Domains for computation in mathematics, physics and exact real arithmetic
Wepresent asurvey of therecent applications ofcontinuous domains forpro- viding simple computational models for classical spaces in mathematics including the real line, countably based locally compact spaces, complete separablemetric spaces, separable Banachspacesandspacesofprobability distributions. Itisshownhowthesemodelshavea logicalandeectivepresentationandhowtheyareusedtogivea computationalframeworkin severalareasinmathematicsandphysics. Theseincludefractalgeometry, wherenewresults on existence and uniqueness of attractors and invariant distributions have been obtained, measureandintegrationtheory,whereageneralizationoftheRiemanntheoryofintegration has been developed, and real arithmetic, where a feasible setting for exact computer arith- metichasbeenformulated. Wegiveanumberofalgorithmsforcomputationinthetheoryof iteratedfunctionsystemswithapplicationsinstatisticalphysicsandinperioddoublingroute tochaos;wealsoshowhowecientalgor ithmshavebeenobtainedfo rcomputingelementary functionsinexactrealarithmetic.