Ramified recurrence with dependent types

Authors:
Norman Danner
Affiliations:
Department of Mathematics, University of California, Los Angeles
Venue:
TLCA'01 Proceedings of the 5th international conference on Typed lambda calculi and applications
Year:
2001

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Abstract

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.