View source for Relational calculus

{{Short description|Theory of relational databases}}
{{No footnotes|date=November 2021}}

The '''relational calculus''' consists of two calculi, the [[tuple relational calculus]] and the [[domain relational calculus]], that is part of the [[relational model]] for databases and provide a declarative way to specify database queries. The raison d'être of relational calculus is the formalization of [[query optimization]], which is finding more efficient manners to execute the same query in a database.

The relational calculus is similar to the [[relational algebra]], which is also part of the relational model: While the relational calculus is meant as a declarative language that prescribes no execution order on the subexpressions of a relational calculus expression, the [[relational algebra]] is meant as an imperative language: the sub-expressions of a relational algebraic expression are meant to be executed from left-to-right and inside-out following their nesting.

Per [[Codd's theorem]], the relational algebra and the domain-independent relational calculus are [[logical equivalence|logically equivalent]].

== Example ==
A [[relational algebra]] expression might prescribe the following steps to retrieve the phone numbers and names of book stores that supply ''Some Sample Book'':

# Join book stores and titles over the BookstoreID.
# Restrict the result of that join to tuples for the book ''Some Sample Book''.
# Project the result of that restriction over StoreName and StorePhone.

A relational calculus expression would formulate this query in the following descriptive or declarative manner:

:Get StoreName and StorePhone for book stores such that there exists a title BK with the same BookstoreID value and with a BookTitle value of ''Some Sample Book''.

== Mathematical properties ==
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The relational algebra and the domain-independent relational calculus are [[logical equivalence|logically equivalent]]: for any algebraic expression, there is an equivalent expression in the calculus, and vice versa. This result is known as [[Codd's theorem]].

== Purpose ==
The raison d'être of the relational calculus is the formalization of [[query optimization]]. Query optimization consists in determining from a query the most efficient manner (or manners) to execute it. Query optimization can be formalized as translating a relational calculus expression delivering an answer A into efficient relational algebraic expressions delivering the same answer A.

== See also ==

* [[Calculus of relations]]

== References ==
* {{cite book | first=Christopher J. | last=Date | author-link=Christopher J. Date | year=2004 | title=An Introduction to Database Systems | url=https://archive.org/details/introductiontoda0000date | url-access=registration | edition=8th | publisher=Addison Wesley  | isbn=0-321-19784-4 }}

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{{DEFAULTSORT:Relational Calculus}}
[[Category:Logical calculi]]
[[Category:Relational model]]
[[Category:Database management systems]]


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