Difference between Tuple Relational Calculus (TRC) and Domain Relational Calculus (DRC)

Last Updated : 09 Oct, 2024

When you work on Relational Calculus which is the main concept in Database Theory, you will find two kinds of variations that play an important role. These two variations are Tuple Relational Calculus (TRC) and Domain Relational Calculus (DRC).

If you want to retrieve data from the database, both TRC and DRC can be used. However, you will find many differences between them while expressing queries. In this article, we will discuss briefly the differences between TRC and DRC.

What is Tuple Relational Calculus (TRC)?

A Tuple Relational Calculus is a non-procedural query language that specifies the selection of the tuples in a relation. It can select the tuples with a range of values or tuples for certain attribute values etc. The resulting relation can have one or more tuples.

Notation: 

{T | P (T)}   or {T | Condition (T)}  
T is the resulting tuples and P(T) is a condition used to fetch T.

Example:

{T | EMPLOYEE (T) AND T.DEPT_ID = 10}

This selects all the tuples of employees who work for Department 10.

Advantages of Tuple Relational Calculus (TRC)

TRC serves as the foundation for many Query Language like SQL.
You can easily write information with TRC.
TRC describes the data rather than the process to get that data.

Disadvantages of Tuple Relational Calculus (TRC)

The practical use of TRC is very much less.
If we use the TRC, there might be some optimization issues.
You can only use TRC for some simple problems.

What is Domain Relational Calculus (DRC)?

A Domain Relational Calculus uses a list of attributes to be selected from the relation based on the condition. It is the same as TRC but differs by selecting the attributes rather than selecting whole tuples.

Notation:

{ a1, a2, a3, ..., an | P (a1, a2, a3, ..., an) } 
Where a1, a2, a3, … an are attributes of the relation and P is the condition.

Example:

{ |  < EMPLOYEE > DEPT_ID = 10 }

Select EMP_ID and EMP_NAME of employees who work for department 10.

Advantages of Domain Relational Calculus (DRC)

DRC helps work on the individual attribute values.
DRC helps to generate the data getting process than the definition of the data.

Disadvantages of Domain Relational Calculus (DRC)

The system developed with DRC is hard to maintain.
DRC can't work with multiple domains at the same time.

Difference Between Tuple Relational Calculus (TRC) and Domain Relational Calculus (DRC)

Basis of Comparison	Tuple Relational Calculus (TRC)	Domain Relational Calculus (DRC)
Definition	The Tuple Relational Calculus (TRC) is used to select tuples from a relation. The tuples with specific range values, tuples with certain attribute values, and so on can be selected.	The Domain Relational Calculus (DRC) employs a list of attributes from which to choose based on the condition. It's similar to TRC, but instead of selecting entire tuples, it selects attributes.
Representation of variables	In TRC, the variables represent the tuples from specified relations.	In DRC, the variables represent the value drawn from a specified domain.
Tuple/ Domain	A tuple is a single element of relation. In database terms, it is a row.	A domain is equivalent to column data type and any constraints on the value of data.
Filtering	This filtering variable uses a tuple of relations.	This filtering is done based on the domain of attributes.
Return Value	The predicate expression condition associated with the TRC is used to test every row using a tuple variable and return those tuples that meet the condition.	DRC takes advantage of domain variables and, based on the condition set, returns the required attribute or column that satisfies the criteria of the condition.
Membership condition	The query cannot be expressed using a membership condition.	The query can be expressed using a membership condition.
Query Language	The QUEL or Query Language is a query language related to it,	The QBE or Query-By-Example is a query language related to it.
Similarity	It reflects traditional pre-relational file structures.	It is more similar to logic as a modeling language.
Syntax	Notation: {T \| P (T)} or {T \| Condition (T)}	Notation: { a1, a2, a3, ..., an \| P (a1, a2, a3, ..., an)}
Example	{T \| EMPLOYEE (T) AND T.DEPT_ID = 10}	{ \| < EMPLOYEE > DEPT_ID = 10 }
Focus	Focuses on selecting tuples from a relation	Focuses on selecting values from a relation
Variables	Uses tuple variables (e.g., t)	Uses scalar variables (e.g., a1, a2, ..., an)
Expressiveness	Less expressive	More expressive
Ease of use	Easier to use for simple queries.	More difficult to use for simple queries.
Use case	Useful for selecting tuples that satisfy a certain condition or for retrieving a subset of a relation.	Useful for selecting specific values or for constructing more complex queries that involve multiple relations.

Conclusion

In conclusion, the Tuple Relational Calculus (TRC) represents the Tuples whereas the Domain Relational Calculus (DRC) represents the values of each domain name. Both Tuple Relational Calculus (TRC) and Domain Relational Calculus (DRC) are different, but together they help to understand the basics of Database Query Languages.