Next steps towards content for fixing EXISTS

[hartig]

As suggested in the previous task group meeting, this issue lists the steps that I see for adding content related to EXISTS into the spec.

• Extend the signature of the eval function by adding the "context solution mapping" as a third argument.

  • Hence, we go from writing eval(D(G), A) to writing eval(D(G), A, μ_ctx).
  • Extending the signature of the eval function means to adapt all the definitions in Section 18.6.2 Evaluation Semantics.
  • I would prefer to start working on this step only after PR improves definitions of all algebra operators that involve expressions #291 is merged because that PR makes changes in the same part of the spec. The PR is still waiting for @afs' review (all other editors have already approved it, and Ted is okay with it as well).
  • edit: this step is implemented in PR Extends the signature of the eval function (to be used for EXISTS) #309

• Extend the algebraic syntax with a new symbol that will be used to indicate where the context solution mapping is injected during query evaluation.

  • Formally, adding that symbol would mean adding another base case to the recursive definition of the notion of an algebraic query expression.
  • In an earlier email to the mailing list I proposed to call this new symbol InjectContextMapping, but of course I am also open to other names.

• Extend the translation to the algebraic syntax such that the new symbol from the previous step is added into the algebraic query expression that is produced by the translation.

  • Concretely, the place where this extension needs to be captured is in the case for GroupGraphPattern in Section 18.3.2.6 Translate Graph Patterns, where the initial assignment of G needs to be the new symbol rather than the empty BGP.

• Extend the definition of the eval function by adding a case for the new symbol.

  • The definition for that case would say something like: eval(D(G), InjectContextMapping, μ_ctx) = a multiset of solution mappings that contains only μ_ctx, with a multiplicity of 1

• Add the formal definition of the evaluation of EXISTS expressions.

  • I think the best place for that is Section 17.4.1.4 NOT EXISTS and EXISTS.

[afs]

Looks good.

PR reviewed #291.

Some minor remarks:

1. InjectContextMapping - "inject" could come with connotations - what about simply "contextMapping"? or current query solution?
2. Location for the definition of EXIST expressions. Slightly tricky - this is the point where there is a loop between FILTER functions/expressions and graph patterns. Section 17 seems fine. While 17.4.1 (Functional Forms) could be a place, but maybe in it's own subsection as it is rather different.