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Difference Between Relational Algebra and Relational Calculus

relational-algebra-vs-relational-calculusRelational Algebra and Relational Calculus are the formal query languages for a relational model. Both form the base for the SQL language which is used in most of the relational DBMSs. Relational Algebra is a procedural language.

On the other hands, Relational Calculus is a declarative language. Relational Algebra and Relational Calculus can be further differentiated on many aspects, which I have discussed below with the help of comparison chart.

Content: Relational Algebra Vs Relational Calculus

  1. Comparison Chart
  2. Definition
  3. Key Differences
  4. Conclusion

Comparison Chart

Basis for ComparisonRelational AlgebraRelational Calculus
BasicRelational Algebra is a Procedural language.Relational Claculus is Declarative language.
StatesRelational Algebra states how to obtain the result.Relational Calculus states what result we have to obtain.
OrderRelational Algebra describes the order in which operations have to be performed.Relational Calculus does not specify the order of operations.
DomainRelational Algebra is not domain dependent.Relation Claculus can be domain dependent.
RelatedIt is close to a programming language.It is close to the natural language.

Definition of Relational Algebra

Relational algebra presents the basic set of operations for relational model. It is a procedural language, which describes the procedure to obtain the result. Relational algebra is prescriptive because it describes the order of operations in the query that specifies how to retrieve the result of a query.

The sequence of operations in a relation algebra is called relational algebra expression. The Relational Algebra Expression either takes one relation or two relations as an input to the expression and produces a new relation as a result. The resultant relation obtained from the relational algebra expressions can be further composed to the other relational algebra expression whose result will again be a new relation.

The Relation Algebra forms the framework for implementing and optimizing queries while query processing. Relational algebra is an integral part of relational DBMS.   The fundamental operation included in relational algebra are { Select (σ), Project (π), Union (∪ ), Set Difference (-), Cartesian product (×) and Rename (ρ)}.

Definition of Relational Calculus

Unlike Relational Algebra, Relational Calculus is a higher level Declarative language. In converse to the relational algebra, relational calculus defines what result is to be obtained. Like Relational Algebra, Relational Calculus does not specify the sequence of operations in which query will be evaluated.

The sequence of relational calculus operations is called relational calculus expression that also produces a new relation as a result. The Relational Calculus has two variations namely Tuple Relational Calculus and Domain Relational Calculus.

The Tuple Relational Calculus list the tuples to selected from a relation, based on a certain condition provided. It is formally denoted as:

{ t | P(t) }

Where t is the set of tuples fro which the condition P is true.

The next variation is Domain Relational Calculus, which in contrast to Tuple Relational Calculus list the attributes to be selected from a relation, based on certain condition. The formal definition of Domain Relational Calculus is as follow:

{<X1, X2, X3, . . . Xn> | P(X1, X2, X3, . . . Xn)}

Where X1, X2, X3, . . . Xn are the attributes and P is the certain condition.

Key Differences Between Relational Algebra and Relational Calculus

  1. The basic difference between Relational Algebra and Relational Calculus is that Relational Algebra is a Procedural language whereas, the Relational Calculus is a Non-Procedural, instead it is a Declarative language.
  2. The Relational Algebra defines how to obtain the result whereas, the Relational Calculus define what information the result must contain.
  3. Relational Algebra specifies the sequence in which operations have to be performed in the query. On the other hands, Relational calculus does not specify the sequence of operations to performed in the query.
  4. The Relational Algebra is not domain dependent whereas, the Relational Calculus can be domain dependent as we have Domain Relational Calculus.
  5. The Relational Algebra query language is closely related to programming language whereas, the Relational Calculus is closely related to the Natural Language.

Conclusion

Relational Algebra and Relational Calculus both have equivalent expressive power. The main difference between them is just that Relational Algebra specify how to retrieve data and Relational Calculus defines what data is to be retrieved.

Related Differences:

  1. Difference Between DBMS and RDBMS
  2. Difference Between SOP and POS
  3. Difference Between Procedural and Non-procedural Language
  4. Difference Between SQL and PL/SQL
  5. Difference Between E-R Model and Relational Model in DBMS

Comments

  1. Ameeq says

    April 16, 2017 at 5:52 pm

    Your website is Awesome very informative. I will say that you should also upload on Software Engineering.

    Reply
  2. dipankar pal says

    April 10, 2018 at 3:52 am

    seriously you guys are damn cool ,,,, thanks for the easy table view difference 🙂
    try to write content about software engineering and basic data structure.

    Reply
  3. Vivek says

    November 24, 2018 at 10:07 am

    Awesome

    Reply
  4. Brian Leong says

    May 30, 2019 at 7:17 am

    This website is pretty good.

    Reply
  5. Mintu says

    June 6, 2019 at 5:19 am

    Great Post. Very informative

    Reply
  6. Awais says

    October 21, 2019 at 2:55 pm

    Very great and appreciate-able work.

    Reply
  7. sasank says

    December 23, 2020 at 4:00 am

    very informative

    Reply
  8. Xyz says

    January 12, 2021 at 7:38 am

    Your explanation is very informative. I praise your hard work.

    But I request you to explain Safe relational calculus and unsafe relational calculus. Its differences and relate it with relational algebra.

    Reply

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