%0 Conference Paper %1 RoggenbachEA00 %A Roggenbach, Markus %A Schröder, Lutz %A Mossakowski, Till %B Recent Developments in Algebraic Development Techniques, 14th International Workshop, WADT'99 %D 2000 %E Choppy, Christine %E Bert, Didier %I Springer; Berlin; http://www.springer.de %K CASL numbers real %P 146--161 %T Specifying real numbers in CASL %U http://www.springerlink.com/openurl.asp?genre=article&issn=0302-9743&volume=1827&spage=146 %V 1827 %X 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. %@ 3-540-67898-0

@inproceedings{RoggenbachEA00, 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. }, added-at = {2016-08-05T15:59:03.000+0200}, author = {Roggenbach, Markus and Schr{\"o}der, Lutz and Mossakowski, Till}, biburl = {https://www.bibsonomy.org/bibtex/2393639455726264e3b786884fb1f021d/tillmo}, booktitle = {Recent Developments in Algebraic Development Techniques, 14th International Workshop, WADT'99}, editor = {Choppy, Christine and Bert, Didier}, interhash = {0318fe68022a81e2c358e1d1094f9ae6}, intrahash = {393639455726264e3b786884fb1f021d}, isbn = {3-540-67898-0}, keywords = {CASL numbers real}, pages = {146--161}, psurl = {http://www.informatik.uni-bremen.de/~lschrode/reals.ps.gz}, publisher = {Springer; Berlin; http://www.springer.de}, series = {Lecture Notes in Computer Science}, status = {Reviewed}, timestamp = {2016-08-05T15:59:03.000+0200}, title = {Specifying real numbers in {CASL}}, url = {http://www.springerlink.com/openurl.asp?genre=article&issn=0302-9743&volume=1827&spage=146}, volume = 1827, year = 2000 }