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*From*: "'Martin' via tlaplus" <tlaplus@xxxxxxxxxxxxxxxx>*Date*: Sun, 28 Apr 2024 21:11:44 +0200*References*: <48640047-49ce-4d12-899b-acea04612b3bn@googlegroups.com> <79520297-12e7-4df4-99d0-51e6b1a1dc40@gmail.com> <e7a7f648-facc-43cb-81e0-21b0f582ea05n@googlegroups.com> <09258c76-5002-45c1-8cb0-0c6996ffd05cn@googlegroups.com> <dfb02434-efb5-47c8-ba25-cbc1992b9ed9n@googlegroups.com> <f47132d0-5022-4284-9d66-19a82ab248fd@gmail.com> <cdfd7e38-29ee-4b06-b7c5-07e7353f7798n@googlegroups.com>*User-agent*: Mozilla Thunderbird

cheers, Martin On 4/28/24 20:51, marta zhango wrote:

I understand that proving statements about algorithms does not rely on complex mathematical results. But my quest is to prove statements about mathematics itself (e.g. verifying a mathematical proof of the linearity of a wavelet transform). On Monday, April 29, 2024 at 6:20:24 AM UTC+12 Martin wrote:Most purely mathematical statements in TLA+ I know are about basic properties of the standard library. You can browse through the _proofs.tla files and have a look around. https://github.com/tlaplus/tlapm/tree/main/library As Andrew already mentioned proving statements about algorithms usually does not rely on complex mathematical results. In a way the construction of the algorithm already divides the problem into subtasks that are easier to handle. cheers, Martin On 4/28/24 20:03, marta zhango wrote:It would help me to have a decently long list of mathematical theorems (undergraduate mathematics) proved with TLA+ I can look at. And how to run them and interpret them. On Monday, April 29, 2024 at 2:15:56 AM UTC+12 Andrew Helwer wrote:The introductory material for the TLA+ proof system is admittedly not great at the moment. There is a basic tutorial available on the INRIA website:https://tla.msr-inria.inria.fr/tlaps/content/Documentation/Tutorial/The_example.htmlReally though the best way to learn is to just try to prove a verysimplestatement and see how it goes, reading other peoples' proofs for inspiration. Here are my attempts at some basic proofs:https://github.com/tlaplus/Examples/tree/master/specifications/LearnProofsYou can also look at the tlaplus/examples repo in general, there is a table in the README with checkboxes marking every spec that includes proofs: https://github.com/tlaplus/Examples The TLA+ proof language is usually applied to prove statements that are shallow but broad, as in very simple mathematical statements but a lotofthem. This is what you have to do to prove an algorithm correct. Each individual step in the algorithm is usually mathematically simple, but there are a lot of them. I am not aware of the TLA+ proof language being used to prove "deep" mathematical theorems like you hear coming out oftheRocq and Lean community, but perhaps examples exist. Andrew Helwer On Sunday, April 28, 2024 at 3:42:08 AM UTC-4 marta zhango wrote:Felicitations Martin. The problem I struggle with is that the TLA+ book does not cover the verification of mathematical proofs. purely mathematical. Have scrutinised Stephan's links to actual proofs of Cantor's theorem. But can one use thesoftwareto show that they are indeed correct. This is the field of verification that I have interest in at this moment. Can one find a tutorial about how specific mathematical proofs can be defined and verified ? Thank you so very much Marta

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**Follow-Ups**:

**References**:**[tlaplus] TLA+ for testing computational algorithms rather than verify mathematical proofs***From:*marta zhango

**Re: [tlaplus] TLA+ for testing computational algorithms rather than verify mathematical proofs***From:*'Martin' via tlaplus

**Re: [tlaplus] TLA+ for testing computational algorithms rather than verify mathematical proofs***From:*marta zhango

**Re: [tlaplus] TLA+ for testing computational algorithms rather than verify mathematical proofs***From:*Andrew Helwer

**Re: [tlaplus] TLA+ for testing computational algorithms rather than verify mathematical proofs***From:*marta zhango

**Re: [tlaplus] TLA+ for testing computational algorithms rather than verify mathematical proofs***From:*'Martin' via tlaplus

**Re: [tlaplus] TLA+ for testing computational algorithms rather than verify mathematical proofs***From:*marta zhango

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