Ramied Recurrence with Dependent Types

  • Norman Danner
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2044)


We present a version of Gödel’s system T in which the types are ramified in the style of Leivant and a system of dependent typing is introduced. The dependent typing allows the definition of recursively defined types, where the recursion is controlled by ramification; these recursively defined types in turn allow the definition of functions by repeated iteration. We then analyze a subsystem of the full system and show that it defines exactly the primitive recursive functions. This result supports the view that when data use is regulated (for example, by ramification), standard function constructions are intimately connected with standard type-theoretic constructions.


Inference Rule Product Rule Object Type High Type Dependent Type 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Norman Danner
    • 1
  1. 1.Department of MathematicsUniversity of CaliforniaLos AngelesUSA

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