time-interval is a common lisp library for flexibly encoding time intervals. It relies heavily on the local-time library for the representation of particular points in time, or as local-time calls them, timestamps.
The primary motivation for time-interval is to be able to represent periods of time such as "6 months from July 1, 2008". The idea here isn't to represent the start and dates (or times) explicitly, but rather to flexibly represent the interval. The difficulty arises from the fact that a length of time such as "6 months" can't be uniquely represented as a number of days, hours, minutes, etc... Depending on what the starting point is, the number of days (hours, etc...) in a 6-month interval will change. Therefore, we need a way of representing the time intervals and for computing a new exact time given a starting time and a time interval.
The time-interval class is used for representing a given interval of time, such as 6 months, 2 days, 4 hours and 3 seconds. Each of the components can independenly be positive or negative, so we can have, for instance, an interval that represents 1 hour less than two days, by doing:
(make-instance 'time-interval :hours -1 :days 2)
(time-interval :hours -1 :days 2)