Time Algebra

Note: This is a work in progress, but will give insight into how I am thinking about this.

The timelanguage code supports a set of operations and transformations that are logical outgrowths of this model of time. The simple notation below indicates a derivation with an arrow, and any necessary parameter for the operation as a word in the middle of the arrow, so

CalendarDate ---zone---> TimeInterval

means "A TimeInterval can be derived from a CalendarDate given a zone (TimeZone)."

This "algebra" is slightly different than assigning responsibilities to classes. The goal here is to have a consistent system of logical statements and computations that are expressive and convenient. Although responsibility for each computation will be assigned to some object, that may not be the receiver. To make the language more fluid, and to make a more complete algebra, many "convenience" methods will be added, which simply delegate some computation to the class that does have responsibility.

For example, TimeInterval class is responsible for creating TimeIntervals, but TimePoint has an operation "until" that delegates to TimeInterval. This is to support an expression of an interval like


which should be the same as

TimeInterval.over(fiveOClock, tenOClock)

Time/Calendar Mapping:

Note: all transformations between Time and Calendar also have the implicit argument of a calendar, but the GregorianCalendar is the (currently hard-coded) default. No such default seems prudent for TimeZone (zone), so it is always required.

Calendar Date ---zone-----> TimeInterval

CalendarInterval ---zone----> TimeInterval

TimePoint ---zone---> CalendarDate

TimePoint <---zone & format---> String representation

The following conversions are not possible:

CalendarDate ---X--- TimePoint

Duration of months (calendar) ---X--- Duration of milliseconds (time)

Calendar Duration (Months) --- TimePoint of either endpoint---> TimeInterval

Interval Algebra:

TimeInterval and CalendarInterval are both derived from ComparableInterval, which could be used for any set of objects which implement Comparable interface. Any such extention of ComparableInterval supports the following operations.

interval includes element ---> boolean

interval intersects interval ---> boolean

interval intersection interval ---> interval

Some of the theoretical considerations of intervals are discussed here.

Note: TimeInterval creation methods default to half open, [a, b), which is typical of most time applications. This can be overriden by explicitly specifying the inclusion of the end points.

Time Operations

Note: Some of these operations are not available in the current version.

TimePoint + Duration ---> TimePoint

TimePoint until Duration ---> TimeInterval

TimePoint until TimePoint ---> TimeInterval

TimeInterval start ---> TimePoint

TimeInterval end ---> TimePoint

TimeInterval length ---> Duration

Duration + Duration ---> Duration

Duration - Duration ---> Duration

TimeInterval iterate Duration ---> sub TimeIntervals (count or iterate)

TimeInterval appended by Duration ---> TimeInterval

TimeInterval prepended by Duration ---> TimeInterval

Calendar Time Operations

Calendar Date until Calendar Date ---> Date Interval

Calendar Date until Calendar Duration ---calendar---> Date Interval

Calendar Duration from Calendar Date ---calendar---> Date Interval

*TimePoint until Calendar Duration ---calendar---> Time Interval (*mapping Calendar/Physical)

Calendar Date + Calendar Duration (Months) ---calendar---> Calendar Date

Calendar Interval length---> Calendar Duration

Calendar Duration + Calendar Duration ---> Calendar Duration

DateInterval ---CalendarDuration---> sub DateIntervals (count or iterate)


Business Calendar

Business Calendar is a Time Line of non-overlapping Intervals, either DateIntervals or TimeIntervals.

DateInterval --bus calendar---> Duration

CalendarDate until CalendarDuration ---bus calendar---> Duration


Physical Time Units

Weeks, Days, Hours, Minutes, Seconds, Milliseconds

Duration ---physical units---> Representation

Calendar Based Units

Months, Quarters, Years

Calendar Duration ---calendar units---> Representation