Our professor has solved an example for us. They taught us it's incorrect to use a quantifier (exists or forall) with a variable that's already bound on the left side of the pipe (|, meaning "such that"). They've done that in their example solution. Can quantifiers be used on variables bound on the left side of the pipe in TRC?
Their question and solution:
R consists of three columns (a, b, and, c), and a is the primary key. Similarly, S consists of three columns (d, e, and, f), and d is the primary key.
Write the TRC query that is equivalent to the following Relational Algebra query:
R ⟕ S[natural left outer join].{r.*, s.* | // There are two tuples to join (r ∈ R ∧ s ∈ S ∧ r.a = s.d) ∨ // or there is a tuple in R without a tuple in S (r ∈ R ∧ NOT (∃s ∈ S) (r.a = s.d)) }
Is this correct?
I would've answered:
{r.*, s.* |
// There are two tuples to join
(r ∈ R ∧ s ∈ S ∧ r.a = s.d) ∨
// or there is a tuple in R without a tuple in S
(r ∈ R ∧ (NOT (s ∈ S)) ∧ (r.a = s.d))
}
