Refinement of rational end-points real numbers by means of floating-point numbers

Yamine Ait-Ameur
1999 Science of Computer Programming  
This paper addresses the topic of the refinement of exact real numbers. It presents a three-steps formal development towards the implementation of exact real numbers. It considers real numbers as intervals whose end-points are rational numbers. We investigate the possibility to represent these intervals by floating-point numbers as end-points in order to increase the efficiency of the implementation and to use the hardware resources. We show on an extension of the PCF language that this result
more » ... an be carried out but by losing the adequacy property as defined in (Escardo, 1996) . However, we show that it is possible to introduce a weak version of the adequacy property described by a Galois connection defining an abstract interpretation. Soundness and completeness properties are proved in this context. Accuracy analysis by a program analysis of the representation allows to choose between different representations of real numbers. (~ 1999 Elsevier Science B.V. All rights reserved.
doi:10.1016/s0167-6423(98)00008-2 fatcat:pzu2axqunzgchfrdhzg44mf6oq