第8章データ管理

In a relational database, a tuple is one row with a collection of values separated by a comma and enclosed in parenthesis. An example of a tuple in Python represents the employee Smith, his phone number, age, and zip code.

Data inside a tuple can be of any type such as integer, string, float value, or a tuple type.

Tuple relational calculus uses tuple variables as key building blocks. A tuple variable refers to a tuple of a corresponding relation (also called range relation). A tuple relational calculus expression specifies a range relation for each tuple variable, a condition to select (combinations of) tuples, and a list of attribute types from which the values should be retrieved. As a result, a tuple relational calculus expression looks as follows:

whereby t represents the tuple variable, Ai the attribute type of which the value needs to be retrieved, and Cond(t) the range relation and extra conditions to select relevant tuples. Consider the following example:

A condition is specified using a well-formed (calculus) formula (wff), which can consist of various predicate calculus atoms combined using Boolean operators (and, or, not). The result of applying a formula to a tuple of a range relation can either be true, false, or unknown. If the result is true, the tuple will be selected in the result. Relational calculus also includes quantifiers such as the existential quantifier (∃or EXISTS) and universal quantifier (∀or FOR ALL). A formula with an existential quantifier (∃) evaluates to true if at least one tuple satisfies it. A formula with a universal quantifier (∀) evaluates to true if every tuple from the range relation satisfies the conditions stated.

Instead of tuple variables, domain relational calculus defines domain variables that range over single values of domains of attribute types. A domain calculus expression for a relation of degree n looks as follows:

where v1, v2, …vn represent the domain variables that range over domains of attribute types, and COND represents the extra conditions.

The earlier tuple relational calculus query selecting the student ID and student name of all students who study in program number 3 would now look as follows:

In this case, we defined five domain variables as a for the domain of StudentID, b for the domain of StudentName, c for the domain of StudentAddress, d for the domain of StudentCity, and e for the domain of StudentProgram. The condition e = 3 is a selection condition.

The existential quantifier (∃ or EXISTS) and universal quantifier (∀ or FOR ALL) are also supported in domain relational calculus.

The relational database language based on domain relational calculus is called query-by-example (QBE). QBE queries are expressed via a graphical query language, using visual tables where the user enters commands, example elements, and conditions. A parser converts the QBE graphical queries into statements expressed in a database manipulation language, such as SQL.

The process of logical design involves designing a database based on a specific data model but independent of physical details. The logical design for a relational DBMS includes specifications for tables, relationships, and constraints. The logical design is performed in four steps: map conceptual model to logical model components, validate the logical model using normalization, validate logical model constraints, and validate the logical model against user requirements.

To determine the quality of relation schema design, we follow the informal design guidelines for relational schemas and use simple measures of quality such as making sure attribute semantics are clear, reducing redundant information, and reducing null values. Null values cause redundant work, which wastes storage space and increases the difficulty of performing operations.