Information and Computation - Semantics of Data Types
Infinite objects in type theory
TYPES '93 Proceedings of the international workshop on Types for proofs and programs
Constructive mathematics: a foundation for computable analysis
Theoretical Computer Science - Special issue on computability and complexity in analysis
Computable analysis: an introduction
Computable analysis: an introduction
Codifying Guarded Definitions with Recursive Schemes
TYPES '94 Selected papers from the International Workshop on Types for Proofs and Programs
Constructive Reals in Coq: Axioms and Categoricity
TYPES '00 Selected papers from the International Workshop on Types for Proofs and Programs
A Tour with Constructive Real Numbers
TYPES '00 Selected papers from the International Workshop on Types for Proofs and Programs
Implementing Constructive Real Analysis: Preliminary Report
Constructivity in Computer Science, Summer Symposium
Semantics of Exact Real Arithmetic
LICS '97 Proceedings of the 12th Annual IEEE Symposium on Logic in Computer Science
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
From coinductive proofs to exact real arithmetic
CSL'09/EACSL'09 Proceedings of the 23rd CSL international conference and 18th EACSL Annual conference on Computer science logic
CiE'10 Proceedings of the Programs, proofs, process and 6th international conference on Computability in Europe
Minlog: a tool for program extraction supporting algebras and coalgebras
CALCO'11 Proceedings of the 4th international conference on Algebra and coalgebra in computer science
Coinductive proofs for basic real computation
CiE'06 Proceedings of the Second conference on Computability in Europe: logical Approaches to Computational Barriers
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We implement exact real numbers in the logical framework Coq using streams, i.e., infinite sequences, of digits, and characterize constructive real numbers through a minimal axiomatization. We prove that our construction inhabits the axiomatization, working formally with coinductive types and corecursive proofs. Thus we obtain reliable, corecursive algorithms for computing on real numbers.