A constructive algebraic hierarchy in Coq
Journal of Symbolic Computation - Integrated reasoning and algebra systems
Universal Algebra in Type Theory
TPHOLs '99 Proceedings of the 12th International Conference on Theorem Proving in Higher Order Logics
Formalizing in Coq Hidden Algebras to Specify Symbolic Computation Systems
Proceedings of the 9th AISC international conference, the 15th Calculemas symposium, and the 7th international MKM conference on Intelligent Computer Mathematics
Local Theory Specifications in Isabelle/Isar
Types for Proofs and Programs
Manifest Fields and Module Mechanisms in Intensional Type Theory
Types for Proofs and Programs
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
Effective homology of bicomplexes, formalized in Coq
Theoretical Computer Science
Large formal wikis: issues and solutions
MKM'11 Proceedings of the 18th Calculemus and 10th international conference on Intelligent computer mathematics
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We present a new formalization of the algebraic hierarchy in Coq, exploiting its new type class mechanism to make practical a solution formerly thought infeasible. Our approach addresses both traditional challenges as well as new ones resulting from our ambition to build upon this development a library of constructive analysis in which abstraction penalties inhibiting efficient computation are reduced to a bare minimum. To support mathematically sound abstract interfaces for ℕ, ℤ, and ℚ, our formalization includes portions of category theory and multisorted universal algebra.