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 complex complex-geometry computable-mathematics computer-science constructive cosmology definitions deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration 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 nforum 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).

nLab > Latest Changes: simple type theory

Bottom of Page

1 to 6 of 6

  1.  

  1. (remove dead link to review pdf)

    Burak Emir

    diff, v3, current

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeDec 29th 2022

    added pointer to:

    diff, v4, current

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeFeb 28th 2023

    also added pointer to:

    diff, v6, current

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeFeb 28th 2023

    I have expanded the previous idea-section a fair bit (it used to just say that simple type theory has non-indexed type formation). Now it reads as follows:

    Originally, “simple type theory” was the name of the type theory introduced by Church (1940) (therefore often and more informatively: “Church’s type theory” or similar). This type theory allowed function type-type formation (therefore often: “simply typed lambda-calculus”) based on two elementary types (a kind of type of natural numbers and a type of propositions).

    In mild generalization, if one admits in addition product type-type formation then [e.g. Gunter (1992)] these are the type theories whose categorical semantics is in cartesian closed categories (see also at relation between category theory and type theory).

    More generally, the term “simple type” has come to refer to any type theory whose type formations are not indexed, […]

    Finally I added this reference:

    diff, v6, current

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeApr 8th 2023

    added pointer to:

    diff, v7, current

  6. added reference

    Anonymouse

    diff, v8, current

1 to 6 of 6

  1.