Tuple Relational Calculus (TRC) in DBMS
Tuple Relational Calculus is a non-procedural query language unlike relational algebra. Tuple Calculus provides only the description of the query but it does not provide the methods to solve it. Thus, it explains what to do but not how to do.
In Tuple Calculus, a query is expressed as
{t| P(t)}where t = resulting tuples,
P(t) = known as Predicate and these are the conditions that are used to fetch t
Thus, it generates set of all tuples t, such that Predicate P(t) is true for t.
P(t) may have various conditions logically combined with OR (∨), AND (∧), NOT(¬).
It also uses quantifiers:
∃ t ∈ r (Q(t)) = ”there exists” a tuple in t in relation r such that predicate Q(t) is true.
∀ t ∈ r (Q(t)) = Q(t) is true “for all” tuples in relation r.
Example:
Table-1: Customer Customer name Street City Saurabh A7 Patiala Mehak B6 Jalandhar Sumiti D9 Ludhiana Ria A5 Patiala
Table-2: Branch Branch name Branch city ABC Patiala DEF Ludhiana GHI Jalandhar
Table-3: Account Account number Branch name Balance 1111 ABC 50000 1112 DEF 10000 1113 GHI 9000 1114 ABC 7000
Table-4: Loan Loan number Branch name Amount L33 ABC 10000 L35 DEF 15000 L49 GHI 9000 L98 DEF 65000
Table-5: Borrower Customer name Loan number Saurabh L33 Mehak L49 Ria L98
Table-6: Depositor Customer name Account number Saurabh 1111 Mehak 1113 Sumiti 1114
Queries-1: Find the loan number, branch, amount of loans of greater than or equal to 10000 amount.
{t| t ∈ loan ∧ t[amount]>=10000}Resulting relation: Loan number Branch name Amount L33 ABC 10000 L35 DEF 15000 L98 DEF 65000
In the above query, t[amount] is known as tuple variable.
Queries-2: Find the loan number for each loan of an amount greater or equal to 10000.
{t| ∃ s ∈ loan(t[loan number] = s[loan number]
∧ s[amount]>=10000)}Resulting relation: Loan number L33 L35 L98
Queries-3: Find the names of all customers who have a loan and an account at the bank.
{t | ∃ s ∈ borrower( t[customer-name] = s[customer-name])
∧ ∃ u ∈ depositor( t[customer-name] = u[customer-name])}Resulting relation: Customer name Saurabh Mehak
Queries-4: Find the names of all customers having a loan at the “ABC” branch.
{t | ∃ s ∈ borrower(t[customer-name] = s[customer-name]
∧ ∃ u ∈ loan(u[branch-name] = “ABC” ∧ u[loan-number] = s[loan-number]))}Resulting relation: Customer name Saurabh
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