Related papers: Domain Theory for Modeling OOP: A Summary
We explore a new connection between synthetic domain theory and Grothendieck topoi related to the distributive lattice classifier. In particular, all the axioms of synthetic domain theory (including the inductive fixed point object and the…
The expression problem describes how most types can easily be extended with new ways to produce the type or new ways to consume the type, but not both. When abstract syntax trees are defined as an algebraic data type, for example, they can…
Brouwer's constructivist foundations of mathematics is based on an intuitively meaningful notion of computation shared by all mathematicians. Martin-L\"of's meaning explanations for constructive type theory define the concept of a type in…
First the basic definition of information as a selection from a set of possibilities resp. domain is recalled. This also applies to digital information. The bits of digital information are parts of number sequences which represent a…
Pattern-Oriented Analysis and Design (POAD) is the practice of building complex software by applying proven designs to specific problem domains. Although a great deal of research and practice has been devoted to formalizing existing design…
This paper lays down the research agenda for a domain-specific foundation model for operating systems (OSes). Our case for a foundation model revolves around the observations that several OS components such as CPU, memory, and network…
In the paper a new programming construct, called concept, is introduced. Concept is pair of two classes: a reference class and an object class. Instances of the reference classes are passed-by-value and are intended to represent objects.…
Internet-based economies and societies are drowning in deceptive attacks. These attacks take many forms, such as fake news, phishing, and job scams, which we call "domains of deception." Machine-learning and natural-language-processing…
We introduce a continuous domain for function spaces over topological spaces which are not core-compact. Notable examples of such topological spaces include the real line with the upper limit topology, which is used in solution of initial…
The success of software model checking depends on finding an appropriate abstraction of the subject program. The choice of the abstract domain and the analysis configuration is currently left to the user, who may not be familiar with the…
A theory is developed which uses "networks" (directed acyclic graphs with some extra structure) as a formalism for expressions in multilinear algebra. It is shown that this formalism is valid for arbitrary PROPs (short for 'PROducts and…
Automatic (i.e., computer-assisted) theorem proving (ATP) can come in many flavors. This document presents early steps in our effort towards defining object-oriented theorem proving (OOTP) as a new style of ATP. Traditional theorem proving…
Any function can be constructed using a hierarchy of simpler functions through compositions. Such a hierarchy can be characterized by a binary rooted tree. Each node of this tree is associated with a function which takes as inputs two…
We present an extension to the $\mathtt{mathlib}$ library of the Lean theorem prover formalizing the foundations of computability theory. We use primitive recursive functions and partial recursive functions as the main objects of study, and…
This paper studies the role that ontologies can play in establishing conceptual data models during the process of information systems development. A mapping algorithm has been proposed and embedded in a special purpose Transformation-Engine…
The foundational concepts of semantic numeration systems theory are briefly outlined. The action of cardinal semantic operators unfolds over a set of cardinal abstract entities belonging to the cardinal semantic multeity. The cardinal…
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…
The problem of domain generalization is to learn, given data from different source distributions, a model that can be expected to generalize well on new target distributions which are only seen through unlabeled samples. In this paper, we…
In the problem of domain generalization (DG), there are labeled training data sets from several related prediction problems, and the goal is to make accurate predictions on future unlabeled data sets that are not known to the learner. This…
While the engineering of operating systems is well understood, their formal structure and properties are not. The latter needs a clear definition of the purpose of an OS and an identification of the core. In this paper I offer definitions…