An algorithmic approach to p-adic integers

  • Steven Vickers
Part VI New Directions
Part of the Lecture Notes in Computer Science book series (LNCS, volume 298)


The ring of p-adic integers can be embedded as the maximal elements in a Scott domain with algebraic structure. We show how definitions and proofs in the mathematical theory of p-adics can be replaced by algorithms on the partial elements and formal programming methods working on the algorithms. Certain types of argument translate naturally into non-deterministic algorithms using the Smyth power domain.


Commutative Ring Maximal Element Domain Theory Congruence Class Refined Function 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • Steven Vickers
    • 1
  1. 1.Dept of ComputingImperial CollegeLondon

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