Implementing Real Numbers With RZ

Andrej Bauer, Iztok Kavkler
2008 Electronical Notes in Theoretical Computer Science  
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
more » ... ion 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.
doi:10.1016/j.entcs.2008.03.027 fatcat:jahsbjrqdvanrfgjudjgmpkzpi