#ProofAssistant

Pelletier’s Problem 24 in Mizar There are probably several different ways to prove Pelletier’s Problem 24, so we will just investigate one way. Informal Roadmap for the Proof The first thing to do, whenever formalizing anyt…

4 months ago

I worked through one possible solution to proving Pelletier's problem 24 in the #Mizar #proofassistant, but there are others.

thmprover.wordpress.com/2025/10/19/p...

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Schemas and Proofs: A worked example Today, we will work through proving one of Pelletier’s Seventy Five Problems for Testing Automated Theorem Provers. The focus will be on the proof of the claim. Then we will give several &#82…

5 months ago

Despite the tornados and thunder storms, I wrote a brief "worked example" of how to prove one of Pelletier's problems in the #Mizar #proofassistant.

This is part of the "Mizar 101" series of posts.

thmprover.wordpress.com/2025/10/14/s...

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How to check you installed Mizar correctly We will be starting a “Mizar 101” series of posts, which will focus on “first steps in Mizar”. This post will discuss, among other things, “How to check you installed …

5 months ago

I've started a "Mizar 101" series of posts oriented towards people who have just installed the #Mizar #proofassistant, but don't really know what to do from there.

The first thing to check is that you installed Mizar correctly, that it "works".

thmprover.wordpress.com/2025/10/11/h...

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Literate Implementations of Proof Assistants I have been experimenting with literate programming applied to the implementation of a toy HOL, and transcribing the Mizar proof assistant into Knuth’s WEB. This post will be more “prog…

5 months ago

I wrote a little about "literate programming" used to implement proof assistants, mostly about the "literate programming".

#LiterateProgramming #ProofAssistant #Logic #Mathematics

thmprover.wordpress.com/2025/09/16/l...

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Readings shared August 1, 2025 The readings shared in Bluesky on 1 August 2025 are Unconstrained optimization (in Isabelle/HOL). ~ Dustin Bryant. #ITP #IsabelleHOL #Math Seed-Prover: Deep and broad reasoning for automated theorem

7 months ago

Readings shared August 1, 2025. jaalonso.github.io/vestigium/po... #Haskell #LeanProver #Math #ProofAssistant

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Readings shared July 31, 2025 The readings shared in Bluesky on 31 July 2025 are The math is haunted. ~ Dan Abramov. #ProofAssistant #LeanProver #Math #Exercitium: Problemas de programación con Haskell (julio de 2018). #Haskell #

7 months ago

Readings shared July 31, 2025. jaalonso.github.io/vestigium/po... FunctionalProgramming #Haskell #LeanProver #Math #ProofAssistant

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The Math Is Haunted — overreacted A taste of Lean.

7 months ago

The math is haunted. ~ Dan Abramov. overreacted.io/the-math-is-... #ProofAssistant #LeanProver #Math

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Universal Pairs for Diophantine Equations Universal Pairs for Diophantine Equations in the Archive of Formal Proofs

7 months ago

Universal pairs for diophantine equations (in Isabelle/HOL). ~ Marco David et als. www.isa-afp.org/entries/Diop... #ITP #ProofAssistant #IsabelleHOL #Math

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Readings shared July 29, 2025 The readings shared in Bluesky on 29 July 2025 are Algorithmic conversion with surjective pairing: A syntactic and untyped approach. ~ Yiyun Liu, Stephanie Weirich. #FormalVerification #ProofAssistan

7 months ago

Readings shared July 29, 2025. jaalonso.github.io/vestigium/po... #CoqProver #FormalVerification #FunctionalProgramming #Haskell #IMO #ITP #LLMs #LeanProver #MachineLearning #Math #ProofAssistant #Rocq #Rust

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GitHub - harmonic-ai/IMO2025 Contribute to harmonic-ai/IMO2025 development by creating an account on GitHub.

7 months ago

Harmonic's IMO 2025 results (Harmonic's model Aristotle achieved gold medal performance, solving 5 problems). github.com/harmonic-ai/... #FormalVerification #ProofAssistant #LeanProver #LLMs #Math #IMO

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Readings shared July 28, 2025 The readings shared in Bluesky on 28 July 2025 are Gödel's first incompleteness theorem (in Lean4). #FormalVerification #ProofAssistant #LeanProver #Logic #Math Formalized formal logic (in Lean4). #F

7 months ago

Readings shared July 28, 2025. jaalonso.github.io/vestigium/po... #FormalVerification #FunctionalProgramming #Haskell #LeanProver #Logic #Math #ProofAssistant

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7 months ago

Formalized formal logic (in Lean4). formalizedformallogic.github.io/Book/ #FormalVerification #ProofAssistant #LeanProver #Logic #Math

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7 months ago

Gödel's first incompleteness theorem (in Lean4). formalizedformallogic.github.io/Book/first_o... #FormalVerification #ProofAssistant #LeanProver #Logic #Math

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7 months ago

Encoding finite state automata in Agda using coinduction (Evaluating the support for coinduction in Agda). ~ Noky Soekarman. repository.tudelft.nl/file/File_56... #FormalVerification #ProofAssistant #Agda

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7 months ago

Modelling cyclic structures in Agda (Evaluating Agda’s coinduction through modelling graphs). ~ Faizel Mangroe. repository.tudelft.nl/file/File_64... #ProofAssistant #Agda

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Irrationality and Transcendence Criteria for Infinite Series in Isabelle/HOL We give an overview of our formalizations in the proof assistant Isabelle/HOL of certain irrationality and transcendence criteria for infinite series from three different research papers: by Erdős and Straus, Hančl, and Hančl and Rucki. Our formalizations in Isabelle/HOL can be found on the Archive of Formal Proofs. Here we describe selected aspects of the formalization and discuss what this reveals about the use and potential of Isabelle/HOL in formalizing modern mathematical research, particularly in these parts of number theory and analysis.

8 months ago

"Irrationality and Transcendence Criteria for Infinite Series in Isabelle/HOL" by Angeliki Koutsoukou-Argyraki, Wenda Li, and Lawrence Paulson. #ExperimentalMath #ProofAssistant #MathSky

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Ross Duncan

@rossquantum.bsky.social

8 months ago

Hey #quantum people! Are you using #lean? Are you using another theorem prover or proof assistant? What are you using it for? Papers and source repos are especially appreciated.
#automatedreasoning #proofassistant #ai1.0 #quantumcomputing

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Formalizing Ordinal Partition Relations Using Isabelle/HOL This is an overview of a formalization project in the proof assistant Isabelle/HOL of a number of research results in infinitary combinatorics and set theory (more specifically in ordinal partition relations) by Erdős–Milner, Specker, Larson and Nash-Williams, leading to Larson’s proof of the unpublished result by E.C. Milner asserting that for all m \in\mathbb{N}, \omega^\omega \rightarrow (\omega^\omega,m). This material has been recently formalised by Paulson and is available on the Archive of Formal Proofs; here we discuss some of the most challenging aspects of the formalization process. This project is also a demonstration of working with Zermelo–Fraenkel set theory in higher-order logic.

8 months ago

"Formalizing Ordinal Partition Relations Using Isabelle/HOL" by Mirna Džamonja, Angeliki Koutsoukou-Argyraki, and Lawrence Paulson. #ExperimentalMath #ProofAssistant #MathSky

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Simple Type Theory is not too Simple: Grothendieck’s Schemes Without Dependent Types Church’s simple type theory is often deemed too simple for elaborate mathematical constructions. In particular, doubts were raised whether schemes could be formalized in this setting and a challenge was issued. Schemes are sophisticated mathematical objects in algebraic geometry introduced by Alexander Grothendieck in 1960. In this article we report on a successful formalization of schemes in the simple type theory of the proof assistant Isabelle/HOL, and we discuss the design choices which make this work possible. We show in the particular case of schemes how the powerful dependent types of Coq or Lean can be traded for a minimalist apparatus called locales.

9 months ago

"Simple Type Theory is not too Simple: Grothendieck’s Schemes Without Dependent Types" by Anthony Bordg, Lawrence Paulson, and Wenda Li. #ExperimentalMath #Lean #AlgebraicGeometry #ProofAssistant #MathSky

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iMathTutor®

@imathtutor.bsky.social

10 months ago

Terry Tao has mad some progress on developing a proof assistant for asymptotic analysis
#mathematics #math #AsymptoticAnalysis #ProofAssistant.
Source: buff.ly/pEuagHN

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Xena Mathematicians learning Lean by doing.

10 months ago

Also be sure to check the @xenaproject.bsky.social blog to learn more about #Lean #ProofAssistant #MachineLearning #LLM The potential to revolutionise how we do #Math is phenominal.
xenaproject.wordpress.com

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Building the Mathematical Library of the Future A small community of mathematicians is using a software program called Lean to build a new digital repository. They hope it represents the future of their field.

10 months ago

@quantamagazine.bsky.social published a nice article on #Lean #ProofAssistant
www.quantamagazine.org/building-the...

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Schemes in Lean We tell the story of how schemes were formalized in three different ways in the Lean theorem prover.

10 months ago

"Schemes in Lean" by Kevin Buzzard @xenaproject.bsky.social , Chris Hughes, Kenny Lau, Amelia Livingston, Ramon Fernández, and Scott Morrison. #ExperimentalMath #Lean #ProofAssistant #MathSky

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rzeta0

@rzeta0.bsky.social

1 year ago

book cover - maths proofs in lean first steps

if you think writing #maths proofs in code is only for PhDs ...

.. this cause was designed just for you!

* small bite-size examples
* concepts over code
* easy exercises to build confidence

www.amazon.com/dp/B0DWHS1RDJ

#mathematics #lean #lean4 #proofassistant

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Grégoire Locqueville

@glocq.mathstodon.xyz.ap.brid.gy

1 year ago

[Not actually true]

Fun fact: they wanted to rename the Coq proof assistant to "glocq", but since the username was already taken on mathstodon they settled on "rocq" instead.

#coq #proofAssistant #formalMethods

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