Complexity theory of real functions
Complexity theory of real functions
Completing the rationals and metric spaces in LEGO
Papers presented at the second annual Workshop on Logical environments
Computable analysis: an introduction
Computable analysis: an introduction
Implementing Constructive Real Analysis: Preliminary Report
Constructivity in Computer Science, Summer Symposium
Applied Semantics, International Summer School, APPSEM 2000, Caminha, Portugal, September 9-15, 2000, Advanced Lectures
A Universal Characterization of the Closed Euclidean Interval
LICS '01 Proceedings of the 16th Annual IEEE Symposium on Logic in Computer Science
A certified, corecursive implementation of exact real numbers
Theoretical Computer Science - Real numbers and computers
Inverting monotone continuous functions in constructive analysis
CiE'06 Proceedings of the Second conference on Computability in Europe: logical Approaches to Computational Barriers
Formalising exact arithmetic in type theory
CiE'05 Proceedings of the First international conference on Computability in Europe: new Computational Paradigms
Coinductive correctness of homographic and quadratic algorithms for exact real numbers
TYPES'06 Proceedings of the 2006 international conference on Types for proofs and programs
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We describe two representations for real numbers, signed digit streams and Cauchy sequences. We give coinductive proofs for the correctness of functions converting between these two representations to show the adequacy of signed digit stream representation. We also show a coinductive proof for the correctness of a corecursive program for the average function with regard to the signed digit stream representation. We implemented this proof in the interactive proof system Minlog. Thus, reliable, corecursive functions for real computation can be guaranteed, which is very helpful in formal software development for real numbers.