Abstract
The R/G approach to the development of interfering programs was initiated by the pioneering work of Cliff Jones (1981) on a relational basis. R/G has been the subject of much research since then, most of it deviating from the original relational set-up. This paper looks at such early work from a historical perspective and shows how it can be approached and extended using state-of-the-art relational algebra. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.

Abstract
Humans are good at understanding subjective or vague statements which, however, are hard to express in classical logic. Fuzzy logic is an evolution of classical logic that can cope with vague terms by handling degrees of truth and not just the crisp values true and false. Logic is the formal basis of computing, enabling the formal design of systems supported by tools such as model checkers and theorem provers.This paper shows how a model checker such as Alloy can evolve to handle both classical and fuzzy logic, enabling the specification of high-level quantitative relational models in the fuzzy domain. In particular, the paper showcases how QAlloy-F (a conservative, general-purpose quantitative extension to standard Alloy) can be used to tackle fuzzy problems, namely in the context of validating the design of fuzzy controllers. The evaluation of QAlloy-F against examples taken from various classes of fuzzy case studies shows the approach to be feasible.

Abstract
For the average programmer, adjunctions are (if at all known) more respected than loved. At best, they are regarded as an algebraic device of theoretical interest only, not useful in common practice. This paper is aimed at showing the opposite: that adjunctions underlie most of the work we do as programmers, in particular those using the functional paradigm. However, functions alone are not sufficient to express the whole spectrum of programming, with its dichotomy between specifications—what is (often vaguely) required—and implementations—how what is required is (hopefully well) implemented. For this, one needs to extend functions to relations. Inspired by the pioneering work of Ralf Hinze on “adjoint (un)folds”, the core of the so-called (relational) Algebra of Programming is shown in this paper to arise from adjunctions. Moreover, the paper also shows how to calculate recursive programs from specifications expressed by Galois connections—a special kind of adjunction. Because Galois connections are easier to understand than adjunctions in general, the paper adopts a tutorial style, starting from the former and leading to the latter (a path usually not followed in the literature). The main aim is to reconcile the functional programming community with a concept that is central to software design as a whole, but rarely accepted as such. © 2023, Springer Nature Switzerland AG.

Abstract
The notion of a difunction was introduced by Jacques Riguet in 1948. Since then it has played a prominent role in database theory, type theory, program specification and process theory. The theory of difunctions is, however, less known in computing than it perhaps should be. The main purpose of the current paper is to give an account of difunction theory in relation algebra, with the aim of making the topic more mainstream.As is common with many important concepts, there are several different but equivalent characterisations of difunctionality, each with its own strength and practical significance. This paper compares different proofs of the equivalence of the characterisations. A well-known property is that a difunction is a set of completely disjoint rectangles. This property suggests the introduction of the (general) notion of the core of a relation; we use this notion to give a novel and, we believe, illuminating characterisation of difunctionality as a bijection between the classes of certain partial equivalence relations.& COPY; 2023 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons .org /licenses /by /4 .0/).

Abstract
A two-level data transformation consists of a type-level transformation of a data format coupled with value-level transformations of data instances corresponding to that format. Examples of two-level data transformations include XML schema evolution coupled with document migration, and data mappings used for interoperability and persistence. We provide a formal treatment of two-level data transformations that is type-safe in the sense that the well-formedness of the value-level transformations with respect to the type-level transformation is guarded by a strong type system. We rely on various techniques for generic functional programming to implement the formalization in Haskell. The formalization addresses various two-level transformation scenarios, covering fully automated as well as user-driven transformations, and allowing transformations that are information-preserving or not. In each case, two-level transformations are disciplined by one-step transformation rules and type-level transformations induce value-level transformations. We demonstrate an example hierarchical-relational mapping and subsequent migration of relational data induced by hierarchical format evolution.

Abstract
Confined separation logic is a new extension to separation logic designed to deal with problems involving dangling references within shared mutable structures. In particular it allows for reasoning about confinement in object-oriented programs. In this paper, we discuss the semantics of such an extension by defining a relational model for the overall logic, parametric on the shapes of both the store and the heap. This model provides a simple and elegant interpretation of the new confinement connectives and helps in seeking for duals. A number of properties of this logic are proved calculationally.