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  1. Decidable language =/= decidable type checking.

    Arvid Marx

    diff, v23, current

    • CommentRowNumber2.
    • CommentAuthorMike Shulman
    • CommentTimeDec 22nd 2019

    I don’t think I even know what a “decidable language” is. Do you mean decidability of type inhabitation?

    • CommentRowNumber3.
    • CommentAuthorGuest
    • CommentTimeJan 6th 2020
    Yes, that's what I meant in this case, and it read like this was the intended meaning despite very obviously being wrong.

    -- Arvid Marx
    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeMay 13th 2021
    • (edited May 13th 2021)

    added pointer to:

    diff, v24, current

    • CommentRowNumber5.
    • CommentAuthornLab edit announcer
    • CommentTimeAug 31st 2022
    • (edited Oct 17th 2022 by Christian Sattler)

    Adding XTT as an example of an extensional cubical type theory, and adding a paper where XTT was defined as a reference:


    diff, v26, current

  2. adding reference


    diff, v27, current

    • CommentRowNumber7.
    • CommentAuthorMike Shulman
    • CommentTimeSep 1st 2022

    Added explanation of why “extensional”.

    diff, v28, current

    • CommentRowNumber8.
    • CommentAuthorMike Shulman
    • CommentTimeSep 1st 2022

    I would kind of like to split this page into “extensional type theory”, referring only to the historically accurate definitionally extensional type theory, and another page called something like “set-level type theory” that includes also the so-called “propositionally extensional” type theories like MLTT+UIP, Agda-with-K, OTT, and XTT. I think the expansion of the meaning of “extensional type theory” to the latter class was a mistake and we should try to fix it. We probably can’t immediately fix all the pages that use that terminology, but we can make a note at “extensional type theory” that you might have meant “set-level type theory” and fix them as we find them.


    • CommentRowNumber9.
    • CommentAuthorjonsterling
    • CommentTimeSep 1st 2022

    I strongly agree.

    • CommentRowNumber10.
    • CommentAuthorMike Shulman
    • CommentTimeSep 3rd 2022

    An anonymous contributor created set-level type theory. Since no one seems to be objecting, we can move anything relevant from this page over there and refocus it on the definitionally-extensional sort.

    • CommentRowNumber11.
    • CommentAuthorMike Shulman
    • CommentTimeSep 4th 2022

    Removed set-level type theory material. This page is now only about definitionally extensional type theories.

    diff, v30, current