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    • CommentRowNumber1.
    • CommentAuthorDavid_Corfield
    • CommentTimeJun 20th 2016

    Do others also not see the category theoretic diagrams of dependent sum natural deduction - table?

    • CommentRowNumber2.
    • CommentAuthorMatt Earnshaw
    • CommentTimeJun 20th 2016

    For some reason they were (broken) hotlinks to quicklatex.com rather than inline mathjax. Looking at revision #3, I suppose the issue was that p 1 p_1 overlaps \in in the type formation diagram (at least it does on my system), so I have (speculatively) rolled it back to that with an extra space thrown in.

    • CommentRowNumber3.
    • CommentAuthorDavid_Corfield
    • CommentTimeJun 20th 2016

    dependent product natural deduction - table also has a problem, but now there are only two versions and neither shows anything.

    • CommentRowNumber4.
    • CommentAuthorTobyBartels
    • CommentTimeJul 8th 2016
    • (edited Jul 8th 2016)

    I started to fill in the missing diagrams in dependent product natural deduction - table. Unfortunately, these diagrams don't really make sense to me ―I think that they're using a bad paradigm―, and I can't figure out what all of them should be. Presumably Urs knows.

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeJul 9th 2016

    They were supposed to depict the interpretation of the type theory in a categry, with dependent types as display morphisms, etc. I might try to look into it again later.

    • CommentRowNumber6.
    • CommentAuthorDavid_Corfield
    • CommentTimeJan 28th 2018

    Coming back to these tables,

    dependent sum natural deduction - table: should we have (x,a)(x, a) as the label on the horizontal arrow in the row for term introduction, then tt similarly for the next row? And the diagram in the type formation row is OK? How about if we had p 1:XA𝒞/Xp_1: X \to A \in \mathcal{C}/X? And can’t we fit the p 2p_2 relations as we do at product natural deduction - table?

    dependent product natural deduction - table: lacks diagrams for some rows.

    • CommentRowNumber7.
    • CommentAuthorDavid_Corfield
    • CommentTimeJan 28th 2018

    I dabbled with a revised version at dependent sum natural deduction - table, leaving the original for comparison. Not sure about the term introduction row.

    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTimeJan 28th 2018

    should we have (x,a)(x, a) as the label on the horizontal arrow in the row for term introduction, then tt similarly for the next row?

    Yes, that seems good.

    The diagrams represent the syntax on the left only somewhat coarsely. Not sure if it can be made more precise while still being brief enough for an overview table instead of a detailed account.

    • CommentRowNumber9.
    • CommentAuthorMike Shulman
    • CommentTimeJan 29th 2018

    Yes, e.g. there’s not much non-tautological that can be said briefly about the semantic computation rule for p 2p_2.