A Coq library for constructive real analysis and algebra, including a model of real numbers and exact real computation.
C-CoRN is a Coq library that formalizes constructive real analysis and algebra, providing a verified framework for reasoning about real numbers, algebraic structures, and calculus. It solves the problem of ensuring mathematical correctness in computational mathematics by offering formally proven results and enabling exact real computation within Coq.
Researchers and developers working in formal verification, constructive mathematics, or theorem proving who need a reliable library for real analysis and algebra in Coq.
Developers choose C-CoRN for its comprehensive, constructively verified approach to real analysis and algebra, unique integration of exact real computation, and strong foundation in Coq's proof assistant ecosystem.
Coq Repository at Nijmegen [maintainers=@spitters,@VincentSe,@Lysxia]
Open-Awesome is built by the community, for the community. Submit a project, suggest an awesome list, or help improve the catalog on GitHub.
Provides axiomatic formalization of structures like setoids, monoids, groups, and fields, enabling rigorous algebraic reasoning in Coq as detailed in the README.
Includes formally proven results for continuity, differentiability, integration, and the Fundamental Theorem of Calculus, ensuring mathematical correctness for real calculus.
Supports fast verified computation inside Coq for real numbers, functions, and integrals, allowing practical applications with guaranteed accuracy per the README.
Emphasizes constructive mathematics, making it suitable for intuitionistic logic and computational implementations where proofs are executable.
Requires manual installation of dependencies like Math-Classes and Bignums with multiple build steps, as noted in the README, which can be error-prone for new users.
Limited to Coq proof assistant, making it unusable outside this environment and reducing interoperability with other mathematical software tools.
Assumes proficiency in Coq and formal verification, with sparse beginner-friendly documentation, hindering adoption by casual developers or students.