Intervals are a common concept used in SQL Server databases, yet there is often inconsistency in how they are handled. This lack of consistency stems from the absence of a native SQL data type for intervals. In this article, we will introduce basic terms and definitions to SQL Server DBAs and developers, aiming to establish a more consistent approach to handling intervals.

What are Intervals?

Intervals, also known as ranges, are representations of a range of data. They are commonly used to represent periods of time with a start date and an end date. For example, in a student database, an interval can represent the period between when a student first matriculated and when they graduated. During this interval, they are considered a student, and after this interval, they become an alum.

It is crucial for intervals to have a well-defined order. For instance, one cannot graduate from a school before becoming a student at that school.

In databases, intervals are typically represented with two fields: one indicating the beginning of the range and the other indicating the end of the range.

Examples of Intervals

Let’s explore some common examples of intervals:

• Age Ranges: Age groups such as 16-19, 20-24, 25-34, etc.
• Temperature Ranges: High and low temperatures reported for a specific period.
• Snow/Rain Fall: Expected amounts of snow or rain during a particular time frame.
• Salary Ranges: Ranges of salaries for job listings.
• Names: Registration tables at events often have intervals based on the first letter of the last name to expedite the registration process.

Datetime intervals are among the most common types of intervals. Many reports that involve datetime data use datetime intervals to group records. Examples of datetime intervals include hourly, daily, weekly, monthly, quarterly, and yearly intervals.

Types of Intervals

There are three types of intervals based on the inclusion of the endpoints:

• Closed Interval: Includes both endpoints. For example, a week running from Sunday through Saturday is a closed interval.
• Open Interval: Excludes both endpoints.
• Half-Closed (or Half-Open) Interval: Includes one endpoint and excludes the other. This is a hybrid of the previous two interval types.

Some people distinguish the types of intervals by specifying whether each endpoint is included or excluded. The different types would then be closed-closed, closed-open, open-closed, and open-open. However, since datetime intervals are typically closed-open, there is usually no need to distinguish between the two types of half-closed intervals.

It is important to note that when working with intervals involving datetime data, confusion can arise between closed intervals and half-closed intervals. This confusion often stems from thinking in terms of full days, while SQL translates dates to datetime data by converting them to midnight. Therefore, it is crucial to use the correct interval type when converting between date and datetime.

Other Terminology

There are a few other terms that are commonly used when discussing intervals:

• Invalid Interval: An interval with a begin point that is greater than the end point.
• Degenerate Interval: An interval with the same value for both endpoints.
• Closed Degenerate Interval: A degenerate interval that contains a single value.
• Open Degenerate Interval: An empty degenerate interval.
• Half-Closed Degenerate Interval: An invalid interval where the same point cannot be both included and excluded.

Interval Relationships

One of the most common challenges with intervals is understanding how they relate to other intervals. For example, when scheduling a room, it is essential to know if anyone else has reserved that room during a specific time period. Similarly, when job hunting, it is important to determine if your desired salary falls within the salary range for the job(s) you are applying for.

James F. Allen introduced a framework for specific types of interval relations, known as Allen’s Relationship Algebra. This framework provides a way to describe the relationships between intervals, such as precedes, meets, overlaps, contains, equals, started by, etc.

By establishing a widely used framework for discussing intervals within the SQL community, we can simplify conversations and improve our ability to work with intervals effectively.

Intervals play a crucial role in SQL Server databases, and understanding their concepts and terminology is essential for DBAs and developers. By adopting a consistent approach to handling intervals, we can enhance the accuracy and efficiency of our database operations.

References:
[1] Allen’s Interval Algebra