Data structures and program transformation
Science of Computer Programming
Handbook of logic in computer science (vol. 3)
Applied Semantics, International Summer School, APPSEM 2000, Caminha, Portugal, September 9-15, 2000, Advanced Lectures
Realizability of Monotone Coinductive Definitions and Its Application to Program Synthesis
MPC '98 Proceedings of the Mathematics of Program Construction
Real functions incrementally computable by finite automata
Theoretical Computer Science - Mathematical foundations of programming semantics
A certified, corecursive implementation of exact real numbers
Theoretical Computer Science - Real numbers and computers
Iteration and coiteration schemes for higher-order and nested datatypes
Theoretical Computer Science - Foundations of software science and computation structures
Affine functions and series with co-inductive real numbers
Mathematical Structures in Computer Science
Constructive analysis, types and exact real numbers
Mathematical Structures in Computer Science
Semantics of a sequential language for exact real-number computation
Theoretical Computer Science
A Functional Algorithm for Exact Real Integration with Invariant Measures
Electronic Notes in Theoretical Computer Science (ENTCS)
Coinduction for Exact Real Number Computation
Theory of Computing Systems
Realizability interpretation of proofs in constructive analysis
Theory of Computing Systems
Recursive coalgebras from comonads
Information and Computation - Special issue: Seventh workshop on coalgebraic methods in computer science 2004
A computer-verified monadic functional implementation of the integral
Theoretical Computer Science
CiE'10 Proceedings of the Programs, proofs, process and 6th international conference on Computability in Europe
Computer certified efficient exact reals in Coq
MKM'11 Proceedings of the 18th Calculemus and 10th international conference on Intelligent computer mathematics
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
Typed vs. Untyped Realizability
Electronic Notes in Theoretical Computer Science (ENTCS)
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We give a coinductive characterization of the set of continuous functions defined on a compact real interval, and extract certified programs that construct and combine exact real number algorithms with respect to the binary signed digit representation of real numbers. The data type corresponding to the coinductive definition of continuous functions consists of finitely branching non-wellfounded trees describing when the algorithm writes and reads digits. This is a pilot study in using proof-theoretic methods for certified algorithms in exact real arithmetic.