Relational Model¶

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Structure of Relational Databases¶

Basic Structure¶

Formally, given set \(D_1, D_2, \cdots, D_n\), a relation \(r\) is a subset of \(D_1 \times D_2 \times \cdots \times D_n\). —— a Cartesian product (笛卡儿积) of a list of domain \(D_i\) Thus a relation is a set of n-tuple \((a_{1j}, a_{2j}, \cdots, a_{nj})\) where each \(a_{ij} \in D_i(i \in [1, n])\)

Attribute Types¶

Each attribute of a relation has a name.
The set of allowed values for each attribute is called the domain (域) of the attribute.
The special value null is a member of every domain.

Relation Schema¶

Assume \(A_1, A_2, \cdots, A_n\) are attributes, then \(R = (A_1, A_2, \cdots, A_n)\) is a relation schema. e.g. instructor = (ID, name, dept_name, salary).

A relation instance \(r\) defined over schema \(R\) is denoted by \(r(R)\). (or \(r(R)\) us a relation on relation schema \(R\)) e.g. instructor(instructor-schema) = instructor(ID, name, dept_name, salary)

Relation Instance¶

The current values (i.e. relation instance) of a relation are specified by a table.

An element \(t\) of \(r\) is a tuple, represented by a row in a table.

若 \(t\) 是一个元组，那么 \(t[name]\) 表示元组 \(t\) 中名称为 \(name\) 的属性的值。