dev-notes/docs/databases/database-systems/databases.md

Databases

Organized collection of inter-related data that models some aspect of the real-world. Databases are the core component of most computer applications.

A DBMS is the software that allows applications to store and analyze information in a database.
A general-purpose DBMS is designed to allow the definition, creation, querying, update and administration of database Management System

A data model is a collection of concepts for describing the data in a database. A schema is a description of a particular collection of data, using a given data model.

Relational Model

It was proposed by Ted Codd in 1970. It's an abstraction to avoid high maintenance of the DBMS software:

• store database in simple data structures-
• access data through high level language.
• physical storage left to the implementation.
• store database in simple data structures-
• access data through high level language.
• physical storage left to the implementation.

Concepts:

• Structure: the definition of relations and their contents.
• Integrity: ensures that the database's contents satisfy constraints.
• Manipulation: how to access and modify a database's content.

Relations

A relation (aka table)is an unordered set that contains the relationship of the attributes (aka fields) that represent entities.
The domain of a relation is the set of possible values that the relation can contain.
A tuple (aka record) is a set of attribute values in a relation. Values are (normally) atomic/scalar. The special value NULL is a member of every domain.

Primary Keys (PK)

A relation's primary key uniquely identifies a single tuple. Some DBMSs automatically create an internal primary key if one is not provided.

Foreign Keys (FK)

A foreign key specifies that an attribute from one relation has to map to a tuple in another relation.

Data Manipulation Language (DML)

The data manipulation language describes how to store and retrieve information from a database.

Kinds of DMLs:

• Procedural: the query specifies the (high-level) strategy that the DBMS should use to find the desired result. (Relational Algebra)
• Non-Procedural: the query specifies only what data is wanted and not how to find it. (Relational Calculus)

Relational Algebra

Set of fundamental operations to retrieve and manipulate tuples in a relation. Each operator takes one or more relations as inputs and outputs a new relation. This allows to chain operations together to create more complex operations.

Relational algebra describes the steps needed to obtain a particular result. The order of the steps does influence the performance of the complete operation.

Fundamental Operators:

• Selection (σ)
• Projection (π)
• Union (U)
• Intersection (∩)
• Difference (-)
• Product (x)
• Natural Join (|X|)

Extra Operators:

• Rename (p)
• Assignment (R ← S)
• Duplicate Elimination
• Aggregation (Y)
• Sorting (τ)
• Division (÷)

Note

: reactional algebra operates on sets. A set is an unordered list of unique values.

Select (σ)

Choose a subset of tuples from a relation that satisfies a selection predicate. Predicates acts a filters to retain only tuples that fulfill its qualifying requirements. It's possible to combine multiple predicates using conjunctions/disjunctions.

Syntax: σ(R)

SELECT * FROM R WHERE <predicate>;

Projection (π)

Generate a relation with tuples that contain only the specified attributes. Allows to rearrange attribute ordering and can manipulate values.

Syntax: π(R)

SELECT (<tuple>) FROM R;

Union (U)

Generate a relation that contains all tuples that appear in either only one ore both input relations.

Syntax: (R U S)

(SELECT * FROM R) UNION ALL (SELECT * FROM S);

Intersection (∩)

Generate a relation that contains only the tuples that appear in both of the input relations.

Syntax: (R ∩ S)

(SELECT * FROM R) INTERSECT (SELECT * FROM S);

Difference (-)

Generate a relation that contains only the tuples that appear in the first and not the second of the input relations.

Syntax: (R - S)

(SELECT * FROM R) EXCEPT (SELECT * FROM S);

Product (x)

Generate a relation that contains all possible combinations of tuples from the input relations.

Syntax: (R x S)

SELECT * FROM R CROSS JOIN S;
SELECT * FROM R, S;

Natural Join (|X|)

Generate a relation that contains all tuples that are a combination of two tuples (one from each relation) with common value(S) for one or more attributes.

Note

: the matching values must be on the same fields.

Syntax: (R |X| S)

SELECT * FROM R NATURAL JOIN S;