Domain Relational Calculus in DBMS

Domain Relational Calculus (DRC) is a non-procedural query language used to retrieve information from a relational database. It is based on predicate logic and allows the user to specify what data they want to retrieve, but not how to retrieve it, making it a declarative query language.

Domain Relational Calculus (DRC)

Domain Relational Calculus (DRC) is a formal query language for relational databases. It describes queries by specifying a set of conditions or formulas that the data must satisfy. These conditions are written using domain variables and predicates, and it returns a relation that satisfies the specified conditions.

A general form of a DRC query is written as:

{ < x₁, x₂, x₃, ..., x_n > | P (x₁, x₂, x₃, ..., x_n ) }

where, <x₁, x₂, x₃, ..., x_n> represents resulting domains variables and P (x₁, x₂, x₃, ..., x_n) represents the condition or formula equivalent to the Predicate calculus.

The query returns a relation where each tuple consists of values for the domain variables x1,x2,…,xn such that the predicate PPP is true.

Key Characteristics of DRC:

• Non-procedural: Specifies what data to retrieve without describing the steps for retrieval.
• Based on Predicate Calculus: Utilizes logical expressions (predicates) to describe the query.
• Relational Database Queries: Primarily used for querying relational databases.

Components of Domain Relational Calculus (DRC)

1. Domain Variables

Domain variables represent the attributes (fields) that will appear in the resulting relation of the query. These variables are the placeholders that will hold the actual values in the result.

2. Predicate

A predicate is a logical condition or formula that the data must satisfy. It is expressed using comparison operators, connectives, and quantifiers.

• Comparison operators: =, >, <, >=, <=, !=.
• Connectives: AND, OR, NOT.
• Quantifiers: FOR ALL, EXISTS.

3. Quantifiers

Quantifiers are used to express the scope of a query:

• Existential quantifier (∃): Denotes that there exists at least one instance that satisfies a condition.
• Universal quantifier (∀): Denotes that all instances in the domain satisfy a condition.

4. Domains and Relations

A domain refers to a specific set of values (like integers, strings) that a variable can take. A relation is a table in the database, and the tuples in the relation represent data that matches the query conditions.

Writing Queries in Domain Relational Calculus (DRC)

Writing a query in DRC involves describing the desired result by specifying the domain variables and predicates that define the conditions the data must meet. Below are examples:

Table 1: Customer

Table 2: Loan

Table 3: Borrower

Example 1: Finding Loans with Amount >= 100

To find all loans with an amount greater than or equal to 100, we use the following query in DRC:

{≺l, b, a≻ | ≺l, b, a≻ ∈ loan ∧ (a ≥ 100)}

Resulting relation:

This query specifies that the result will contain the loan number (l), branch name (b), and amount (a) from the loan relation where the amount is greater than or equal to 100.

Example 2: Finding Loan Numbers >= 150

To find loan numbers where the amount is greater than or equal to 150, we write:

{≺l≻ | ∃ b, a (≺l, b, a≻ ∈ loan ∧ (a ≥ 150))}

Resulting Relation:

Example 3: Finding Customers with Loans from "Main" Branch

To find the names of customers who have a loan at the "Main" branch, along with their loan amounts:

{≺c, a≻ | ∃ l (≺c, l≻ ∈ borrower ∧ ∃ b (≺l, b, a≻ ∈ loan ∧ (b = “Main”)))}

Resulting relation:

Advantages of Domain Relational Calculus (DRC)

1. Declarative Nature: DRC allows the user to describe what data they need without having to specify how to retrieve it. This makes it easier to write queries and understand them.
2. Mathematical Foundation: Being based on predicate logic, DRC provides a solid theoretical foundation for relational databases.
3. Non-Procedural: Unlike procedural query languages, DRC focuses on describing the result, not the procedure to get it.
4. Flexible and Powerful: It supports complex queries involving multiple relations, predicates, and conditions.

Limitations of Domain Relational Calculus (DRC)

1. Complexity: DRC can be difficult to use for complex queries due to its reliance on logical formulas. It requires a good understanding of predicate calculus.
2. No Specification of Query Execution: Since it is non-procedural, DRC does not specify how queries should be executed, which can sometimes lead to inefficiencies in query execution.
3. Lack of Optimization: Unlike SQL, DRC does not provide built-in optimization mechanisms, meaning that users must rely on the DBMS for query optimization.
4. Less User-Friendly: As a formal query language, DRC is not as user-friendly as SQL, which is more widely used and has a simpler syntax.

DRC vs TRC (Tuple Relational Calculus) Comparison

While both DRC and TRC are non-procedural query languages that allow users to query relational databases, DRC focuses on individual attributes (domain variables), while TRC focuses on tuples (rows). TRC is more widely used because it is more intuitive and easier to understand.