Sixth normal form

Sixth normal form (6NF) is a term in relational database theory, used in two different ways.

6NF (C. Date's definition)

Christopher J. Date and others have defined sixth normal form as a normal form, based on an extension of the relational algebra.

Relational operators, such as join, are generalized to support a natural treatment of interval data, such as sequences of dates or moments in time, for instance in temporal databases. Sixth normal form is then based on this generalized join, as follows:

A relvar R [table] is in sixth normal form (abbreviated 6NF) if and only if it satisfies no nontrivial join dependencies at all — where, as before, a join dependency is trivial if and only if at least one of the projections (possibly U_projections) involved is taken over the set of all attributes of the relvar [table] concerned.

Date et al. have also given the following definition:

Relvar R is in sixth normal form (6NF) if and only if every JD [Join Dependency] of R is trivial — where a JD is trivial if and only if one of its components is equal to the pertinent heading in its entirety.

Any relation in 6NF is also in 5NF.

Sixth normal form is intended to decompose relation variables to irreducible components. Though this may be relatively unimportant for non-temporal relation variables, it can be important when dealing with temporal variables or other interval data. For instance, if a relation comprises a supplier's name, status, and city, we may also want to add temporal data, such as the time during which these values are, or were, valid (e.g., for historical data) but the three values may vary independently of each other and at different rates. We may, for instance, wish to trace the history of changes to Status; a review of production costs may reveal that a change was caused by a supplier changing city and hence what they charged for delivery.

For further discussion on Temporal Aggregation in SQL, see also Zimanyi. For a different approach, see TSQL2.

DKNF

Some authors have used the term sixth normal form differently: as a synonym for Domain/key normal form (DKNF). This usage predates Date et al.'s work.

Usage

The sixth normal form is currently being used in some data warehouses where the benefits outweigh the drawbacks, for example using Anchor Modeling. Although using 6NF leads to an explosion of tables, modern databases can prune the tables from select queries (using a process called 'table elimination') where they are not required and thus speed up queries that only access several attributes.

Examples

In order for a table to be in 6NF, it has to comply with the 5NF first and then it requires that each table satisfies only trivial join dependencies. Let’s take a simple example with a table already in 5NF: Here, in the users table, every attribute is non null and the primary key is the username:

Users_table

Username	Department	Status

This table is in 5NF because each join dependency is implied by the unique candidate key of the table (Username). More specific, the only possible join dependencies are: {username, status}, {username,department}.

The 6NF version would look like this:

Users

Username	Status

Users_dept

Username	Department

So, from one table in 5NF, 6NF produces two tables.

Another example in which we can demonstrate the 6NF is when we look at the space occupied. For this we chose the healthcare domain with this table:

TABLE 1

Medic Name	Occupation	Type	Practice in years
Smith James	orthopedic	specialist	23
Miller Michael	orthopedic	probationer	4
Thomas Linda	neurologist	probationer	5
Scott Nancy	orthopedic	resident	1
Allen Brian	neurologist	specialist	12
Turner Steven	ophthalmologist	probationer	3
Collins Kevin	ophthalmologist	specialist	7
King Donald	neurologist	resident	1
Harris Sarah	ophthalmologist	resident	2

The healthcare domain contains several specializations up until the maximum development in this domain. These are: - resident - probationer - specialist

To get promoted to a higher position, it will take several years for someone to obtain his or her proper training. If a doctor has practiced in the field less than the required period, he or she won’t be able to advance in rank. For example: If Michael Miller, orthopedic probationer, has worked in the medical field for 3 years and 11 months, he won’t be able to become an orthopedic specialist because the minimum period to promote from probationare to specialist is 4 years.

The transition from one position to another is based on an exam. The exam, required to make the progress from one grade to another (for example: from probationer to specialist), can be taken after a period of 4 years.

The next step in applying the 6NF for the Table 1, is to eliminate all non-trivial join dependencies.

TABLE 2.1

Medic Name	Occupation	Practice in years
Smith James	orthopedic	23
Miller Michael	orthopedic	4
Thomas Linda	neurologist	5
Scott Nancy	orthopedic	1
Allen Brian	neurologist	12
Turner Steven	ophthalmologist	3
Collins Kevin	ophthalmologist	7
King Donald	neurologist	1
Harris Sarah	ophthalmologist	2

TABLE 2.2

Type	Min practice	Max practice
resident	0	2
probationer	3	5
specialist	6	45

We will show now that passing from 5NF to 6NF also reduces the space occupied by the table. In the brackets, it is indicated how much space each field of the table occupies (in bytes).

Medic Name	Occupation	Type	Practice in years
Smith James[12]	orthopedic[11]	specialist[11]	23[4]
Miller Michael[15]	orthopedic[11]	probationer[12]	4[4]
Thomas Linda[13]	neurologist[12]	probationer[12]	5[4]
Scott Nancy[12]	orthopedic[11]	resident[9]	1[4]
Allen Brian[12]	neurologist[12]	specialist[11]	12[4]
Turner Steven[14]	ophthalmologist[16]	probationer[12]	3[4]
Collins Kevin[14]	ophthalmologist[16]	specialist[11]	7[4]
King Donald[12]	neurologist[12]	resident[9]	1[4]
Harris Sarah[13]	ophthalmologist[16]	resident[9]	2[4]

TABLE 1 = [366] (bytes)

We can see that Table 1, which is in 5NF, occupies, in total, 366 bytes. This table translated into 6NF will consist of tables Table 2.1 and Table 2.2. The last 2 will occupy together 326 bytes.

Medic Name	Occupation	Practice in years
Smith James[12]	orthopedic[11]	23[4]
Miller Michael[15]	orthopedic[11]	4[4]
Thomas Linda[13]	neurologist[12]	5[4]
Scott Nancy[12]	orthopedic[11]	1[4]
Allen Brian[12]	neurologist[12]	12[4]
Turner Steven[14]	ophthalmologist[16]	3[4]
Collins Kevin[14]	ophthalmologist[16]	7[4]
King Donald[12]	neurologist[12]	1[4]
Harris Sarah[13]	ophthalmologist[16]	2[4]

TABLE 2.1 = [270]

Type	Min practice	Max practice
resident[9]	0[4]	2[4]
probationer[12]	3[4]	5[4]
specialist[11]	6[4]	45[4]

TABLE 2.2 = [56] => TABLE 2.1 + TABLE 2.2 = [326] (bytes)

We can see that, in this example, 6NF occupies less than 5NF (more specific, less with 40 bytes). Going into the 6NF reduces the occupied space. If the initial table is larger, after going into the 6NF, the reduced space will also be larger.

In practice though, row overhead makes this separation of information in multiple tables occupy more space. It doesn't however detract from the increased flexibility, consistency - and query complexity.

Bibliography

• Date, Chris J.; Darwen, Hugh; Lorentzos, Nikos A. (January 2003). Temporal Data and the Relational Model: A Detailed Investigation into the Application of Interval and Relation Theory to the Problem of Temporal Database Management. Oxford: Elsevier LTD. ISBN 1-55860-855-9. {{cite book}}: Invalid |ref=harv (help)
• Date, Chris J.; Darwen, Hugh; Lorentzos, Nikos A. (12 August 2014). Time and relational theory - Temporal databases in the relational model and SQL. Elsevier-Morgan Kaufmann. ISBN 9780128006313. {{cite book}}: Invalid |ref=harv (help)
• Snodgrass, Richard T. "TSQL2 Temporal Query Language". {{cite web}}: Invalid |ref=harv (help)
• Zimanyi, E. (June 2006). "Temporal Aggregates and Temporal Universal Quantification in Standard SQL" (PDF). ACM SIGMOD Record, volume 35, number 2, page 16. ACM. {{cite web}}: Invalid |ref=harv (help)
• Date, Chris J. "ON DK/NF NORMAL FORM". Archived from the original on 6 April 2012.
• Harrington, Jan L. (2009). Relational Database Design and Implementation: Clearly Explained. Elsevier-Morgan Kaufmann. ISBN 9780123747303. {{cite book}}: Invalid |ref=harv (help)

Further reading

• Date, C.J. (2006). The relational database dictionary: a comprehensive glossary of relational terms and concepts, with illustrative examples. O'Reilly Series Pocket references. O'Reilly Media, Inc. p. 90. ISBN 978-0-596-52798-3.