Bend 2: a fast language that blocks AI mistakes via proof. Install: curl -fsSL https://bend-lang.com/install.sh | sh
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The Rocq Prover is an interactive theorem prover, or proof assistant. It provides a formal language to write mathematical definitions, executable algorithms and theorems together with an environment for semi-interactive development of machine-checked proofs.
- proof-assistant
- coq
- theorem-proving
- dependent-types
A modern proof language
- formality
- lambda-calculus
- type-theory
- proof-language
A Proof-oriented Programming Language
- programming-language
- verification
- dependent-types
- smt
Agda is a dependently typed programming language / interactive theorem prover.
- dependent-types
- programming-language
- proof-assistant
- agda
Formal verification for AI: a Lean 4 + Dafny proof checker that catches fake AI proofs (reward hacking), and verified recursive self-improvement (RSI) for coding agents. AI for math, physics and software engineering.
- proof-assistant
- lean4
- ai-agents
- ai-for-math
Lean certificates accompanying Navier-Stokes and Euler results
A port of Coq to Javascript -- Run Coq in your Browser
- coq
- proof-assistant
- javascript
- integrated-development-environment
The Ott tool for writing definitions of programming languages and calculi
NASA PVS Library of Formal Developments
A Library for Representing Recursive and Impure Programs in Coq
Verifying Signal's security at the machine-code level
A formalization of geometry in Coq based on Tarski's axiom system
A library of mechanised undecidability proofs in the Coq proof assistant.
A library of Coq definitions, theorems, and tactics. [maintainers=@gmalecha,@liyishuai]
- coq
- library
- programming
- coq-platform
Hoare Type Theory
- hoare-logic
- hoare-monads
- separation-logic
- coq
Variations on Kirby & Paris' hydra battles and other entertaining math in Coq (collaborative, documented, includes exercises) [maintainer=@Casteran]
- coq
- hydra-battles
- ordinal-notations
- formal-proofs
Monadic effects and equational reasoning in Rocq
- monads
- monad-transformers
- probabilistic-programming
- nondeterminism
A Rocq formalization of information theory and linear error-correcting codes
- information-theory
- error-correcting-codes
- probability
- convexity
The formal proof of the Odd Order Theorem
- coq
- ssreflect
- mathcomp
- feit-thompson-theorem
Partial Commutative Monoids
- partial-commutative-monoid
- separation-logic
- coq
- coq-library
Coq library for reasoning on randomized algorithms [maintainers=@anton-trunov,@volodeyka]
- coq
- randomized-algorithms
- probability
- monad
Coqtail is a library of mathematical theorems and tools proved inside the Coq proof assistant. Results range mostly from arithmetic to real and complex analysis. [maintainer=@jmadiot]
- coq
- complex-analysis
- real-analysis
Completeness and Decidability of Modal Logic Calculi [maintainer=@chdoc]
- coq
- mathcomp
- modal-logics
- ctl