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Generally, the language feature for interval computations, which distinguishes it from traditional programming languages is the following: any operation that generates a new object or modifying an existing representation of the object is performed using directed rounding. This is achieved by receiving a guaranteed lower and / or the upper bound of each scalar component of the desired size.

Special mention should be on the operations of the division of two intervals. While in most publications on interval mathematics (and this book is no exception), their authors prohibit division by an interval containing zero.
1.2.3. Syntactic processing. Once the selected object classes and define a set of operations necessary to develop a syntactic processing of language. So far, virtually all of the authors went through the expansion of any known programming language. Basic language expanded in the following areas.
a) The syntax and semantics of the base language does not change. When describing the custom object (interval, interval vector, etc.) each time it is necessary to describe how it is constructed from simple objects, the standard for the base language (predefined in it). Introduction of non-standard language for the basic operations carried out through a description of realizing their routines (routines themselves can also be written in another language).
1.2.4. Using the capabilities of computer algebra. Of particular interest is the tendency to merge "interval" programming language with a computer algebraic system. In such integrated systems can quickly obtain a numerical (interval) value function obtained by analytic transformations on one of the previous stages of the decision.
.1.3. Level interpreter primitives. The result of translation from the language of interval computation is a sequence of primitive objects and operations on them, designed for direct execution of software, firmware or hardware interpreter.
. Among the requirements, which are naturally present in a "good" system for interval calculations can be found and the requirement to give the user the greatest opportunity to increase the accuracy of the results (which usually involved additional resources).