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The Proof Society Seminar (https://www.proofsociety.org/proof-theory-seminar/index.html) presents talks by leading researchers in proof theory and from all areas of logic related to proofs. We are affiliated with the Proof Society, and our aims with this seminar are closely aligned with the Proof Society's Manifesto, particularly in enabling communication within the broader scientific community. Everyone who is interested in the subject is warmly invited to attend!

The talks take place online via Zoom, usually on Mondays, approximately once per month. They start at 13:00 UTC and may last up to 75 minutes plus questions.

The seminar organizer is Lev D. Beklemishev (levbekl@gmail.com). The seminar board consists of the committee members of the Proof Society.

03 February 2025, 13:00 UTC

Jeremy Avigad (Carnegie Mellon University)

Verifying Proofs on Blockchain

In cryptography, a *club227889084 (*proof) system* is a protocol between a prover and a verifier that enables the prover to convince the verifier that a claim is true. They are often probabilistic; given a source of randomness, it is often more efficient to convince the verifier only that it is very likely that the claim is true. Such proof systems now have interesting applications to blockchain technology, where they are used, among other things, to validate the execution of smart contracts.

It is easy to make mistakes when implementing cryptographic protocols and designing smart contracts, and billions of dollars are lost to hacks every year. Fortunately, another proof technology can help: interactive proof assistants, which have long been used to verify hardware and software systems, can also be used to verify the correctness of cryptographic protocols.

In this talk, I will describe some formal verification efforts I have carried out with colleagues at StarkWare Industries using the Lean proof assistant. I will explain some of the ideas behind smart contracts and interactive proof assistants without assuming familiarity with either.

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