From: Juan Sequeda <juanfederico@gmail.com>

Date: Tue, 8 Jun 2010 10:08:49 -0500

Message-ID: <AANLkTikzTRPm1L4cn0K0s4pBRrBKZwyRCcEMJbYS5XMZ@mail.gmail.com>

To: "Eric Prud'hommeaux" <eric@w3.org>

Cc: Richard Cyganiak <richard@cyganiak.de>, RDB2RDF WG <public-rdb2rdf-wg@w3.org>

Date: Tue, 8 Jun 2010 10:08:49 -0500

Message-ID: <AANLkTikzTRPm1L4cn0K0s4pBRrBKZwyRCcEMJbYS5XMZ@mail.gmail.com>

To: "Eric Prud'hommeaux" <eric@w3.org>

Cc: Richard Cyganiak <richard@cyganiak.de>, RDB2RDF WG <public-rdb2rdf-wg@w3.org>

I thought this was going to be on a wiki first and not published immediately? Juan Sequeda +1-575-SEQ-UEDA www.juansequeda.com On Tue, Jun 8, 2010 at 5:41 AM, Eric Prud'hommeaux <eric@w3.org> wrote: > * Richard Cyganiak <richard@cyganiak.de> [2010-06-08 09:56+0100] > > Hi Eric, > > > > That's a good start. > > I'm hoping that by actually including the URL (!) > http://www.w3.org/2001/sw/rdb2rdf/directGraph/ > I can clarify many of these questions. > > In penance, I will go through your comments and point to where they > should be answered in the doc. > > > 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? > > http://www.w3.org/2001/sw/rdb2rdf/directGraph/#Rel-Database > > > >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)? > > http://www.w3.org/2001/sw/rdb2rdf/directGraph/#direct-scalar > http://www.w3.org/2001/sw/rdb2rdf/directGraph/#direct-reference > > > > ∣ 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? > > http://www.w3.org/2001/sw/rdb2rdf/directGraph/#LD > > > Shouldn't there be an rdf:type triple somewhere? If not, then how do > > you SPARQL for all records in a single DB? > > Would you be satisfied with a TypeAnnotation extension? > http://www.w3.org/2001/sw/rdb2rdf/directGraph/#extend > It feels like keeping the direct mapping agnostic to types > simplifies later math. > > > 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. > > The direct mapping is defined in terms of a <code>stem</code> > http://www.w3.org/2001/sw/rdb2rdf/directGraph/#alg > > > >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 } > > Any seconds on this? I'm pretty agnostic to notation. > > Did the scala notation resonate with you at all? > > > 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 > > > > > > > -- > -ericP > >Received on Tuesday, 8 June 2010 15:16:24 GMT

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