Re: Understanding some issues on the denotational semantics

I don't think it's a math vs cs thing. I'm cs and I'm a bit confused. But I think I got it :)

I'm planning to finish my example today-tomorrow and then share it with the group to see if I got it correctly. 

Juan Sequeda
www.juansequeda.com

On Feb 18, 2011, at 11:45 AM, Ivan Herman <ivan@w3.org> wrote:

> I guess what screws me up all the time is that the notation always reminds me of what I was trained namely that {...} is a set, and f:A->B is a function between sets. But these are not sets, these are types, and that is what makes it difficult for me. I guess this is the difference between the mathematician (that I was trained for) and a computer scientists (that you guys are...)
> 
> I will have to look at this again... tomorrow!
> 
> Cheers
> 
> Ivan
> 
> 
> 
> On Feb 18, 2011, at 18:04 , Eric Prud'hommeaux wrote:
> 
>> * Ivan Herman <ivan@w3.org> [2011-02-18 17:49+0100]
>>> 
>>> On Feb 18, 2011, at 17:32 , Eric Prud'hommeaux wrote:
>>> 
>>>> * Ivan Herman <ivan@w3.org> [2011-02-18 11:40+0100]
>>>>> Alex,
>>>>> 
>>>>> 
>>>>> On Feb 17, 2011, at 16:18 , Alexandre Bertails wrote:
>>>>> 
>>>>> [snip]
>>>>>> 
>>>>>> Sorry, I did not understand your comment this way as I think that the
>>>>>> type is already correct.
>>>>>> 
>>>>>>> But does that specification means that for every table t, primaryKey(t) will give me a set s=primaryKey(t) where size(s)<=1? Ie, that, for every table, the primaryKey is either empty or restricted to one single column? That is the discrepancy with section 2.2 that explicitly speaks about multi-column primary keys...
>>>>>> 
>>>>>>> From you comment:
>>>>>> s/the primaryKey is either empty or restricted to one single column/the primaryKey is either empty or restricted to one single CandidateKey/
>>>>>> 
>>>>> 
>>>>> Sorry, right
>>>>> 
>>>>>> So primaryKey's type tells you that primaryKey gives you either 0 or 1
>>>>>> CandidateKey. The definition for CandidateKey is
>>>>>> [[
>>>>>> CandidateKey ::= List(ColumnName)
>>>>>> ]]
>>>>>> 
>>>>>> So you do have multi-columns for a Primary Key (if there is one).
>>>>>> 
>>>>>> Am I getting it right? I may be not introducing this one the right way.
>>>>>> 
>>>>> 
>>>>> I think I get it now but... why do I need this? Why not define
>>>>> 
>>>>> primaryKey : Table → CandidateKey
>>>> 
>>>> I think this would say there is exactly one primary key per table.
>>> 
>>> Hm. Indeed, one primary key, though that primary key would consist, possibly, of several columns. Isn't this what we want? I am really confused:-(
>> 
>> What we want is zero or one primary key with 1 or more columns, which I believe is captured by
>> 
>> candidateKeys : Table → {l:List(CandidateKey)  |  size(l) ≥ 1}
>> primaryKey    : Table → {s:Set(CandidateKey)  |  size(s) ≤ 1}
>> 
>> (I added a size constraint on CandidateKey and note that a Set of 0 or 1 is the same as a List of 0 or 1.)
>> 
>>> Ivan
>>> 
>>> 
>>>> 
>>>>> or is a List necessarily non-empty, ie, 
>>>>> 
>>>>> CandidateKey ::= List(ColumnName)
>>>>> 
>>>>> means that there _is_ at least one column (ie, the no primary Key alternative would not be covered?)
>>>> 
>>>> I read this as saying there are 0 or more primary keys, and, including the specification "size(s) ≤ 1" gives us 0 or 1 primary keys, modelling an optional without inventing a new type.
>>>> 
>>>>> Ivan
>>>>> 
>>>>> ----
>>>>> Ivan Herman, W3C Semantic Web Activity Lead
>>>>> Home: http://www.w3.org/People/Ivan/
>>>>> mobile: +31-641044153
>>>>> PGP Key: http://www.ivan-herman.net/pgpkey.html
>>>>> FOAF: http://www.ivan-herman.net/foaf.rdf
>>>>> 
>>>>> 
>>>>> 
>>>>> 
>>>>> 
>>>> 
>>>> 
>>>> 
>>>> -- 
>>>> -ericP
>>> 
>>> 
>>> ----
>>> Ivan Herman, W3C Semantic Web Activity Lead
>>> Home: http://www.w3.org/People/Ivan/
>>> mobile: +31-641044153
>>> PGP Key: http://www.ivan-herman.net/pgpkey.html
>>> FOAF: http://www.ivan-herman.net/foaf.rdf
>>> 
>>> 
>>> 
>>> 
>>> 
>> 
>> 
>> 
>> -- 
>> -ericP
> 
> 
> ----
> Ivan Herman, W3C Semantic Web Activity Lead
> Home: http://www.w3.org/People/Ivan/
> mobile: +31-641044153
> PGP Key: http://www.ivan-herman.net/pgpkey.html
> FOAF: http://www.ivan-herman.net/foaf.rdf
> 
> 
> 
> 
>

Received on Friday, 18 February 2011 17:59:18 UTC