On arithmetic computations with hereditarily finite sets, functions and types

Authors:
Paul Tarau
Affiliations:
Department of Computer Science and Engineering, University of North Texas
Venue:
ICTAC'10 Proceedings of the 7th International colloquium conference on Theoretical aspects of computing
Year:
2010

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Abstract

Starting from an executable "shared axiomatization" of a number of bi-interpretable theories (Peano arithmetic, hereditarily finite sets and functions) we introduce generic algorithms that can be instantiated to implement the usual arithmetic operations in terms of (purely symbolic) hereditarily finite constructs, as well as the type language of Gödel's System T. The Haskell code in the paper is available at http://logic.cse.unt.edu/tarau/research/2010/short_shared.hs.