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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 resultdoi:10.1016/s0167-6423(98)00008-2 fatcat:pzu2axqunzgchfrdhzg44mf6oq