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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeJun 18th 2013

    this MO comment made me realize that we didn’t have an entry proof assistant, so I started one

    • CommentRowNumber2.
    • CommentAuthorGuest
    • CommentTimeAug 18th 2019
    This is Roger Witte. I don't know why metamath is so frequently forgotten in these discussions!

    It is at

    The core language is tiny and so there are many independently written proof verifiers - ¿might be useful for those worried about a bug in the implementation? - if I remember rightly, in the comments to Stefan O'Rear implements a metamath verifier in turing machine to lower the bound on the smallest busy beaver number that cannot be proved to exist in ZF

    It only admits one rule of deduction - textual substitution of all occurrences of a variable in a term by a term subject to distinct variable constraints.

    This gives rise to a very Hilbert style - lot's of axioms (especially since there's no difference between an axiom and a definition).
    There is a large ZFC library, a decent NFU library, and the beginnings of an IZF library.
    • CommentRowNumber3.
    • CommentAuthoratmacen
    • CommentTimeAug 18th 2019
    1. Added Metamath using the URL Roger Witte just commented about on the nForum thread. Also added Arend, why not?

    2. Removed prototype CLF from the list of example proof assistant software. Thanks, but it isn’t implemented yet, so no. That page is about design work leading towards a prototype.

    diff, v21, current

    • CommentRowNumber4.
    • CommentAuthoratmacen
    • CommentTimeAug 18th 2019

    Roger, I think it would’ve been fine for you to add the link yourself. Metamath does seem to be a proof assistant, after all. The regular editors of nLab don’t seem fussy about what kind of information goes on pages as long as it’s relevant, and attempts to be accurate and useful. If they don’t like a change, they discuss it and and possibly undo it.

    Since you have some things to say about Metamath, would you like to create a page for it? Then this page could link to that.

    • CommentRowNumber5.
    • CommentAuthoratmacen
    • CommentTimeSep 12th 2019

    Changed the first sentence saying a proof assistant is a kind of programming language. I don’t think that’s right. Now it says it’s a kind of software. Also added right afterward: Many proof assistants resemble and/or include a programming language.

    diff, v25, current

  1. I changed

    There are two threads of current development in proof systems: foundational and coverage.


    The only thread of current development in proof systems is foundational.

    The reason is that the coverage thread is not cover in the article.


    diff, v26, current

    • CommentRowNumber7.
    • CommentAuthoratmacen
    • CommentTimeApr 16th 2020

    Anonymous, there is a difference between a thread of development not being discussed in a given place, and not existing at all. So I’d say your change is totally wrong.

    Unrelatedly, reading the article just now, it already didn’t make much sense to me. This problem is carried over from the MO comment it copied.

    • CommentRowNumber8.
    • CommentAuthorMike Shulman
    • CommentTimeApr 16th 2020

    Yes, your justification given for that change does not make sense. But i don’t know what “coverage” means either; does it just mean formalizing more and more of mathematics?

    • CommentRowNumber9.
    • CommentAuthorDavid_Corfield
    • CommentTimeApr 16th 2020

    I don’t know what ’foundational’ means on its own. But like Mike I didn’t know what coverage meant. What’s the contrast?

    • CommentRowNumber10.
    • CommentAuthorMike Shulman
    • CommentTimeApr 16th 2020

    Rereading the original comment, I think the “coverage” was supposed to be explained in the paragraph beginning “The much larger work”. I edited the page to clarify this (and reverted the previous change).

    • CommentRowNumber11.
    • CommentAuthorUrs
    • CommentTimeJan 25th 2023

    trying to polish-up the list of references (and failing)

    Deleting this item

    • Oscar Lanford III., Computer assisted proofs in analysis, Proceedings of the International Congress of Mathematicians, 1986 (pdf)

    because the link is dead and I haven’t found a quick fix for it.

    But added this which looks like it might be the text in question, or close to it:

    removed this item

    because it doesn’t really seem to fit here (it might fit at Coq, as “Simpson’s personal Coq code” or something)

    diff, v29, current