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Real number computability and domain theory

  • Pietro Di Gianantonio
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 711)

Abstract

We propose a possible implementation, using lazy functional programming, of the exact computation on real numbers. Using domain theory we can analyze this kind of computation and give a definition of computability for the functions on the real number. This definition turns out to be equivalent to other definitions given in the literature using different methods.

Domain theory is a useful tool to study higher order computability on the real numbers. An interesting connection between Scott Topology and the topologies on the real line and on the space of the real functions is stated. The main original result in this work is the proof that every computable functional on real numbers is continuous w.r.t. the compact open topology.

Keywords

Computable Function Canonical Representation Domain Theory Compact Open Topology Real Continuous Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Pietro Di Gianantonio
    • 1
  1. 1.Dip. di Matematica e InformaticaUniversità di UdineUdineItaly

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