Theorem Proving with the Real Numbers

Authors:
John Harrison
Affiliations:
-
Venue:
Theorem Proving with the Real Numbers
Year:
2011

Citing 0
Cited 31

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TPHOLs '99 Proceedings of the 12th International Conference on Theorem Proving in Higher Order Logics
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TPHOLs '00 Proceedings of the 13th International Conference on Theorem Proving in Higher Order Logics
Using Theorem Proving for Numerical Analysis (Correctness Proof of an Automatic Differentiation Algorithm)

TPHOLs '02 Proceedings of the 15th International Conference on Theorem Proving in Higher Order Logics
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TYPES '00 Selected papers from the International Workshop on Types for Proofs and Programs
A Survey of Exact Arithmetic Implementations

CCA '00 Selected Papers from the 4th International Workshop on Computability and Complexity in Analysis
VSDITLU: a verifiable symbolic definite integral table look-up

CADE-16 Proceedings of the 16th International Conference on Automated Deduction: Automated Deduction
The rational numbers as an abstract data type

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Affine functions and series with co-inductive real numbers

Mathematical Structures in Computer Science
A few exercises in theorem processing

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Engineering and theoretical underpinnings of retrenchment

Science of Computer Programming
Formalization of the Standard Uniform random variable

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Rewriting with Equivalence Relations in ACL2

Journal of Automated Reasoning
Formalization of Continuous Probability Distributions

CADE-21 Proceedings of the 21st international conference on Automated Deduction: Automated Deduction
Formal Analysis of Optical Waveguides in HOL

TPHOLs '09 Proceedings of the 22nd International Conference on Theorem Proving in Higher Order Logics
A constructive formalization of the fundamental theorem of calculus

TYPES'02 Proceedings of the 2002 international conference on Types for proofs and programs
Combining equational reasoning

FroCoS'09 Proceedings of the 7th international conference on Frontiers of combining systems
Quotients revisited for Isabelle/HOL

Proceedings of the 2011 ACM Symposium on Applied Computing
Formal probabilistic analysis: a higher-order logic based approach

ABZ'10 Proceedings of the Second international conference on Abstract State Machines, Alloy, B and Z
A design structure for higher order quotients

TPHOLs'05 Proceedings of the 18th international conference on Theorem Proving in Higher Order Logics
Real number calculations and theorem proving

TPHOLs'05 Proceedings of the 18th international conference on Theorem Proving in Higher Order Logics
Formal proof of a wave equation resolution scheme: the method error

ITP'10 Proceedings of the First international conference on Interactive Theorem Proving
On the formalization of the lebesgue integration theory in HOL

ITP'10 Proceedings of the First international conference on Interactive Theorem Proving
Improving real analysis in coq: a user-friendly approach to integrals and derivatives

CPP'12 Proceedings of the Second international conference on Certified Programs and Proofs
Wave Equation Numerical Resolution: A Comprehensive Mechanized Proof of a C Program

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Formal analysis of steady state errors in feedback control systems using HOL-light

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Formal verification of cyber-physical systems: coping with continuous elements

ICCSA'13 Proceedings of the 13th international conference on Computational Science and Its Applications - Volume 1
An approach for lifetime reliability analysis using theorem proving

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Abstract

The Distinguished Dissertation series is published on behalf of the Conference of Professors and Heads of Computing and the British Computer Society, who annually select the best British PhD dissertations in computer science for publication. The dissertations are selected on behalf of the CPHC by a panel of eight academics. Each dissertation chosen makes a noteworthy contribution to the subject and reaches a high standard of exposition, placing all results clearly in the context of computer science as a whole. In this way computer scientists with significantly different interests are able to grasp the essentials - or even find a means of entry - to an unfamiliar research topic. Theorem Proving with the Real Numbers discusses the formal development of classical mathematics using a computer. It combines traditional lines of research in theorem proving and computer algebra and shows the usefulness of real numbers in verification.