Abstract
This paper sketches a reverse engineering discipline which combines formal and semi-formal methods. Central to the former is denotational semantics, expressed in the ISO/IEC 13817-1 standard specification language (VDM-SL). This is strengthened with algebra of programming, which is applied in "reverse order" so as to reconstruct formal specifications from legacy code. The latter include code slicing, a "shortcut" which trims down the complexity of handling the formal semantics of all program variables at the same time. A key point of the approach is its constructive style. Reverse calculations go as far as absorbing auxiliary variables, introducing mutual recursion (if applicable) and reversing semantic denotations into standard generic programming schemata such as cata/paramorphisms. The approach is illustrated for a small piece of code already studied in the code-slicing literature: Kernighan and Richtie's word count C programming "bagatelle".

Abstract
This paper addresses objectification, a formal specification technique which inspects the potential for object-orientation of a declarative model and brings the 'implicit objects' explicit. Criteria for such objectification are formalized and implemented in a runnable prototype tool which embeds VDM-SL into VDM++. The paper also includes a quick presentation of a (coinductive) calculus of such generated objects, framed as generalised Moore machines.

Abstract
Although much of mathematics is algorithmic in nature, the skills needed to formulate and solve algorithmic problems do not form an integral part of mathematics education. In particular, logic, which is central to algorithm development, is rarely taught explicitly at pre-university level, under the justification that it is implicit in mathematics and therefore does not need to be taught as an independent topic. This paper argues in the opposite direction, describing a one-week workshop done at the University of Minho, in Portugal, whose goal was to introduce to high-school students calculational principles and techniques of algorithmic problem solving supported by calculational logic. The workshop resorted to recreational problems to convey the principles and to software tools, the Alloy Analyzer and Netlogo, to animate models.

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
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.