Formal Verification Reference - Aura

Tutorial: Introduction to Formal Verification with Lean (Part 1) - HashCloak

A tutorial Formal Verification using Lean for cryptographic engineers. Implement and prove correctness of the One-Time pad following a cryptography book.

Automated Verification of Proofs in the Universal Composability Framework with Markov Decision Processes

Designing cryptographic protocols and proving these rigorously secure is an arduous and challenging task. Among the methods commonly used to prove security of cryptographic protocols, formalizing it in Canneti's Universal Composability (UC) Framework offers several benefits: (1) Modular design, (2) demonstrating that security remains under arbitrary composition and concurrent execution, (3) the security against any computationally polynomially bound adversary. However, working within the UC Framework can be cumbersome, requires a long time commitment by the prover, and it is prone to errors. While utilization of proof assistants in Cryptography and IT Security is a prominent research area, proof assistants for UC are still in their infancy. Here we show our ongoing work to utilize model checking for verification of proofs in the UC Framework, which to the best of our knowledge is the first attempt to do so. In this work we (1) formally create a Markov Decision Process (MDP) encoding a given proof in the UC Framework, (2) define and proof notions of soundness and completeness for the constructed MDP, (3) implement a proof of concept and (4) demonstrate practical feasibility through experimental evaluation. In summary, in this work we lay out the formal foundations for model checking UC proofs and create a tool that can not only be used for proof verification but also as an assistant for developing proofs in the UC Framework.

The Case Against Formal Verification, 50 Years Later - Ivan Gavran

Writings on software correctness, AI, formal verification, and other technical topics.

Theorizing Protocolization II: Atomic Protocol Questions

Solving real coordination problems to discover the formal laws of protocols.

The Unreasonable Sufficiency of Protocols | Summer of Protocols

DRAFT Version 0.99, March 6th, 2023

A modal analysis of staged computation | Journal of the ACM

We show that a type system based on the intuitionistic modal logic S4 provides an expressive framework for specifying and analyzing computation stages in the context of typed λ-calculi and functional languages. We directly demonstrate the sense in which ...

Protocol Reader - Summer of Protocols

The Protocol Reader The Protocol Reader is an 358-page book (currently only available as an epub) comprising 26 foundational essays by 31 authors from the Summer of Protocols program, carefully edited and sequenced to introduce you to the fascinating new discipline of Protocol Studies. It can serve as

Compiling Higher-Order Specifications to SMT Solvers: How to Deal with Rejection Constructively | Proceedings of the 12th ACM SIGPLAN International Conference on Certified Programs and Proofs

We present a decision procedure that combines reasoning about datatypes and codatatypes. The dual of the acyclicity rule for datatypes is a uniqueness rule that identifies observationally equal codatatype values, including cyclic values. The procedure ...

Introducing attested.network: Proof of Payment for ATProtocol - Nick's Blog

attested.network is an open spec for decentralized proof of payments on ATProtocol, built on what we learned making atprotofans.com. It formalizes the three-party attestation model and opens it up for any app to implement.

. · openai/ten-proofs@d0e1ae7

Lean certificates accompanying proofs in mathematics and theoretical computer science - . · openai/ten-proofs@d0e1ae7

Verifying gpt-oss implementations

The OpenAI gpt-oss models are introducing a lot of new concepts to the open-model ecosystem and getting them to perform as expected might ta

Foundations of Algebraic Specification and Formal Software Development

This book provides foundations for software specification and formal software development from the perspective of work on algebraic specification, concentrating on developing basic concepts and studying their fundamental properties. These foundations are built on a solid mathematical basis, using elements of universal algebra, category theory and logic, and this mathematical toolbox provides a convenient language for precisely formulating the concepts involved in software specification and development. Once formally defined, these notions become subject to mathematical investigation, and this interplay between mathematics and software engineering yields results that are mathematically interesting, conceptually revealing, and practically useful. The theory presented by the authors has its origins in work on algebraic specifications that started in the early 1970s, and their treatment is comprehensive. This book contains five kinds of material: the requisite mathematicalfoundations; traditional algebraic specifications; elements of the theory of institutions; formal specification and development; and proof methods. While the book is self-contained, mathematical maturity and familiarity with the problems of software engineering is required; and in the examples that directly relate to programming, the authors assume acquaintance with the concepts of functional programming. The book will be of value to researchers and advanced graduate students in the areas of programming and theoretical computer science.

Mathematics with large language models as provers and verifiers

During 2024 and 2025 the discussion about the theorem-proving capabilities of large language models started reporting interesting success stories, mostly to do with difficult exercises (such as problems from the International Mathematical Olympiad), but also with conjectures [Feldman & Karbasi, arXiv:2509.18383v1] formulated for the purpose of verifying whether the artificial intelligence could prove it. In this paper we report a theorem proving feat achieved by ChatGPT by using a protocol involving different prover and verifier instances of the gpt-5 model working collaboratively. To make sure that the produced proofs do not suffer from hallucinations, the final proof is formally verified by the lean proof assistant, and the conformance of premises and conclusion of the lean code is verified by a human. Our methodology is by no means complete or exact. It was nonetheless able to solve five out of six 2025 IMO problems, and close about a third of the sixty-six number theory conjectures in [Cohen, Journal of Integer Sequences, 2025].

Mathematics with large language models as provers and verifiers

During 2024 and 2025 the discussion about the theorem-proving capabilities of large language models started reporting interesting success stories, mostly to do with difficult exercises (such as problems from the International Mathematical Olympiad), but also with conjectures [Feldman & Karbasi, arXiv:2509.18383v1] formulated for the purpose of verifying whether the artificial intelligence could prove it. In this paper we report a theorem proving feat achieved by ChatGPT by using a protocol involving different prover and verifier instances of the gpt-5 model working collaboratively. To make sure that the produced proofs do not suffer from hallucinations, the final proof is formally verified by the lean proof assistant, and the conformance of premises and conclusion of the lean code is verified by a human. Our methodology is by no means complete or exact. It was nonetheless able to solve five out of six 2025 IMO problems, and close about a third of the sixty-six number theory conjectures in [Cohen, Journal of Integer Sequences, 2025].

The 2026-07-28 Specification

The 2026-07-28 Model Context Protocol specification is out, bringing a stateless protocol core, Multi Round-Trip Requests, header-based routing, cacheable list results, authorization hardening, a formal extensions framework, and updated Tier 1 SDKs.