A Unified Formal Description of Arithmetic and Set Theoretical Data Types
Symbolic Computation
2010-07-01 v1 Logic in Computer Science
Abstract
We provide a "shared axiomatization" of natural numbers and hereditarily finite sets built around a polymorphic abstraction of bijective base-2 arithmetics. The "axiomatization" is described as a progressive refinement of Haskell type classes with examples of instances converging to an efficient implementation in terms of arbitrary length integers and bit operations. As an instance, we derive algorithms to perform arithmetic operations efficiently directly with hereditarily finite sets. The self-contained source code of the paper is available at http://logic.cse.unt.edu/tarau/research/2010/unified.hs .
Keywords
Cite
@article{arxiv.1006.5768,
title = {A Unified Formal Description of Arithmetic and Set Theoretical Data Types},
author = {Paul Tarau},
journal= {arXiv preprint arXiv:1006.5768},
year = {2010}
}
Comments
15 pages, preprint of CALCULEMUS 2010 conference paper