols (OMS) vs. references (OMR):
> I've developed an RDF representation for OpenMath objects that allows to encode arbitrary OM objects in RDF.
>
> For example, the expression "x^2" may be encoded as (using the Turtle notation):
>
> @prefix : <http://numerateweb.org/vocab/math#> .
> _:expr a :Application ; :operator <http://www.openmath.org/cd/arith1#power> ; :arguments (_:x 2) .
> _:x a :Variable ; :name "x" .
>
> As can be seen, the operator <http://www.openmath.org/cd/arith1#power> has no type information.
> It may be possible that it is defined (somewhere else) as a symbol by
>
> <http://www.openmath.org/cd/arith1#power> a :Symbol .
>
> or that it is just a reference to some kind of lambda expression.
>
> If i convert the RDF representation to OpenMath XML and I don't know any facts about
> <http://www.openmath.org/cd/arith1#power> should I suppose that it is a symbol or a reference?
>
> Best regards,
> Ken

I'm not sure I fully understand the question, but an OMR doesn't have a
name and always references an explicit openmath object.

thus the named symbol "power" must be an OpenMath Symbol?


David



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