Relational Calculus

Tuple Relational Calculus

• It is a non-procedural query language

• This means that it will mention the required information without specifying the procedure to obtain it

• An expression in tuple relational calculus is denoted as follows: {t | P(t)}

• In other words, it is the set of all tuples t such that predicate P is true for t

• t is a tuple variable and t[A] denotes the value of tuple t for attribute A

• t $\in$ r denotes that tuple t is in relation r

• The predicate can contain:

  • A set of attributes and constants

  • A set of comparison operators: (<, ≤, =, ≠, >, ≥)

  • A set of connectives: and (∧), or (v)‚ not (¬)

  • An implication (⇒): x ⇒ y, i.e. if x if true, then y is true

    x ⇒ y ≡ ¬x v y

  • A set of quantifiers:

    $\exists$ t$\in$r (Q (t)) ≡ "there exists" a tuple t in relation r such that predicate Q(t) is true

    $\forall$ t$\in$r (Q (t)) ≡ Q(t) is true "for all" tuples t in relation r

• Ex. Finding ID, name, dept_name and salary of all instructors who have salary greater than 80000: {t | t ∈ instructor ∧ t [salary] > 80000}

Domain Relational Calculus

• It is a non-procedural language as well

• It is as powerful as tuple relational calculus

• An expression in domain relational calculus is denoted as follows: {<$x_1, x_2, ... x_n$>|P($x_1, x_2, ..., x_n$)}

  where $x_1, x_2, ..., x_n$ are domain variables and P is the predicate
• Ex. Finding ID, name, dept_name and salary of all instructors who have salary greater than 80000:

  {<i, n, d, s> | <i, n, d, s> ∈ instructor ∧ s > 80000}