Proof, language, and interaction
HOL Light: A Tutorial Introduction
FMCAD '96 Proceedings of the First International Conference on Formal Methods in Computer-Aided Design
Dependently Typed Records for Representing Mathematical Structure
TPHOLs '00 Proceedings of the 13th International Conference on Theorem Proving in Higher Order Logics
Modular Structures as Dependent Types in Isabelle
TYPES '98 Selected papers from the International Workshop on Types for Proofs and Programs
Interactive Theorem Proving and Program Development
Interactive Theorem Proving and Program Development
Organizing Numerical Theories Using Axiomatic Type Classes
Journal of Automated Reasoning
A modular formalisation of finite group theory
TPHOLs'07 Proceedings of the 20th international conference on Theorem proving in higher order logics
A HOL theory of euclidean space
TPHOLs'05 Proceedings of the 18th international conference on Theorem Proving in Higher Order Logics
Proving bounds for real linear programs in Isabelle/HOL
TPHOLs'05 Proceedings of the 18th international conference on Theorem Proving in Higher Order Logics
Floats and Ropes: A Case Study for Formal Numerical Program Verification
ICALP '09 Proceedings of the 36th Internatilonal Collogquium on Automata, Languages and Programming: Part II
Finite Groups Representation Theory with Coq
Calculemus '09/MKM '09 Proceedings of the 16th Symposium, 8th International Conference. Held as Part of CICM '09 on Intelligent Computer Mathematics
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
A formal quantifier elimination for algebraically closed fields
AISC'10/MKM'10/Calculemus'10 Proceedings of the 10th ASIC and 9th MKM international conference, and 17th Calculemus conference on Intelligent computer mathematics
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
Incidence simplicial matrices formalized in Coq/SSReflect
MKM'11 Proceedings of the 18th Calculemus and 10th international conference on Intelligent computer mathematics
Point-free, set-free concrete linear algebra
ITP'11 Proceedings of the Second international conference on Interactive theorem proving
On the bright side of type classes: instance arguments in Agda
Proceedings of the 16th ACM SIGPLAN international conference on Functional programming
How to make ad hoc proof automation less ad hoc
Proceedings of the 16th ACM SIGPLAN international conference on Functional programming
PLPV '12 Proceedings of the sixth workshop on Programming languages meets program verification
Formal proof of a wave equation resolution scheme: the method error
ITP'10 Proceedings of the First international conference on Interactive Theorem Proving
An efficient coq tactic for deciding kleene algebras
ITP'10 Proceedings of the First international conference on Interactive Theorem Proving
Proof, message and certificate
CICM'12 Proceedings of the 11th international conference on Intelligent Computer Mathematics
Constructive completeness for modal logic with transitive closure
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
Journal of Automated Reasoning
Computing persistent homology within Coq/SSReflect
ACM Transactions on Computational Logic (TOCL)
Canonical structures for the working coq user
ITP'13 Proceedings of the 4th international conference on Interactive Theorem Proving
A machine-checked proof of the odd order theorem
ITP'13 Proceedings of the 4th international conference on Interactive Theorem Proving
Kleene algebra with tests and coq tools for while programs
ITP'13 Proceedings of the 4th international conference on Interactive Theorem Proving
The rooster and the butterflies
CICM'13 Proceedings of the 2013 international conference on Intelligent Computer Mathematics
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In this paper, we present an approach to describe uniformly iterated "big" operations, like $\sum_{i=0}^n f(i)$ or max i茂戮驴 If(i) and to provide lemmas that encapsulate all the commonly used reasoning steps on these constructs.We show that these iterated operations can be handled generically using the syntactic notation and canonical structure facilities provided by the Coqsystem. We then show how these canonical big operations played a crucial enabling role in the study of various parts of linear algebra and multi-dimensional real analysis, as illustrated by the formal proofs of the properties of determinants, of the Cayley-Hamilton theorem and of Kantorovitch's theorem.