Related papers: Dependent dreams: recounting types
Model checking properties are often described by means of finite automata. Any particular such automaton divides the set of infinite trees into finitely many classes, according to which state has an infinite run. Building the full type…
We begin a systematic development of structure theory for a first order theory, which is stable over a monadic predicate. We show that stability over a predicate implies quantifier free definability of types over stable sets, introduce an…
Long-range dependency is one of the most desired properties of recent sequence models such as state-space models (particularly Mamba) and transformer models. New model architectures are being actively developed and benchmarked for…
One takes advantage of some basic properties of every homotopic $\lambda$-model (e.g.\ extensional Kan complex) to explore the higher $\beta\eta$-conversions, which would correspond to proofs of equality between terms of a theory of…
We construct a realizability model of linear dependent type theory from a linear combinatory algebra. Our model motivates a number of additions to the type theory. In particular, we add a universe with two decoding operations: one takes…
Infinite types and formulas are known to have really curious and unsound behaviors. For instance, they allow to type {\Omega}, the auto- autoapplication and they thus do not ensure any form of normalization/productivity. Moreover, in most…
We show that for any uncountable cardinal $\lambda$, the category of sets of cardinality at least $\lambda$ and monomorphisms between them cannot appear as the category of point of a topos, in particular is not the category of models of a…
We consider global analogues of model-theoretic tree properties. The main objects of study are the invariants related to Shelah's tree property $\kappa_{\text{cdt}}(T)$, $\kappa_{\text{sct}}(T)$, and $\kappa_{\text{inp}}(T)$ and the…
Was paper 839 in the author's list until winter 2023 when it was divided into three. Part I: We would like to generalize imaginary elements, weight of ortp$(a,M,N), {\mathbf P}$-weight, ${\mathbf P}$-simple types, etc. from [She90, Ch.…
The first part of this dissertation defines "dependently typed algebraic theories", which are a strict subclass of the generalised algebraic theories (GATs) of Cartmell. We characterise dependently typed algebraic theories as finitary…
Let $X$ be a set, $\ka$ be a cardinal number and let $\iH$ be a family of subsets of $X$ which covers each $x\in X$ at least $\ka$ times. What assumptions can ensure that $\iH$ can be decomposed into $\kappa$ many disjoint subcovers? We…
Dependently typed programs contain an excessive amount of static terms which are necessary to please the type checker but irrelevant for computation. To separate static and dynamic code, several static analyses and type systems have been…
We introduce regular graph constraints and explore their decidability properties. The motivation for regular graph constraints is 1) type checking of changing types of objects in the presence of linked data structures, 2) shape analysis…
A trichotomy theorem for countable, stable, unsuperstable theories is offered. We develop the notion of a `regular ideal' of formulas and study types that are minimal with respect to such an ideal.
A theory $T$ is said to be relatively decidable if for every model of $T$, one can compute the elementary diagram of that model from its atomic diagram together with $T$. We verify a conjecture of Chubb, Miller, and Solomon by showing that…
We define an extension of lambda-calculus with dependents types that enables us to encode transparent and opaque probabilistic programs and prove a strong normalisation result for it by a reducibility technique. While transparent…
A hierarchy of type universes is a rudimentary ingredient in the type theories of many proof assistants to prevent the logical inconsistency resulting from combining dependent functions and the type-in-type rule. In this work, we argue that…
A popular framework for false discovery control is the random effects model in which the null hypotheses are assumed to be independent. This paper generalizes the random effects model to a conditional dependence model which allows…
We prove the undecidability of the third order pattern matching problem in typed lambda-calculi with dependent types and in those with type constructors by reducing the second order unification problem to them.
A cornerstone of the theory of lambda-calculus is that intersection types characterise termination properties. They are a flexible tool that can be adapted to various notions of termination, and that also induces adequate denotational…