Sökning: "Models of dependent type theory"

Visar resultat 1 - 5 av 27 avhandlingar innehållade orden Models of dependent type theory.

  1. 1. Univalent Types, Sets and Multisets : Investigations in dependent type theory

    Författare :Håkon Robbestad Gylterud; Erik Palmgren; Nicola Gambino; Stockholms universitet; []
    Nyckelord :NATURAL SCIENCES; NATURVETENSKAP; type theory; homotopy type theory; dependent types; constructive set theory; databases; formalisation; agda; matematik; Mathematics;

    Sammanfattning : This thesis consists of four papers on type theory and a formalisation of certain results from the two first papers in the Agda language. We cover topics such as models of multisets and sets in Homotopy Type Theory, and explore ideas of using type theory as a language for databases and different ways of expressing dependencies between terms. LÄS MER

  2. 2. Cubical Intepretations of Type Theory

    Författare :Simon Huber; Göteborgs universitet; Göteborgs universitet; Gothenburg University; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Dependent Type Theory; Univalence Axiom; Models of Type Theory; Identity Types; Cubical Sets;

    Sammanfattning : The interpretation of types in intensional Martin-Löf type theory as spaces and their equalities as paths leads to a surprising new view on the identity type: not only are higher-dimensional equalities explained as homotopies, this view also is compatible with Voevodsky's univalence axiom which explains equality for type-theoretic universes as homotopy equivalences, and formally allows to identify isomorphic structures, a principle often informally used despite its incompatibility with set theory. While this interpretation in homotopy theory as well as the univalence axiom can be justified using a model of type theory in Kan simplicial sets, this model can, however, not be used to explain univalence computationally due to its inherent use of classical logic. LÄS MER

  3. 3. String Theory at the Horizon : Quantum Aspects of Black Holes and Cosmology

    Författare :Martin Olsson; Ulf Danielsson; Lárus Thorlacius; Uppsala universitet; []
    Nyckelord :NATURAL SCIENCES; NATURVETENSKAP; Theoretical physics; theoretical physics; string theory; black holes; cosmology; de Sitter space; c=1 matrix models; 2D string theory; topological string theory; conifolds; 4D BPS black holes; Gödel universe; closed time-like curves; Teoretisk fysik; Physics; Fysik;

    Sammanfattning : String theory is a unified framework for general relativity and quantum mechanics, thus being a theory of quantum gravity. In this thesis we discuss various aspects of quantum gravity for particular systems, having in common the existence of horizons. LÄS MER

  4. 4. A Model of Type Theory in Cubical Sets

    Författare :Simon Huber; Göteborgs universitet; Göteborgs universitet; Gothenburg University; []
    Nyckelord :NATURVETENSKAP; NATURVETENSKAP; NATURAL SCIENCES; NATURAL SCIENCES; Models of dependent type theory; cubical sets; Univalent Foundations;

    Sammanfattning : The intensional identity type is one if the most intricate concepts of dependent type theory. The recently discovered connection between homotopy theory and type theory gives a novel perspective on the identity type. LÄS MER

  5. 5. Homogenization of some new mathematical models in lubrication theory

    Författare :Afonso Fernando Tsandzana; Peter Wall; Lars- Erik Persson; John Fabricius; Anders Holmbom; Luleå tekniska universitet; []
    Nyckelord :NATURAL SCIENCES; NATURVETENSKAP; NATURVETENSKAP; NATURAL SCIENCES; lubrication theory; homogenization theory; Reynolds equation; cavitation; surfaces roughness; Stokes equation; Matematik; Mathematics;

    Sammanfattning : We consider mathematical modeling of thin film flow between two rough surfaces which are in relative motion. For example such flows take place in different kinds of bearings and gears when a lubricant is used to reduce friction and wear between the surfaces. LÄS MER