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nLab > Latest Changes: proof assistants and formalization projects -- list

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  1.  
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeSep 12th 2019

    This is the list from proof assistant – Examples, and was (incompleteky) copied by hand into related entries, but we should make it (as done hereby) a standalone to be !includeed under “Related concepts” in relevant entries

    All I did in editing was to group the proof assistants into “based on type/set theory” and “applicable to homotopy type theory”. Experts please hit “edit” and improve on it

    v1, current

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeSep 12th 2019

    Should Haskell be part of the list?

    • CommentRowNumber3.
    • CommentAuthoratmacen
    • CommentTimeSep 12th 2019

    Re #2, no. Haskell is an ordinary programming language. Actually, I think it’s not really right that a proof assistant is a kind of programming language. Most proof assistants resemble and/or include a programming language though. Going to edit.

    • CommentRowNumber4.
    • CommentAuthoratmacen
    • CommentTimeSep 12th 2019

    Removed Haskell.

    diff, v2, current

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeSep 12th 2019

    Better than removing it would be to include it with proper heading. Maybe “Type-checked programming languages”?

    • CommentRowNumber6.
    • CommentAuthoratmacen
    • CommentTimeSep 12th 2019

    But why would that go on this include? I see Haskell is listed at programming language.

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeSep 12th 2019

    Is there a good chance that a newbie reader stumbling upon a page for proof assistants might be interested in learning about the existence of fully typed programming languages?

    • CommentRowNumber8.
    • CommentAuthoratmacen
    • CommentTimeSep 12th 2019
    • (edited Sep 12th 2019)
    I wouldn’t know. What do you mean by “fully typed”? (I probably wouldn’t know anyway.)
    • CommentRowNumber9.
    • CommentAuthorTim_Porter
    • CommentTimeSep 12th 2019

    Haskell is‘a statically typed, purely functional programming language with type inference and lazy evaluation.” I suggest that a link be added to related pages to include mention of functional programming languages and Haskell in particular.

    • CommentRowNumber10.
    • CommentAuthorMike Shulman
    • CommentTimeSep 12th 2019

    We could, I guess, include a link to a functional programming languages page, but that doesn’t really seem to be to be part of the purpose of a “list of proof assistants” intended to be included in other pages. If some including page also wants a list of functional programming languages, why not have it directly include that?

    Actually, looking at some of the pages where this is included, it also seems a bit weird to me to collapse a list of proof assistants with a list of formalization projects. Why not make them two separate lists?

    Also, why is Metamath given its own bullet point while Mizar/NuPRL/Isabelle/HOL have to share one? Surely the latter four differ among themselves at least as much as they differ from Metamath.

    What distinguishes a “project for formalization of mathematics” from a “library of code in a proof assistant”? For instance, I generally talk about the HoTT/Coq library in the same breath as UniMath as libraries for HoTT in Coq.

    Should we list quantomatic?

    • CommentRowNumber11.
    • CommentAuthorUrs
    • CommentTimeSep 12th 2019
    • (edited Sep 12th 2019)

    There is no deep theory of bullet points underlying this. Please go ahead and edit as you see fit.

    • CommentRowNumber12.
    • CommentAuthorUrs
    • CommentTimeDec 8th 2020

    added item for DisCoPy

    diff, v4, current

  13. added a few proof assistants based upon cubical type theory and modal type theory, as well as the Andromeda proof assistant

    Anonymous

    diff, v5, current

  14. The UniMath project has also started a library in Agda (called unimath-agda)

    Anonymous

    diff, v5, current

    • CommentRowNumber15.
    • CommentAuthorUrs
    • CommentTimeJun 15th 2022
    • (edited Jun 15th 2022)

    I see that you added (here) a bunch of links for cubital type checkers.

    The link you had for cubical Agda I have bent to point to the nLab page section Cubical Agda

    diff, v6, current

    • CommentRowNumber16.
    • CommentAuthorUrs
    • CommentTimeFeb 2nd 2023

    added pointer to 1lab

    diff, v7, current

1 to 16 of 16

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