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Algebraic methods in semantics
Algebraic specifications of computable and semicomputable data types
Theoretical Computer Science
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Handbook of logic in computer science (vol. 1)
Handbook of logic in computer science (vol. 2)
Handbook of logic in computer science (vol. 4)
Journal of the ACM (JACM)
Concrete models of computation for topological algebras
Theoretical Computer Science - Special issue on computability and complexity in analysis
Computable functions and semicomputable sets on many-sorted algebras
Handbook of logic in computer science
On abstract data types presented by multiequations
Theoretical Computer Science
Specifying Real Numbers in CASL
WADT '99 Selected papers from the 14th International Workshop on Recent Trends in Algebraic Development Techniques
Rewrite Systems for Natural, Integral, and Rational Arithmetic
RTA '97 Proceedings of the 8th International Conference on Rewriting Techniques and Applications
Mathematical Structures in Computer Science
Abstract versus concrete computation on metric partial algebras
ACM Transactions on Computational Logic (TOCL)
Case study on algebraic software methodologies for scientific computing
Scientific Programming
Elementary algebraic specifications of the rational function field
CiE'06 Proceedings of the Second conference on Computability in Europe: logical Approaches to Computational Barriers
Theorem Proving with the Real Numbers
Theorem Proving with the Real Numbers
Parametric Linear Arithmetic over Ordered Fields in Isabelle/HOL
Proceedings of the 9th AISC international conference, the 15th Calculemas symposium, and the 7th international MKM conference on Intelligent Computer Mathematics
Meadows and the equational specification of division
Theoretical Computer Science
MetiTarski: An Automatic Theorem Prover for Real-Valued Special Functions
Journal of Automated Reasoning
Fields, meadows and abstract data types
Pillars of computer science
A Process Calculus with Finitary Comprehended Terms
Theory of Computing Systems
Data Linkage Algebra, Data Linkage Dynamics, and Priority Rewriting
Fundamenta Informaticae
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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?