Related papers: Canonicity and Computability in Homotopy Type Theo…
Algebraic theories with dependency between sorts form the structural core of Martin-L\"of type theory and similar systems. Their denotational semantics are typically studied using categorical techniques; many different categorical…
This is an introduction to Homotopy Type Theory and Univalent Foundations for philosophers, written as a chapter for the book "Categories for the Working Philosopher" (ed. Elaine Landry)
We present a logical framework that enables us to define a formal theory of computational trust in which this notion is analysed in terms of epistemic attitudes towards the possible objects of trust and in relation to existing evidence in…
LF is a dependent type theory in which many other formal systems can be conveniently embedded. However, correct use of LF relies on nontrivial metatheoretic developments such as proofs of correctness of decision procedures for LF's…
This book describes some computational methods to deal with modular characters of finite groups. It is the theoretical background of the MOC system of the same authors. This system was, and is still used, to compute the modular character…
This thesis embarks on a comprehensive exploration of formal computational models that underlie typed programming languages. We focus on programming calculi, both functional (sequential) and concurrent, as they provide a compelling rigorous…
We introduce a topology on the space of all isomorphism types represented in a given class of countable models, and use this topology as an aid in classifying the isomorphism types. This mixes ideas from effective descriptive set theory and…
This is the first installment of a series of papers whose aim is to lay a foundation for homotopy probability theory by establishing its basic principles and practices. The notion of a homotopy probability space is an enrichment of the…
We explore connections between homotopy type theory and information theory through homotopy cardinality. We define probability types and random variable types, prove that homotopy cardinality respects dependent sums under truncation and…
This paper is focused on the development of the notions of canonical and canonoid transformations within the framework of Hamiltonian Mechanics on locally conformal symplectic manifolds. Both, time-independent and time-dependent dynamics…
The univalence axiom expresses the principle of extensionality for dependent type theory. However, if we simply add the univalence axiom to type theory, then we lose the property of canonicity - that every closed term computes to a…
This article reformulates the theory of computable physical models, previously introduced by the author, as a branch of applied model theory in first-order logic. It provides a semantic approach to the philosophy of science that…
We study otopy classes of equivariant local maps and prove the Hopf type theorem for such maps in the case of a real finite dimensional orthogonal representation of a compact Lie group.
We combine dependent types with linear type systems that soundly and completely capture polynomial time computation. We explore two systems for capturing polynomial time: one system that disallows construction of iterable data, and one,…
The process of evolutionary diversification unfolds in a vast genotypic space of potential outcomes. During the past century there have been remarkable advances in the development of theory for this diversification, and the theory's success…
The goal of this dissertation is to present results from synthetic homotopy theory based on homotopy type theory (HoTT). After an introduction to Martin-L\"of's dependent type theory and homotopy type theory, key results include a synthetic…
Inductive and coinductive types are commonly construed as ontological (Church-style) types, denoting canonical data-sets such as natural numbers, lists, and streams. For various purposes, notably the study of programs in the context of…
Unlike Martin-L\"of randomness and Schnorr randomness, computable randomness has not been defined, except for a few ad hoc cases, outside of Cantor space. This paper offers such a definition (actually, several equivalent definitions), and…
It is well known that general recursion cannot be expressed within Martin-Loef's type theory and various approaches have been proposed to overcome this problem still maintaining the termination of the computation of the typable terms. In…
We present a type theory combining both linearity and dependency by stratifying typing rules into a level for logics and a level for programs. The distinction between logics and programs decouples their semantics, allowing the type system…