Paper Info
Title
A unified formal description of arithmetic and set theoretical data types
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
Year
DOI
Venue
2010
10.1007/978-3-642-14128-7_21
artificial intelligence and symbolic computation
Keywords
DocType
Volume
unified formal description,theoretical data type,peano arithmetic and hereditarily,shared axiomatization,base-2 arithmetics,haskell type class,formal description of arithmetic and set theoretical data types,polymorphic abstraction,efficient implementation,arbitrary length integer,natural number,bit operation,hereditarily finite set,arithmetic operation,polymorphism,peano arithmetic,computational mathematics,source code,data type
Conference
abs/1006.5768
ISSN
ISBN
Citations 
0302-9743
3-642-14127-7
2
PageRank 
References 
Authors
0.45
9
1
Name
Order
Citations
PageRank
Paul Tarau11529113.14