An interval is a subset S of a totally ordered set T with the property that whenever x and y are in S and x < z < y then z is in S.
Interval Constraint is a generic term used to denote a constraint in which variables are linked with intervals.
The first is that the input errors and the round-off errors are automatically incorporated into the result interval. Thus, interval evaluation can be viewed as automatically performing both a calculation and an error analysis.
The second is that IA allows one to compute provably correct upper and lower bounds on the range of a function over an interval, and this proves useful in the construction of verifiable constraint solvers, which return intervals that are guaranteed to contain all the real solutions.
Several programs exist to solve interval constraint systems.. Few are mentioned below.