First normal form

First normal form (1NF or Minimal Form) is a normal form used in database normalization. A relational database table that adheres to 1NF is one that meets a certain minimum set of criteria. These criteria are basically concerned with ensuring that the table is a faithful representation of a relation and that it is free of repeating groups.

The concept of a "repeating group" is, however, understood in different ways by different theorists. As a consequence, there is no universal agreement as to which features would disqualify a table from being in 1NF. Most notably, 1NF as defined by some authors (for example, Ramez Elmasri and Shamkant B. Navathe, following the precedent established by Edgar F. Codd) excludes relation-valued attributes (tables within tables); whereas 1NF as defined by other authors (for example, Chris Date) permits them.

1NF tables as representations of relations
According to Date's definition of 1NF, a table is in 1NF if and only if it is "isomorphic to some relation", which means, specifically, that it satisfies the following five conditions:

Violation of any of these conditions would mean that the table is not strictly relational, and therefore that it is not in 1NF.

Examples of tables (or views) that would not meet this definition of 1NF are:


 * A table that lacks a unique key. Such a table would be able to accommodate duplicate rows, in violation of condition 3.
 * A view whose definition mandates that results be returned in a particular order, so that the row-ordering is an intrinsic and meaningful aspect of the view. This violates condition 1.  The tuples in true relations are not ordered with respect to each other.
 * A table with at least one nullable attribute. A nullable attribute would be in violation of condition 4, which requires every field to contain exactly one value from its column's domain.  It should be noted, however, that this aspect of condition 4 is controversial.  It marks an important departure from Codd's later vision of the relational model, which made explicit provision for nulls.

Repeating groups
Date's fourth condition, which expresses "what most people think of as the defining feature of 1NF", is concerned with repeating groups. The following scenario illustrates how a database design might incorporate repeating groups, in violation of 1NF.

Domains and values
Suppose a novice designer wishes to record the names and telephone numbers of customers. He defines a customer table which looks like this:

The designer then becomes aware of a requirement to record multiple telephone numbers for some customers. He reasons that the simplest way of doing this is to allow the "Telephone Number" field in any given record to contain more than one value:

Assuming, however, that the Telephone Number column is defined on some Telephone Number-like domain (e.g. the domain of strings 12 characters in length), the representation above is not in 1NF. 1NF (and, for that matter, the RDBMS) prohibits a field from containing more than one value from its column's domain.

Repeating groups across columns
The designer might attempt to get around this restriction by defining multiple Telephone Number columns:

This representation, however, makes use of nullable columns, and therefore does not conform to Date's definition of 1NF. Even if the view is taken that nullable columns are allowed, the design is not in keeping with the spirit of 1NF. Tel. No. 1, Tel. No. 2., and Tel. No. 3. share exactly the same domain and exactly the same meaning; the splitting of Telephone Number into three headings is artificial and causes logical problems. These problems include:


 * Difficulty in querying the table. Answering such questions as "Which customers have telephone number X?" and "Which pairs of customers share a telephone number?" is awkward.
 * Inability to enforce uniqueness of Customer-to-Telephone Number links through the RDBMS. Customer 789 might mistakenly be given a Tel. No. 2 value that is exactly the same as her Tel. No. 1 value.
 * Restriction of the number of telephone numbers per customer to three. If a customer with four telephone numbers comes along, we are constrained to record only three and leave the fourth unrecorded.  This means that the database design is imposing constraints on the business process, rather than (as should ideally be the case) vice-versa.

Repeating groups within columns
The designer might, alternatively, retain the single Telephone Number column but alter its domain, making it a string of sufficient length to accommodate multiple telephone numbers:

This design is not consistent with 1NF, and presents several design issues. The Telephone Number heading becomes semantically woolly, as it can now represent either a telephone number, a list of telephone numbers, or indeed anything at all. A query such as "Which pairs of customers share a telephone number?" is more difficult to formulate, given the necessity to cater for lists of telephone numbers as well as individual telephone numbers. Meaningful constraints on telephone numbers are also very difficult to define in the RDBMS with this design.

A design that complies with 1NF
A design that is unambiguously in 1NF makes use of two tables: a Customer Name table and a Customer Telephone Number table.

Repeating groups of telephone numbers do not occur in this design. Instead, each Customer-to-Telephone Number link appears on its own record.

Atomicity
Some definitions of 1NF, most notably that of Edgar F. Codd, make reference to the concept of atomicity. Codd states that the "values in the domains on which each relation is defined are required to be atomic with respect to the DBMS." Codd defines an atomic value as one that "cannot be decomposed into smaller pieces by the DBMS (excluding certain special functions)."

Hugh Darwen and Chris Date have suggested that Codd's concept of an "atomic value" is ambiguous, and that this ambiguity has led to widespread confusion about how 1NF should be understood. In particular, the notion of a "value that cannot be decomposed" is problematic, as it would seem to imply that few, if any, data types are atomic:


 * A character string would seem not be atomic, as the RDBMS typically provides operators to decompose it into substrings.
 * A date would seem not to be atomic, as the RDBMS typically provides operators to decompose it into day, month, and year components.
 * A fixed-point number would seem not to be atomic, as the RDBMS typically provides operators to decompose it into integer and fractional components.

Date suggests that "the notion of atomicity has no absolute meaning": a value may be considered atomic for some purposes, but may be considered an assemblage of more basic elements for other purposes. If this position is accepted, 1NF cannot be defined with reference to atomicity. Columns of any conceivable data type (from string types and numeric types to array types and table types) are then acceptable in a 1NF table—although perhaps not always desirable. Date argues that relation-valued attributes, by means of which a field within a table can contain a table, are useful in rare cases.

Normalization beyond 1NF
Any table that is in second normal form (2NF) or higher is, by definition, also in 1NF (each normal form has more stringent criteria than its predecessor). On the other hand, a table that is in 1NF may or may not be in 2NF; if it is in 2NF, it may or may not be in 3NF, and so on.

Normal forms higher than 1NF are intended to deal with situations in which a table suffers from design problems that may compromise the integrity of the data within it. For example, the following table is in 1NF, but is not in 2NF and therefore is vulnerable to logical inconsistencies:

The table's key is {Subscriber ID, Email Address}.

If Carol Robertson changes her surname by marriage, the change must be applied to two rows. If the change is only applied to one row, a contradiction results: the question "What is Customer 252's name?" has two conflicting answers. 2NF addresses this problem.