What is a Query Language?

Definition

A relational database query language takes a collection of relation instances $R_1, R_2, \ldots, R_k$ as input and returns a single relation instance as output:

$Q(R_1, R_2, \ldots, R_k)$

To meet Codd’s goals, the query language should be high-level: the user specifies what data they want, not how to retrieve it. The language is independent of physical data representation — indexes, file structures, and access paths are managed internally by the DBMS.

Relational Algebra (RA)

The Relational Algebra is the formal basis for relational query languages. It provides a small set of operations that take relations as input and produce relations as output. Because each operation returns a relation, operations can be composed to form complex queries.

Abstract syntax

Form	Name	Meaning
$Q ::= R$	Base relation	The relation $R$ itself
$Q ::= \sigma_p(Q)$	Selection	Rows satisfying predicate $p$
$Q ::= \pi_X(Q)$	Projection	Columns in set $X$, duplicates removed
$Q ::= Q \times Q$	Product	Concatenation of every pair of tuples
$Q ::= Q - Q$	Difference	Tuples in first but not second
$Q ::= Q \cup Q$	Union	Tuples in either (or both)
$Q ::= Q \cap Q$	Intersection	Tuples in both
$Q ::= \rho_M(Q)$	Renaming	Change column names per map $M$

Where:

• $p$ is a Boolean predicate over attribute values (e.g., $A > 12$, $B = \text{'CS'}$).
• $X$ is a set of attribute names to keep.
• $M$ is a renaming map, e.g., $\{B \mapsto B'\}$.

Well-formedness conditions

A query $Q$ must be well-formed: all column names of the result must be distinct. This imposes constraints on certain operators:

• In $Q_1 \times Q_2$, the two sub-queries cannot share any column names (they must be disjoint).
• In $Q_1 \cup Q_2$, $Q_1 \cap Q_2$, and $Q_1 - Q_2$, the two sub-queries must share all column names (they must be union-compatible).

If needed, $\rho$ is used to rename columns to satisfy these conditions.

SQL

SQL (Structured Query Language) is the dominant relational query language. It originated at IBM in the early 1970s and has been standardised across multiple revisions:

Version	Year	Key features
SQL-86	1986	First standard
SQL-89	1989	Minor revision
SQL-92	1992	Major expansion (outer joins, CHECK constraints)
SQL:1999	1999	Recursive queries, triggers, OO features
SQL:2003	2003	Window functions, XML support
SQL:2008	2008	MERGE, TRUNCATE
SQL:2011	2011	Temporal databases
SQL:2016	2016	JSON support
SQL:2023	2023	Property graph queries, ANY_VALUE

SQL contains several sub-languages:

• Query Language (QL): SELECT, FROM, WHERE, GROUP BY, etc.
• Data Definition Language (DDL): CREATE TABLE, ALTER TABLE, DROP TABLE.
• Data Manipulation Language (DML): INSERT, UPDATE, DELETE.
• Data Control Language (DCL): GRANT, REVOKE.
• System Administration Language: backup, restore, user management.

Why study RA if we have SQL?

1. RA’s simple syntax and semantics make it easier to reason about complex queries. Understanding what a query means in RA helps debug SQL.
2. The RA lends itself to Tripos questions. It provides a compact, unambiguous notation for defining queries — ideal for exam settings.
3. SQL is vast and continually evolving. RA captures its core relational logic in a handful of operators.

Summary

• A query language maps a collection of relation instances to a single relation instance.
• RA provides the formal mathematical basis: six core operations plus renaming.
• SQL is the practical language, standardised from SQL-86 through SQL:2023.
• RA is studied for clarity and exam support; SQL is used in practice.