[Om] Tuple and list : any distinction?

[Olga Caprotti]

Joe,

I also think that you might need a new CD - unless you find something in the new
ones from the interGeo efforts:
http://i2geo.net/xwiki/bin/view/Main/About

(if it is geometry you are interested in)

I do not think the Pair-Tuple symbols from ecc is what you want to use
for a coordinate system.


--olga


On Fri, Feb 19, 2010 at 6:04 AM, Michael Kohlhase
<m.kohlhase at jacobs-university.de> wrote:
> Dear Joe,
>
> On 18.02.10 18:56, Joe Collins wrote:
>> Dear Michael,
>>
>> Most of what you write is roughly consistent with what I have understood, and
>> helps a little more with the OpenMath flavor.
>> I was a little thrown by "Semantics of OpenMath and MathML3", Kohlhase&  Rabe,
>> where:
>>
>> Definition 3 (OM Context). An OM context C is an n-tuple of variables
>> which we will write as<x1 , . . . , xn>. We will use + for tuple
>> concatenation and $\in$ for tuple membership.
>>
>> implies tuple concatenation is normal.
>>
> Ha, nice answer,
>> (Sorry, I didn't mean to knock you for inconsistency).
>>
> this definition was actually written by my (formalist) co-author, who
> was aware of the same isomorphism you were enquiring about. Indeed we
> were talking about argument sequences there where lists and tuples are
> equally far from the "real intuition", therefore I went along with this.
>
> BTW, I consider the representation of argument sequences as one of the
> remaining problems of OpenMath, as we do not have a real means to
> represent equations like f(a,x_1,...,x_n) = g(x_1,...x_n)-a. Mathematica
> has a good way of doing this which OM lacks.
>> Let me, however, get straight to my real concern.
>> I want to represent a coordinate variable tuple like (X, Y, Z) or
>> (r, theta, phi). I do NOT consider these "vectors" in general.
>> I was considering using tuple to construct them, but then needed a
>> means of indexing them. Either adding a "tuple_selector" symbol or using the
>> existing list symbols seemed to be the two best options, with my preference
>> towards the "tuple_selector" symbol.
>> After this feedback on the OpenMath flavor of things, my preference has
>> increased in that direction.
>>
>> If you ask "Why not 'vectors'?", I'll ask
>> "What does it mean to add
>> (r1, theata1, phi1) + (r2, theata2, phi2)  ?".
>>
>> (Things aren't sufficiently interesting if you stay in Cartesian coordinates!)
>>
> I think that in this case you really are nearer to "vectors". But you
> can always make your own tuples CD that does what you want. I am pretty
> sure that you do not want to use ECC, since with the tuple constructor
> you would "buy" all the rest of a (very complex) lambda calculus that
> most people would probably consider a Meta-Logic.
>
> I encourage you to make a CD and contribute it to OM.
>
> Michael
>>
>> Regards,
>> Joe
>>
>> Michael Kohlhase wrote:
>>
>>> Dear Joe,
>>>
>>> there are at least two possible answers to this question:
>>>
>>> Mathematical:
>>>
>>> generally spoken, tuples and lists are isomorphic as data raw
>>> structures, but support conceptually different operations. Tuples are
>>> usually thought of as having fixed length and operations are between
>>> tuples of same length. Operations are mostly from linear algebra. In the
>>> ecc CD we have dependent tuples that are mostly used for defining
>>> functions.
>>>
>>> Lists are thought of as of variable length, and the operations are
>>> mostly constructing lists from the empty list by prepending, appending
>>> lists, mapping functions over lists,.... Moreover, lists typically only
>>> have members of the same "type".
>>>
>>> So, even though everything you do with tuples,  the mathematical,
>>> operational  intuitions are quite different.
>>>
>>> Formally:
>>>
>>> The levels of formality in the descirption of ecc and list1/2 are vastly
>>> different. ECC (Extended Calculus of Construction) is a logical system,
>>> where tupling has a very well-defined role. list1/2 is a (intendedly)
>>> vague description of a vocabulary of lists without going into too much
>>> detail, so that it can be universally used.
>>>
>>> hope this helps,
>>>
>>> Michael
>>>
>>> On 17.02.10 14:51, Joe Collins wrote:
>>>
>>>> The OpenMath ecc CD defines Tuple and the list1 CD defines list.
>>>>
>>>> Is there any essential distinction between Tuple and list?
>>>> If so, what?
>>>>
>>>> Some of the definitions in list1, list2 suggest (to me) that the order
>>>> of the
>>>> list elements are arbitrary. Is this actually the case?
>>>>
>>>> Joe
>>>>
>>>>
>>>
>>
>
> --
> ----------------------------------------------------------------------
>  Prof. Dr. Michael Kohlhase,        Office: Research 1, Room 62
>  Professor of Computer Science  Campus Ring 1,
>  Jacobs University Bremen           D-28759 Bremen, Germany
>  tel/fax: +49 421 200-3140/-493140  skype: m.kohlhase
>  m.kohlhase at jacobs-university.de http://kwarc.info/kohlhase
> ----------------------------------------------------------------------
>
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