Paper Info
Title
The rational numbers as an abstract data type
Abstract
We give an equational specification of the field operations on the rational numbers under initial algebra semantics using just total field operations and 12 equations. A consequence of this specification is that 0−1 = 0, an interesting equation consistent with the ring axioms and many properties of division. The existence of an equational specification of the rationals without hidden functions was an open question. We also give an axiomatic examination of the divisibility operator, from which some interesting new axioms emerge along with equational specifications of algebras of rationals, including one with the modulus function. Finally, we state some open problems, including: Does there exist an equational specification of the field operations on the rationals without hidden functions that is a complete term rewriting system?
Year
DOI
Venue
2007
10.1145/1219092.1219095
Journal of the ACM
Keywords
DocType
Volume
abstract data types,field operation,axiomatic examination,open problem,interesting new axiom,equations,initial algebra,complete term,total versus partial functions,total field operation,field,rational numbers,algebraic specification,interesting equation,computable algebras,open question,meadow,division-by-zero,abstract data type,rational number,equational specification,hidden function
Journal
54
Issue
ISSN
Citations 
2
0004-5411
33
PageRank 
References 
Authors
2.90
20
2
Name
Order
Citations
PageRank
Jan A. Bergstra11445140.42
John V. Tucker260379.06