Search for dissertations about: "type theory"

Showing result 1 - 5 of 874 swedish dissertations containing the words type theory.

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

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

    Abstract : 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. READ MORE

  2. 2. Localic Categories of Models and Categorical Aspects of Intuitionistic Ramified Type Theory

    Author : Johan Lindberg; Erik Palmgren; Peter LeFanu Lumsdaine; Henrik Forssell; Benno van den Berg; Stockholms universitet; []
    Keywords : NATURAL SCIENCES; NATURVETENSKAP; NATURVETENSKAP; NATURAL SCIENCES; Topos theory; predicative topos theory; ramified type theory; type theory; localic groupoids; matematik; Mathematics;

    Abstract : This thesis contains three papers, all in the general area of categorical logic, together with an introductory part with some minor results and proofs of known results which does not appear to be (easily) available in the literature.In Papers I and II we investigate the formal system Intuitionistic Ramified Type Theory (IRTT), introduced by Erik Palmgren, as an approach to predicative topos theory. READ MORE

  3. 3. Cubical Intepretations of Type Theory

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

    Abstract : 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. READ MORE

  4. 4. Relations in Dependent Type Theory

    Author : Carlos Gonzalía; Göteborgs universitet; Göteborgs universitet; Gothenburg University; []
    Keywords : NATURVETENSKAP; NATURAL SCIENCES; formalized mathematics; relational systems; category theory; programming logics; constructive type theory; logical frameworks; relational database model;

    Abstract : This thesis investigates how to express and reason about relational concepts and methods inside the constructive logical framework of Martin-Löf's monomorphic type theory. We cover several areas where the notion of relation is central, and show how to formalize the basic concepts of each area. READ MORE

  5. 5. Ramsey's Theorem in type theory

    Author : Daniel Fridlender; Chalmers University of Technology; []
    Keywords : NATURVETENSKAP; NATURAL SCIENCES; Ramsey s theorem; HIgman s lemma; type theory;

    Abstract : .... READ MORE