Sökning: "Dependent Type Theory"

Visar resultat 1 - 5 av 125 avhandlingar innehållade orden 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 :NATURVETENSKAP; NATURAL SCIENCES; type theory; homotopy type theory; dependent types; constructive set theory; databases; formalisation; agda; Mathematics; matematik;

    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

  3. 2. Relations in Dependent Type Theory

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

    Sammanfattning : 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. LÄS MER

  4. 3. Towards a practical programming language based on dependent type theory

    Författare :Ulf Norell; Chalmers tekniska högskola; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; dependent types; type theory; metavariables; programming; pattern matching; type checking;

    Sammanfattning : Dependent type theories have a long history of being used for theorem proving. One aspect of type theory which makes it very powerful as a proof language is that it mixes deduction with computation. LÄS MER

  5. 4. Cubical Intepretations of Type Theory

    Författare :Simon Huber; Göteborgs universitet; []
    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

  7. 5. Type Theory with First-Order Data Types and Size-Change Termination

    Författare :David Wahlstedt; Chalmers tekniska högskola; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Pattern-matching; Reducibility; Size-Change Termination; Logical Framework; Lambda-calculus; Term rewriting.; Type Theory; Dependent types; Normalization; Type system;

    Sammanfattning : We prove normalization for a dependently typed lambda-calculus extended with first-order data types and computation schemata for first-order size-change terminating recursive functions. Size-change termination, introduced by C.S. Lee, N. LÄS MER