An informal introduction to a high level language with applications to interval mathematics

The main problem of interval computations is as follows:given sets of possible valuesX _i for variablesx _i, and an algorithmf:R ⁿ → R, to.estimate the rangef(X ₁, ..,X _n ) of the possible values off(x ₁, ...,x _n ). In many real-life, situations setsX _i are not intervals. To handle such problems, it is desirable to add set data type and operations with sets to a programming language. it is well known that the entire mathematics can be formulated in terms of sets. So, if we already have a set as a data type, why have anything else. The main reason, is that expression in terms of sets is often clumsy. To avoid this clumsiness, it has been suggested to use not only sets, but alsobags (multisets), in which an element can have multiple occurrences. Bags are used in many areas of Computer Science, and recently, several languages have appeared that use the bag as a basic data type. In this paper, we explain the main ideas behind bag languages, and we also show:

· that bag languages are naturally parallelizable, thus leading to a parallelization of the coresponding generalized interval computations;

· and that bag languages can be also helpfully applied to traditional interval computations (where setsX _i are intervals).