Constructing the real numbers in HOL
HOL'92 Proceedings of the IFIP TC10/WG10.2 Workshop on Higher Order Logic Theorem Proving and its Applications
A Constructive Proof of the Fundamental Theorem of Algebra without Using the Rationals
TYPES '00 Selected papers from the International Workshop on Types for Proofs and Programs
Some combinatorial Lemmas in topology
IBM Journal of Research and Development
A proof-producing decision procedure for real arithmetic
CADE' 20 Proceedings of the 20th international conference on Automated Deduction
TPHOLs '08 Proceedings of the 21st International Conference on Theorem Proving in Higher Order Logics
Formal Verification of C Systems Code
Journal of Automated Reasoning
Isabelle Theories for Machine Words
Electronic Notes in Theoretical Computer Science (ENTCS)
TPHOLs '09 Proceedings of the 22nd International Conference on Theorem Proving in Higher Order Logics
Flyspeck II: the basic linear programs
Annals of Mathematics and Artificial Intelligence
Formally verified conditions for regularity of interval matrices
AISC'10/MKM'10/Calculemus'10 Proceedings of the 10th ASIC and 9th MKM international conference, and 17th Calculemus conference on Intelligent computer mathematics
Point-free, set-free concrete linear algebra
ITP'11 Proceedings of the Second international conference on Interactive theorem proving
Three chapters of measure theory in Isabelle/HOL
ITP'11 Proceedings of the Second international conference on Interactive theorem proving
LCF-style bit-blasting in HOL4
ITP'11 Proceedings of the Second international conference on Interactive theorem proving
A Certified Proof of the Cartan Fixed Point Theorems
Journal of Automated Reasoning
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
Reconstruction of z3's bit-vector proofs in HOL4 and Isabelle/HOL
CPP'11 Proceedings of the First international conference on Certified Programs and Proofs
Coquet: a coq library for verifying hardware
CPP'11 Proceedings of the First international conference on Certified Programs and Proofs
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
The HOL Light Theory of Euclidean Space
Journal of Automated Reasoning
Wave Equation Numerical Resolution: A Comprehensive Mechanized Proof of a C Program
Journal of Automated Reasoning
Formal analysis of steady state errors in feedback control systems using HOL-light
Proceedings of the Conference on Design, Automation and Test in Europe
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
Type classes and filters for mathematical analysis in Isabelle/HOL
ITP'13 Proceedings of the 4th international conference on Interactive Theorem Proving
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We describe a formalization of the elementary algebra, topology and analysis of finite-dimensional Euclidean space in the HOL Light theorem prover. (Euclidean space is ${\mathbb R}^{N}$ with the usual notion of distance.) A notable feature is that the HOL type system is used to encode the dimension N in a simple and useful way, even though HOL does not permit dependent types. In the resulting theory the HOL type system, far from getting in the way, naturally imposes the correct dimensional constraints, e.g. checking compatibility in matrix multiplication. Among the interesting later developments of the theory are a partial decision procedure for the theory of vector spaces (based on a more general algorithm due to Solovay) and a formal proof of various classic theorems of topology and analysis for arbitrary N-dimensional Euclidean space, e.g. Brouwer's fixpoint theorem and the differentiability of inverse functions.