Computable analysis: an introduction
Computable analysis: an introduction
The realizability approach to computable analysis and topology
The realizability approach to computable analysis and topology
Interactive Theorem Proving and Program Development
Interactive Theorem Proving and Program Development
RealLib: An efficient implementation of exact real arithmetic
Mathematical Structures in Computer Science
RZ: A Tool for Bringing Constructive and Computable Mathematics Closer to Programming Practice
CiE '07 Proceedings of the 3rd conference on Computability in Europe: Computation and Logic in the Real World
The dedekind reals in abstract stone duality
Mathematical Structures in Computer Science
The world's shortest correct exact real arithmetic program?
Information and Computation
Some steps into verification of exact real arithmetic
NFM'12 Proceedings of the 4th international conference on NASA Formal Methods
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RZ is a tool which translates axiomatizations of mathematical structures to program specifications using the realizability interpretation of logic. This helps programmers correctly implement data structures for computable mathematics. RZ does not prescribe a particular method of implementation, but allows programmers to write efficient code by hand, or to extract trusted code from formal proofs, if they so desire. We used this methodology to axiomatize real numbers and implemented the specification computed by RZ. The axiomatization is the standard domain-theoretic construction of reals as the maximal elements of the interval domain, while the implementation closely follows current state-of-the-art implementations of exact real arithmetic. Our results shows not only that the theory and practice of computable mathematics can coexist, but also that they work together harmoniously.