Abstract
We present a weak theory of the real numbers in the first order specification language CASL. The aim is to provide a datatype for practical purposes, including the central notions and results of basic analysis. Our theory captures for instance e and pi, as well as the trigonometric and other standard functions. Concepts such as continuity, differentiation and integration are shown to be definable and tractable in this setting; Newton's Method is presented as an example of a numerical application. Finally, we provide a proper connection between the specified datatype and specifications of the real numbers in higher order logic and various set theories.
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