Analysis
A formal real analysis library for the Coq/Rocq proof assistant, built on the Mathematical Components library.
What is Analysis?
MathComp-Analysis is a formal real analysis library for the Coq/Rocq proof assistant. It provides a comprehensive suite of theories for classical analysis, topology, and measure theory, built on top of the Mathematical Components library. It solves the problem of rigorously formalizing advanced mathematical concepts in a proof assistant while maintaining compatibility with existing algebraic hierarchies.
Researchers and formal verification engineers working in mathematical analysis, theorem proving, or dependent type theory who need to formalize and verify real analysis theorems in Coq/Rocq.
Developers choose MathComp-Analysis for its deep integration with the Mathematical Components ecosystem, its structured approach to mathematical hierarchies, and its comprehensive coverage of analysis topics from basic topology to advanced measure theory.
Overview
Mathematical Components compliant Analysis Library
Use Cases
Best For
- Formalizing topology and normed spaces in Coq
- Verifying measure theory and integration theorems
- Building upon Mathematical Components for analysis proofs
- Developing formal proofs for probabilistic programs
- Teaching real analysis with formal verification
- Extending Coq's standard library with advanced analysis
Not Ideal For
- Projects using proof assistants other than Coq/Rocq, such as Lean or Isabelle
- Informal mathematical development or rapid prototyping without formal verification requirements
- Teams without prior experience in Coq and the Mathematical Components library
- Applications focused on numerical computation or real-time simulation rather than proof formalization
Pros & Cons
Pros
Provides a layer for classical reasoning within Coq's constructive environment, enabling formalization of classical analysis theorems as highlighted in the classical reasoning feature.
Deeply integrates with Mathematical Components' algebraic hierarchies, offering structured and scalable formalization, as evidenced by its compatibility with MathComp packages.
Includes advanced theories for topology, normed spaces, measure theory, and more, with references to formalizations like the Lebesgue differentiation theorem.
Maintains stability with deprecation warnings and systematic change logging, as noted in the CHANGELOG files to ease transitions.
Cons
Requires specific versions of multiple MathComp packages and Hierarchy Builder, making installation and updates cumbersome, as listed in the dependencies section.
Includes experimental packages like coq-mathcomp-experimental-reals, which may lack stability or full support, as indicated in the package list.
Assumes proficiency in Coq, MathComp, and dependent type theory, posing a significant barrier for newcomers, with documentation primarily in academic papers and source headers.
Frequently Asked Questions
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