Re: Direct Mapping document

I agree with Richard's suggestion re. notation. 
A few explanatory words would make the exposition more accessible.
All the best, Ashok


Richard Cyganiak wrote:
> Hi Eric,
>
> That's a good start.
>
> On 7 Jun 2010, at 16:49, Eric Prud'hommeaux wrote:
>> In order to get some common terminology, I've created a draft of a
>> Direct Mapping.
>
> Maybe start by defining what a database is in your notation? "A 
> database db is a set of relations R_1...R_i" etc?
>
>> This defines a Direct Graph and demonstrates how this
>> definition can be extended.
>>
>> The crux of it is still:
>>
>> directDB(db)       ≝   { directR(r) ∀ r ∈ db }
>> directR(R)       ≝   { directT(R, T) ∀ T ∈ R.Body }
>> directT(R, T)       ≝   { directL(R, S, A) ∀ A ∈ scalar(T) }
>>                     ∪ { directN(R, S, A) ∀ A ∈ reference(T) }
>
> What are scalar(T) and reference(T)?
>
>>                      ∣ S = nodemap(R, pk(T))
>> directL(R, S, A)   ≝ triple(S, predicatemap(R, A), literalmap(A))
>
> What's literalmap?
>
>> directN(R, S, A)   ≝ triple(S, predicatemap(R, A), nodemap(R, A))
>>
>> nodemap(R, A)      ≝ IRI(stem + "/" + R.name "/" A.name + "." + 
>> A.value + "#_")
>> predicatemap(R, A) ≝ IRI(stem + "/" + R.name "#" A.name)
>
> What's the logic for uses hashes in some places and slashes in others?
>
> Shouldn't there be an rdf:type triple somewhere? If not, then how do 
> you SPARQL for all records in a single DB?
>
> To be really useful, this direct mapping should define a URI for the 
> DB itself, for each relation, and for each attribute in the relations.
>
>> I'm still playing with the notation.
>
> I'd prefer classical mathematical sets, so where you have:
>
>   directDB(db)       ≝   { directR(r) ∀ r ∈ db }
>
> I'd rather see:
>
>   directDB(db) = { directR(r) | r ∈ db }
>
> General note: "succinct" and "clear" are correlated, but not the same. 
> The latter should be the goal, not the former.
>
> Best,
> Richard
>
>
>
>
>> It's currently a pretty classic
>> notation:
>>
>>  3.1 Notation for Types
>>    A  : a type
>>    A ⊔ B  : disjoint union of A and B
>>    ( A, B )  : tuple (Cartesian product) of types A and B
>>    [ A ]  : list of elements of type A
>>    { A }  : set of elements of type A
>>    { A→B }  : map of elements of type A to elements of type B
>>  3.2 Notation for Injectors
>>    a  : an instance of an A
>>    ( a1, b1 )  : a tuple with elements a1 and b1
>>    [ a1, a2 ]  : list with elements a1 and a2
>>    { a1, a2 }  : set with elements a1 and a2
>>    { a1→b1, a2→b2 }  : map with elements with key a1 mapped to b1 and 
>> key a2 mapped to b2
>>  3.3 Supporting Functions
>>    AB[a]  : in a map of A to B, the instance of B for a given A*
>>
>> We can get more type-safety if we use something like a scala notation,
>> but I'm not sure how to tersely express things like disjoint union.
>>
>>  3.1 Notation for Types
>>    x:X  : x is an element in the set X
>>    A ?? B : disjoint union of A and B (normally case classes
>>             extending an abstract class, e.g.:
>>               abstract class AB; A extends AB; B extends AB;
>>             )
>>    ( A, B )  : tuple (Cartesian product) of types A and B
>>    List[ A ]  : list of elements of type A
>>    Set[ A ]  : set of elements of type A
>>    Map[ A, B ]  : map of elements of type A to elements of type B
>>  3.2 Notation for Injectors
>>    a  : an instance of an A
>>    ( a1, b1 )  : a tuple with elements a1 and b1
>>    List( a1, a2 )  : list with elements a1 and a2
>>    Set( a1, a2 )  : set with elements a1 and a2
>>    Map( a1→b1, a2→b2 )  : map with elements with key a1 mapped to b1 
>> and key a2 mapped to b2
>>  3.3 Supporting Functions
>>    AB(a)  : in a map of A to B, the instance of B for a given A*
>>
>> -- 
>> -ericP
>>
>
>

Received on Tuesday, 8 June 2010 09:55:55 UTC