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nLab > nLab General Discussions: inductive-inductive type

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  1.  
    • CommentRowNumber1.
    • CommentAuthorDavid_Corfield
    • CommentTimeOct 19th 2016

    Gaëtan Gilbert’s new paper, Formalising Real Numbers in Homotopy Type Theory, ( arXiv:1610.05072) speaks of higher inductive-inductive types. We don’t have anything on this, but I see the other wiki, Homotopy Type Theory, at least has an entry inductive-inductive type. Where are we with regard to the relationship between the wikis? The HoTT one seems not terribly active if you look at their Latest Revisions, so not likely to see something useful out there, like Andrej Bauer’s comments on induction-induction, and add it to an entry. Probably better then to begin our own entry, don’t you think?

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeOct 19th 2016
    • (edited Oct 19th 2016)

    I’d just copy over the material to inductive-inductive type, add attribution, add more hyperlinks, add more references, fine-tune the formatting, and add cross-links.

    • CommentRowNumber3.
    • CommentAuthorDavid_Corfield
    • CommentTimeOct 19th 2016

    So I’ve also started inductive-recursive type.

    • CommentRowNumber4.
    • CommentAuthorDavid_Corfield
    • CommentTimeOct 19th 2016

    Is there anything special to privilege those two combinations over recursive-recursive and recursive-inductive?

    • CommentRowNumber5.
    • CommentAuthorspitters
    • CommentTimeOct 19th 2016

    I am not sure what it would mean for the underlying set to be recursively defined. Recursively over what?

    • CommentRowNumber6.
    • CommentAuthorDavid_Corfield
    • CommentTimeOct 19th 2016

    I was just borrowing from Bauer here who is borrowing from Fredrik Nordvall Forsberg and Anton Setzer. I’ve copied in an example they give.

    The professionals should be writing these entries, but perhaps a nudge will help.

    • CommentRowNumber7.
    • CommentAuthorMike Shulman
    • CommentTimeOct 19th 2016

    A “recursive-recursive type” sounds a little bit like a very dependent function, maybe?

    • CommentRowNumber8.
    • CommentAuthorDavid_Corfield
    • CommentTimeOct 19th 2016

    Oh sorry I see now #5 was addressed to #4.

    • CommentRowNumber9.
    • CommentAuthorspitters
    • CommentTimeJul 3rd 2017

    Added a reference to the QIIT paper.

    • CommentRowNumber10.
    • CommentAuthorspitters
    • CommentTimeJan 23rd 2018

    We sharpened the statement a little in discussion with Ambrus Kaprosi

1 to 10 of 10

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