Information and Computation - Semantics of Data Types
Computational lambda-calculus and monads
Proceedings of the Fourth Annual Symposium on Logic in computer science
A new kind of science
Extensional Constructs in Intensional Type Theory
Extensional Constructs in Intensional Type Theory
A compiled implementation of strong reduction
Proceedings of the seventh ACM SIGPLAN international conference on Functional programming
COLOG '88 Proceedings of the International Conference on Computer Logic
Interactive Theorem Proving and Program Development
Interactive Theorem Proving and Program Development
Affine functions and series with co-inductive real numbers
Mathematical Structures in Computer Science
A monadic, functional implementation of real numbers
Mathematical Structures in Computer Science
Extraction in Coq: An Overview
CiE '08 Proceedings of the 4th conference on Computability in Europe: Logic and Theory of Algorithms
Certified Exact Transcendental Real Number Computation in Coq
TPHOLs '08 Proceedings of the 21st International Conference on Theorem Proving in Higher Order Logics
TPHOLs '08 Proceedings of the 21st International Conference on Theorem Proving in Higher Order Logics
TPHOLs '09 Proceedings of the 22nd International Conference on Theorem Proving in Higher Order Logics
Packaging Mathematical Structures
TPHOLs '09 Proceedings of the 22nd International Conference on Theorem Proving in Higher Order Logics
Formal Verification of Exact Computations Using Newton's Method
TPHOLs '09 Proceedings of the 22nd International Conference on Theorem Proving in Higher Order Logics
A Large-Scale Experiment in Executing Extracted Programs
Electronic Notes in Theoretical Computer Science (ENTCS)
Certified exact real arithmetic using co-induction in arbitrary integer base
FLOPS'08 Proceedings of the 9th international conference on Functional and logic programming
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
A computer-verified monadic functional implementation of the integral
Theoretical Computer Science
Flocq: A Unified Library for Proving Floating-Point Algorithms in Coq
ARITH '11 Proceedings of the 2011 IEEE 20th Symposium on Computer Arithmetic
Extending coq with imperative features and its application to SAT verification
ITP'10 Proceedings of the First international conference on Interactive Theorem Proving
Rigorous polynomial approximation using taylor models in Coq
NFM'12 Proceedings of the 4th international conference on NASA Formal Methods
Towards a certified computation of homology groups for digital images
CTIC'12 Proceedings of the 4th international conference on Computational Topology in Image Context
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Floating point operations are fast, but require continuous effort on the part of the user in order to ensure that the results are correct. This burden can be shifted away from the user by providing a library of exact analysis in which the computer handles the error estimates. We provide an implementation of the exact real numbers in the Coq proof assistant. This improves on the earlier Coq-implementation by O'Connor in two ways: we use dyadic rationals built from the machine integers and we optimize computation of power series by using approximate division. Moreover, we use type classes for clean mathematical interfaces. This appears to be the first time that type classes are used in heavy computation. We obtain over a 100 times speed up of the basic operations and indications for improving the Coq system.