Related papers: Implementing Dependent Type Theory Inhabitation an…
In this paper, we analyze and compare three of the many algebraic structures that have been used for modeling dependent type theories: categories with families, split type-categories, and representable maps of presheaves. We study these in…
We present a unifying framework for type systems for process calculi. The core of the system provides an accurate correspondence between essentially functional processes and linear logic proofs; fragments of this system correspond to…
This paper explores conditions of existence of different types of consistent tests. New links of these types of consistency are also established. The existence of discernible (strong consistent) tests follows from the existence of pointwise…
A new computationally efficient dependence measure, and an adaptive statistical test of independence, are proposed. The dependence measure is the difference between analytic embeddings of the joint distribution and the product of the…
In the problem of composite hypothesis testing, identifying the potential uniformly most powerful (UMP) unbiased test is of great interest. Beyond typical hypothesis settings with exponential family, it is usually challenging to prove the…
This paper improves the treatment of equality in guarded dependent type theory (GDTT), by combining it with cubical type theory (CTT). GDTT is an extensional type theory with guarded recursive types, which are useful for building models of…
First-order resolution has been used for type inference for many years, including in Hindley- Milner type inference, type-classes, and constrained data types. Dependent types are a new trend in functional languages. In this paper, we show…
Cubical type theory is an extension of Martin-L\"of type theory recently proposed by Cohen, Coquand, M\"ortberg and the author which allows for direct manipulation of $n$-dimensional cubes and where Voevodsky's Univalence Axiom is provable.…
A type system combining type application, constants as types, union types (associative, commutative and idempotent) and recursive types has recently been proposed for statically typing path polymorphism, the ability to define functions that…
We find the minimal number of independent preparations and measurements certifying the dimension of a classical or quantum system limited to $d$ states, optionally reduced to the real subspace. As a dimension certificate, we use the linear…
This paper improves the treatment of equality in guarded dependent type theory (GDTT), by combining it with cubical type theory (CTT). GDTT is an extensional type theory with guarded recursive types, which are useful for building models of…
Proof automation is crucial to large-scale formal mathematics and software/hardware verification projects in ITPs. Sophisticated tools called hammers have been developed to provide general-purpose proof automation in ITPs such as Coq and…
This monograph offers a toolbox of mathematical techniques, which have been effective and widely applicable in information-theoretic analysis. The first tool is a generalization of the method of types to Gaussian settings, and then to…
We present a model of dependent type theory (DTT) with Pi-, 1-, Sigma- and intensional Id-types, which is based on a slight variation of the category of AJM-games and history-free winning strategies. The model satisfies Streicher's criteria…
It is often of interest to test a global null hypothesis using multiple, possibly dependent $p$-values by combining their strengths while controlling the type-I error. Recently, several heavy-tailed combination tests, such as the harmonic…
Differentiable logics are a family of quantitative logics originated in the machine learning literature. Because of their origin, differentiable logics often come equipped with analytic properties that guarantee that they are…
We develop domain theory in constructive and predicative univalent foundations (also known as homotopy type theory). That we work predicatively means that we do not assume Voevodsky's propositional resizing axioms. Our work is constructive…
We consider the problem of identifying the signal shared between two one-dimensional target variables, in the presence of additional multivariate observations. Canonical Correlation Analysis (CCA)-based methods have traditionally been used…
This document specifies a core version of the type theory implemented in the Cedille tool. Cedille is a language for dependently typed programming and computer-checked proof. Cedille can elaborate source programs down to Cedille Core, which…
Trainable input embedding tables are a standard component of modern language models. We ask whether they are actually necessary at the input interface. For a vocabulary of size $V$, exact token identity requires only $K=\lceil \log_2…