This book introduces an object oriented approach to compiler design and scientific computation. The main purpose of the book is to introduce safe mathematical data types for mathematical computation. Some of the most important types developed are expanded real number data types, fixed point data types for C++ style languages, and interval data types. Much of the analysis contained herein deals with the interval data type.

The book also gives a fully detailed description of a C++ style language with emphasis on mathematical calculations to be used in the sciences. The idea is to create a user friendly third generation language that would allow for safe computation. This would allow scientists and engineers to focus on the correctness of their algorithms, rather than the nuances of the data types themselves.