Not signed in (Sign In)

Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

  • Sign in using OpenID

Site Tag Cloud

2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics comma complex complex-geometry computable-mathematics computer-science constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration finite foundation foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

Welcome to nForum
If you want to take part in these discussions either sign in now (if you have an account), apply for one now (if you don't).
  1. starting stub on XTT

    Anonymous

    v1, current

  2. adding another paragraph about different properties the type theory has

    Anonymous

    v1, current

  3. section 8.1.2 of the paper explicitly states that decidable type checking wasn’t proven yet for XTT

    Anonymous

    diff, v2, current

  4. adding second reference

    Anonymous

    diff, v2, current

    • CommentRowNumber5.
    • CommentAuthorjonsterling
    • CommentTimeSep 1st 2022

    Changed “strong normalization” to “normalization” as the former is a category error — nobody has proposed any rewriting system for XTT, so strong normalization is neither here nor there. If a rewriting system is proposed, then SN or its failure would be a theorem about that rewriting system, not about XTT.

    diff, v5, current

    • CommentRowNumber6.
    • CommentAuthorGuest
    • CommentTimeSep 1st 2022

    dumb question, but is it “X type theory” or just “X tee tee”?

    • CommentRowNumber7.
    • CommentAuthorMike Shulman
    • CommentTimeSep 2nd 2022

    Added a hyperlink to normal form (which is the appropriate pointer from the disambiguation page normalization), where this distinction should be (but is not currently) discussed.

    diff, v6, current

    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTimeSep 2nd 2022

    I have fixed the arXiv link, from

      https://arxiv.org/abs:1904.08562
    

    to

      https://arxiv.org/abs/1904.08562
    

    here and in the author’s entries.

    Now that I have done this, I see that somebody else was catching the same problem already elsewhere. So maybe there is yet more instances left to be fixed.

    diff, v7, current

    • CommentRowNumber9.
    • CommentAuthorUrs
    • CommentTimeSep 2nd 2022

    re #6

    dumb question: is it “X type theory” or just “X tee tee”?

    Just to say that i don’t find this a dumb question and that at least our nLab entry would deserve to be explicit about what “XTT” is meant to mean. In particular since the evident guess seems to be wrong: It’s not meant to be read as short for “extensional type theory”. Still, “extensional” seems to be the only plausible term that the “X” could be alluding to.

    • CommentRowNumber10.
    • CommentAuthorjonsterling
    • CommentTimeSep 4th 2022

    Hi all, I did indeed name XTT as a pun on “eXtensional Type Theory” — but it is meant to be read aloud only as XTT. It doesn’t actually stand for anything.

    • CommentRowNumber11.
    • CommentAuthorUrs
    • CommentTimeSep 4th 2022

    Best to add such explanation to the beginning of the entry!

  5. extensional -> set level

    Anonymous

    diff, v10, current

    • CommentRowNumber13.
    • CommentAuthorjonsterling
    • CommentTimeMar 2nd 2023

    Clarify the name XTT

    diff, v13, current