It is hard to imagine where we would be today without the algorithm or the computer technology and we certainly would miss important luxuries (and even necessities) if there was no data science. During Covid, the world learned to appreciate the computational technology and the value of statistical data collection and analysis and of data mining. But long before Covid, everything around us was being constantly shaped by Algorithms, computations and data. This was prominent for example in the ‘feeding the world challenge’ where the world population is growing at a fast rate (and is expected according to the United Nations to reach 9.8 billion by 2050 and 11.2 billion in 2100), when at the same time, we are losing farmland (e.g. according to the Farmland Partners, the USA is losing 4.3 acres of farmland per minute) and, due to climate change, we are seeing a crop decrease (e.g. according to a recent NASA study, by 2030, we could see a 24% decrease in Maize crop yields). The ‘feeding the world challenge’ was designed to use the latest innovations in algorithms and machine learning in order to increase crop productivity, in a smaller stretch of land and using as little resources (such as fertilizers, seeds and water) as possible. The US department of agriculture championed this idea and purposed it around machine learning where algorithms improve over time, and where AI, models and visualization play a crucial role to help these algorithms learn. Here, the ability to collect and analyze big data was a key to progress and data were used to make farming decisions. Data were (and continues to be) treated as currency, and even as back as 2015, the McKinsey Global Research projected that the value of data per year is currently between 3.6 and 11 trillion US dollars. But, data are useless without the clever algorithms that make sense of this data.

The Capsule Reviews are intended to provide a short succinct review of each paper in the issue in order to bring it to a wider readership. The Capsule Reviews were compiled by Fairouz Kamareddine. Professor Kamareddine is an Associate Editor of The Computer Journal and is based in the Department of Mathematical and Computer Sciences at Heriot-Watt University, Edinburgh, UK.

The Capsule Reviews are intended to provide a short succinct review of each paper in the issue in order to bring it to a wider readership. The Capsule Reviews were compiled by Fairouz Kamareddine. Professor Kamareddine is an Associate Editor of The Computer Journal and is based in the Department of Mathematical and Computer Sciences at Heriot-Watt University, Edinburgh, UK.

The Capsule Reviews are intended to provide a short succinct review of each paper in the issue in order to bring it to a wider readership. The Capsule Reviews were compiled by Fairouz Kamareddine. Professor Kamareddine is an Associate Editor of The Computer Journal and is based in the Department of Mathematical and Computer Sciences at Heriot-Watt University, Edinburgh, UK.

The Capsule Reviews are intended to provide a short succinct review of each paper in the issue in order to bring it to a wider readership. The Capsule Reviews were compiled by Fairouz Kamareddine. Professor Kamareddine is an Associate Editor of The Computer Journal and is based in the Department of Mathematical and Computer Sciences at Heriot-Watt University, Edinburgh, UK.

to provide a short succinct review of each paper in the issue in order to bring it to a wider readership.The Capsule Reviews were compiled by Fairouz Kamareddine.

The Capsule Reviews are intended to provide a short succinct review of each paper in the issue in order to bring it to a wider readership. The Capsule Reviews were compiled by Fairouz Kamareddine. Professor Kamareddine is an Associate Editor of The Computer Journal and is based in the Department of Mathematical and Computer Sciences at Heriot-Watt University, Edinburgh, UK.

The Capsule Reviews are intended to provide a short succinct review of each paper in the issue in order to bring it to a wider readership. The Capsule Reviews were compiled by Fairouz Kamareddine. Professor Kamareddine is an Associate Editor of The Computer Journal and is based in the Department of Mathematical and Computer Sciences at Heriot-Watt University, Edinburgh, UK.

succinct review of each paper in the issue in order to bring it to a wider readership.The Capsule Reviews were compiled by Fairouz Kamareddine.

bring it to a wider readership.The Capsule Reviews were compiled by Fairouz Kamareddine.

Expansion is a crucial operation for calculating principal typings in intersection type systems. Because the early definitions of expansion were complicated, E-variables were introduced in order to make the calculations easier to mechanise and reason

Reducibility, despite being quite mysterious and inflexible, has been used to prove a number of properties of the λ-calculus and is well known to offer general proofs which can be applied to a number of instantiations. In this paper, we look at two r

The Capsule Reviews are intended to provide a short succinct review of each paper in the issue in order to bring it to a wider readership. The Capsule Reviews were compiled by Fairouz Kamareddine. Professor Kamareddine is an Associate Editor of The Computer Journal and is based in the Department of Mathematical and Computer Sciences at Heriot-Watt University, Edinburgh, UK.

The Capsule Reviews are intended to provide a short succinct review of each paper in the issue in order to bring it to a wider readership. The Capsule Reviews were compiled by Fairouz Kamareddine. Professor Kamareddine is an Associate Editor of The Computer Journal and is based in the Department of Mathematical and Computer Sciences at Heriot-Watt University, Edinburgh, UK.

The Capsule Reviews are intended to provide a short succinct review of each paper in the issue in order to bring it to a wider readership. The Capsule Reviews were compiled by Fairouz Kamareddine. Professor Kamareddine is an Associate Editor of The Computer Journal and is based in the Department of Mathematical and Computer Sciences at Heriot-Watt University, Edinburgh, UK.

The Capsule Reviews are intended to provide a short succinct review of each paper in the issue in order to bring it to a wider readership. The Capsule Reviews were compiled by Fairouz Kamareddine. Professor Kamareddine is an Associate Editor of The Computer Journal and is based in the Department of Mathematical and Computer Sciences at Heriot-Watt University, Edinburgh, UK.

The Capsule Reviews are intended to provide a short succinct review of each paper in the issue in order to bring it to a wider readership. The Capsule Reviews were compiled by Fairouz Kamareddine. Professor Kamareddine is an Associate Editor of The Computer Journal and is based in the Department of Mathematical and Computer Sciences at Heriot-Watt University, Edinburgh, UK.

The Capsule Reviews are intended to provide a short succinct review of each paper in the issue in order to bring it to a wider readership. The Capsule Reviews were compiled by Fairouz Kamareddine. Professor Kamareddine is an Associate Editor of The Computer Journal and is based in the Department of Mathematical and Computer Sciences at Heriot-Watt University, Edinburgh, UK.

This paper gives a plant retrieval system which takes an image of a house plant as input and returns the most similar images from a database, so that the Latin name of the plant, the care instructions and other information can be obtained.After an overview of work related to content-based image retrieval, the authors introduce the methodology used for their proposed system.First, the system, interactively with the user, segments the plant from the background (pot, table, etc.).Then, the segmented region is used for feature extraction of well-known colour, shape and texture.Then, the dissimilarity between the query image and a database image is assessed according to the extracted features using different metrics to match colour, shape and texture.The used database consists of 380 plant images from 78 different plant types, and the authors illustrate a rich variety of tests involving different methods for matching the three features and for also involving combinations of methods and features.Test results outline the performance of the retrieval methods for each of these features and for their combinations.The results are followed by a discussion of the challenges involved.

The Capsule Reviews are intended to provide a short succinct review of each paper in the issue in order to bring it to a wider readership. The Capsule Reviews were compiled by Fairouz Kamareddine. Professor Kamareddine is an Associate Editor of The Computer Journal and is based in the Department of Mathematical and Computer Sciences at Heriot-Watt University, Edinburgh, UK.

The Capsule Reviews are intended to provide a short succinct review of each paper in the issue in order to bring it to a wider readership. The Capsule Reviews were compiled by Fairouz Kamareddine. Professor Kamareddine is an Associate Editor of The Computer Journal and is based in the Department of Mathematical and Computer Sciences at Heriot-Watt University, Edinburgh, UK.

The Capsule Reviews are intended to provide a short succinct review of each paper in the issue in order to bring it to a wider readership. The Capsule Reviews were compiled by Fairouz Kamareddine. Professor Kamareddine is an Associate Editor of The Computer Journal and is based in the Department of Mathematical and Computer Sciences at Heriot-Watt University, Edinburgh, UK.

The Capsule Reviews are intended to provide a short succinct review of each paper in the issue in order to bring to a wider readership. The Capsule Reviews were compiled by Fairouz Kamareddine. Professor Kamareddine is an Associate Editor of The Computer Journal and is based in the Department of Mathematical and Computer Sciences at Heriot-Watt University, Edinburgh, UK.

The Capsule Reviews are intended to provide a short succinct review of each paper in the issue in order to bring to a wider readership. The Capsule Reviews were compiled by Fairouz Kamareddine. Professor Kamareddine is an Associate Editor of The Computer Journal and is based in the Department of Mathematical and Computer Sciences at Heriot-Watt University, Edinburgh, UK.

The Capsule Reviews are intended to provide a short succinct review of each paper in the issue in order to bring to a wider readership. The Capsule Reviews were compiled by Fairouz Kamareddine. Professor Kamareddine is an Associate Editor of The Computer Journal and is based in the Department of Mathematical and Computer Sciences at Heriot-Watt University, Edinburgh, UK.

The Capsule Reviews are intended to provide a short succinct review of each paper in the issue in order to bring to a wider readership. The Capsule Reviews were compiled by Fairouz Kamareddine. Professor Kamareddine is an Associate Editor of The Computer Journal and is based in the Department of Mathematical and Computer Sciences at Heriot-Watt University, Edinburgh, UK.

The Capsule Reviews are intended to provide a short succinct review of each paper in the issue in order to bring the content to a wider readership. The Capsule Reviews were compiled by Fairouz Kamareddine. Professor Kamareddine is an Associate Editor of The Computer Journal and is based in the Department of Mathematical and Computer Sciences at Heriot-Watt University, Edinburgh, UK.

The Capsule Reviews are intended to provide a short succinct review of each paper in the issue in order to bring the content to a wider readership. The Capsule Reviews were compiled by Fairouz Kamareddine. Professor Kamareddine is an Associate Editor of The Computer Journal and is based in the Department of Mathematical and Computer Sciences at Heriot-Watt University, Edinburgh, UK.

The Capsule Reviews are intended to provide a short succinct review of each paper in the issue in order to bring to a wider readership. The Capsule Reviews were compiled by Fairouz Kamareddine. Professor Kamareddine is an Associate Editor of The Computer Journal and is based in the Department of Mathematical and Computer Sciences at Heriot-Watt University, Edinburgh, UK.

The Capsule Reviews are intended to provide a short succinct review of each paper in the issue in order to bring the content to a wider readership. The Capsule Reviews were compiled by Fairouz Kamareddine. Professor Kamareddine is an Associate Editor of The Computer Journal and is based in the Department of Mathematical and Computer Sciences at Heriot-Watt University, Edinburgh, UK.

The Capsule Reviews are intended to provide a short succinct review of each paper in the issue in order to bring the content to a wider readership. The Capsule Reviews were compiled by Fairouz Kamareddine. Professor Kamareddine is an Associate Editor of The Computer Journal and is based in the Department of Mathematical and Computer Sciences at Heriot-Watt University, Edinburgh, UK.

The Capsule Reviews are intended to provide a short succinct review of each paper in the issue in order to bring the content to a wider readership. The Capsule Reviews were compiled by Fairouz Kamareddine. Professor Kamareddine is an Associate Editor of The Computer Journal and is based in the Department of Mathematical and Computer Sciences at Heriot-Watt University, Edinburgh, UK.

The Capsule Reviews are intended to provide a short succinct review of each paper in the issue in order to bring the content to a wider readership. The Capsule Reviews were compiled by Fairouz Kamareddine. Professor Kamareddine is an Associate Editor of The Computer Journal and is based in the Department of Mathematical and Computer Sciences at Heriot-Watt University, Edinburgh, UK.

The Capsule Reviews are intended to provide a short succinct review of each paper in the issue in order to bring the content to a wider readership. The Capsule Reviews were compiled by Fairouz Kamareddine. Professor Kamareddine is an Associate Editor of The Computer Journal and is based in the Department of Mathematical and Computer Science at Heriot-Watt University, Edinburgh, UK.

The Capsule Reviews are intended to provide a short succinct review of each paper in the issue in order to bring the content to a wider readership. The Capsule Reviews were compiled by Fairouz Kamareddine. Professor Kamareddine is an Associate Editor of The Computer Journal and is based in the Department of Mathematical and Computer Sciences at Heriot-Watt University, Edinburgh, UK.

The Capsule Reviews are intended to provide a short succinct review of each paper in the issue, in order to bring the content to a wider readership. This issue's Capsule Reviews were compiled by Fairouz Kamareddine. Professor Kamareddine is an Associate Editor of The Computer Journal and is based in the School of Mathematical and Computer Sciences at Heriot-Watt University, Edinburgh, UK.

The Capsule Reviews are intended to provide a short succinct review of each paper in the issue in order to bring the content to a wider readership. The Capsule Reviews were compiled by Fairouz Kamareddine. Professor Kamareddine is an Associate Editor of The Computer Journal and is based in the Department of Mathematical and Computer Sciences at Heriot-Watt University, Edinburgh, UK.

The Capsule Reviews are intended to provide a short succinct review of each paper in the issue in order to bring the content to a wider readership. The Capsule Reviews were compiled by Fairouz Kamareddine. Professor Kamareddine is an Associate Editor of The Computer Journal and is based in the Department of Mathematical and Computer Sciences at Heriot-Watt University, Edinburgh, UK.

The Capsule Reviews are intended to provide a short succinct review of each paper in the issue in order to bring the content to a wider readership. The Capsule Reviews were compiled by Fairouz Kamareddine. Professor Kamareddine is an Associate Editor of The Computer Journal and is based in the Department of Mathematical and Computer Sciences at Heriot-Watt University, Edinburgh, UK.

The Capsule Reviews are intended to provide a short succinct review of each paper in the issue in order to bring the content to a wider readership. The Capsule Reviews were compiled by Fairouz Kamareddine. Professor Kamareddine is an Associate Editor of The Computer Journal and is based in the Department of Mathematical and Computer Sciences at Heriot-Watt University, Edinburgh, UK.

The Capsule Reviews are intended to provide a short succinct review of each paper in the issue, in order to bring the content to a wider readership. This issue's Capsule Reviews were compiled by Fairouz Kamareddine. Professor Kamareddine is an Associate Editor of The Computer Journal and is based in the School of Mathematical and Computer Sciences at Heriot-Watt University, Edinburgh, UK.

The Capsule Reviews are intended to provide a short succinct review of each paper in the issue, in order to bring the content to a wider readership. This issue's Capsule Reviews were compiled by Fairouz Kamareddine. Professor Kamareddine is an Associate Editor of The Computer Journal and is based in the School of Mathematical and Computer Sciences at Heriot-Watt University, Edinburgh, UK.

The Capsule Reviews are intended to provide a short succinct review of each paper in the issue, in order to bring the content to a wider readership. This issue's Capsule Reviews were compiled by Fairouz Kamareddine. Professor Kamareddine is an Associate Editor of The Computer Journal and is based in the School of Mathematical and Computer Sciences at Heriot-Watt University, Edinburgh, UK.

The Capsule Reviews are intended to provide a short succinct review of each paper in the issue, in order to bring the content to a wider readership. This issue's Capsule Reviews were compiled by Fairouz Kamareddine. Professor Kamareddine is an Associate Editor of The Computer Journal and is based in the School of Mathematical and Computer Sciences at Heriot-Watt University, Edinburgh, UK.

Type theory was invented at the beginning of the twentieth century with the aim of avoiding the paradoxes which result from the self-application of functions. $\lambda$ -calculus was developed in the early 1930s as a theory of functions. In 1940, Church added type theory to his $\lambda$ -calculus giving us the influential simply typed $\lambda$ -calculus where types were simple and never created by binders (or abstractors). However, realising the limitations of the simply typed $\lambda$ -calculus, in the second half of the twentieth century we saw the birth of new more powerful typed $\lambda$ -calculi where types are indeed created by abstraction. Most of these calculi use two binders $\lambda$ and $\Pi$ to distinguish between functions (created by $\lambda$ -abstraction) and types (created by $\Pi$ -abstraction). Moreover, these calculi allow $\beta$ -reduction but not $\Pi$ -reduction. That is, $(\pi_{x:A}.B)C \rightarrow B[x:=C]$ is only allowed when $\pi$ is $\lambda$ but not when it is $\Pi$ . This means that, modern systems do not allow types to have the same instantiation right as functions. In particular, when $b$ has type $B$ , the type of $(\lambda_{x:A}.b)C$ is taken immediately to be $B[x:=C]$ instead of $(\Pi_{x:A}.B)C$ . Extensions of modern type systems with both $\Pi$ -reduction and type instantiation have appeared in (Kamareddine, Bloo and Nederpelt, 1999; Kamareddine and Nederpelt, 1996; Peyton-Jones and Meijer, 1997). This makes the $\lambda$ and $\Pi$ very similar and hence leads to the obvious question: why not use a unique binder instead of the $\lambda$ and $\Pi$ ? This makes more sense since already, versions of de Bruijn's Automath unified $\lambda$ and $\Pi$ giving more elegant systems. This paper studies the main properties of type systems with unified $\lambda$ and $\Pi$ .

Nowadays, type theory has many applications and is used in many different disciplines. Within computer science, logic and mathematics there are many different type systems. They serve several purposes and are formulated in various ways. A general framework called Pure Type Systems (PTSs) has been introduced independently by Terlouw and Berardi in order to provide a unified formalism in which many type systems can be represented. In particular, PTSs allow the representation of the simple theory of types, the polymophic theory of types, the dependent theory of types and various other well-known type systems such as the Edinburgh Logical Frameworks and the Automath system. PTSs are usually presented using variable names. In this article, we present a formulation of PTSs with de Bruijn indices. De Bruijn indices avoid the problems caused by variable names during the implementation of type systems. We show that PTSs with variable names and PTSs with de Bruijn indices are isomorphic. This isomorphism enables us to answer questions about PTSs with de Bruijn indices including confluence, termination (strong normalization) and safety (subject reduction).

In this paper, a notation influenced by de Bruijn's syntax of the λ-calculus is used to describe canonical forms of terms and an equivalence relation which divides terms into classes according to their reductional behaviour. We show that this notation helps describe canonical forms more elegantly than the classical notation and we establish the desirable properties of our reduction modulo equivalence classes rather than single terms. Finally, we extend the cube consisting of eight type systems with class reduction and show that this extension satisfies all the desirable properties of type systems.

1Department of Computing and Electrical Engineering, Heriot‐Watt University

This article is a brief review of the type‐free λ‐calculus and its basic rewriting notions, and of the pure type system framework which generalises many type systems. Both the type‐free λ‐calculus and the pure type systems are presented using variable names and de Bruijn indices. Using the presentation of the λ‐calculus with de Bruijn indices, we illustrate how a calculus of explicit substitutions can be obtained. In addition, de Bruijn's notation for the λ‐calculus is introduced and some of its advantages are outlined.

No abstract available.

Postponement of βΚ-contractions and the conservation theorem do not hold for ordinary β but have been established by de Groote for a mixture of β with another reduction relation. In this paper, de Groote's results are generalized for a single reduction relation βe which generalizes β. We show moreover, that βe has the preservation of strong normalization property.

Journal Article Editorial Get access F Kamareddine, F Kamareddine Search for other works by this author on: Oxford Academic Google Scholar JW Klop JW Klop Search for other works by this author on: Oxford Academic Google Scholar Journal of Logic and Computation, Volume 10, Issue 3, June 2000, Pages 321–322, https://doi.org/10.1093/logcom/10.3.321 Published: 01 June 2000

The aim of this article is to compare two styles of Explicit Substitutions: the λσ- and λs-styles. We start by introducing a criterion of adequacy to simulate β-reduction in calculi of explicit substitutions and we apply it to several calculi: λσ, λσ⇑, λv, λs, λt, and λu. The latter is presented here for the first time and may be considered as an adequate variant of λs. By doing so, we establish that calculi à la λs are usually more adequate at simulating β-reduction than calculi in the λσ-style. In fact, we prove that λt is more adequate than λv and that λu is more adequate than λv, λσ⇑ and λs. We also give counterexamples to show that all other comparisons are impossible according to our criterion. Our next step consists in presenting the λω and λωe calculi, the two-sorted (term and substitution) versions of the λs and λse calculi, respectively. We establish an isomorphism between the λse and the term restriction of λωe. Since the λω and λωe calculi are given in the style of the λσ-calculus they are bridge calculi between λs and λσ and between λse and λσ and thus we are able to better understand one calculus in terms of the other. Finally, we present typed versions of all the calculi and check that the above mentioned isomorphism preserves types. As a consequence, the λω-calculus is a calculus in the λσ-style that has the following properties: (a) λω simulates one step β-reduction, (b) λω is confluent (on closed terms), λω preserves strong normalization, (d) λω's associated calculus of substitutions is SN, (e) the simply typed λω calculus is SN, (f) the λω-calculus possesses and extension λωe that is confluent on open terms (terms with eventual metavariables of sort term only), and (g) the simply typed λωe calculus is weakly normalizing (on open term). As far as we know, the λω-calculus is the first calculus in the λσ-style that has all the properties (a)-(g). However, the open problem of the SN of the associated calculus of substitution of λωe remains unsolved and like in the case of λσ, λv and λse, lgr;ωe does not have PSN.

The last 15 years have seen an explosion in work on explicit substitution, most of which is done in the style of the λσ-calculus. In Kamareddine and Ríos (1995a), we extended the λ-calculus with explicit substitutions by turning de Bruijn's meta-operators into object-operators offering a style of explicit substitution that differs from that of λσ. The resulting calculus, λ s , remains as close as possible to the λ-calculus from an intuitive point of view and, while preserving strong normalisation (Kamareddine and Ríos, 1995a), is extended in this paper to a confluent calculus on open terms: the λ s e -caculus. Since the establishment of these results, another calculus, λζ, came into being in Muñoz Hurtado (1996) which preserves strong normalisation and is itself confluent on open terms. However, we believe that λ s e still deserves attention because, while offering a new style to work with explicit substitutions, it is able to simulate one step of classical β-reduction, whereas λζ is not. To prove confluence we introduce a generalisation of the interpretation method (cf. Hardin, 1989; Curien et al ., 1992) to a technique which uses weak normal forms (instead of strong ones). We consider that this extended method is a useful tool to obtain confluence when strong normalisation of the subcalculus of substitutions is not available. In our case, strong normalisation of the corresponding subcalculus of substitutions s e , is still a challenging open problem to the rewrite community, but its weak normalisation is established here via an effective strategy.

Abstract In this article, we extend the Barendregt Cube with ∏-conversion (which is the analogue of β-conversion, on product type level) and study its properties. We use this extension to separate the problem of whether a term is typable from the problem of what is the type of a term.

Abstract We introduce a λ-calculus notation which enables us to detect in a term, more β-redexes than in the usual notation. On this basis, we define an extended β-reduction which is yet a subrelation of conversion. The Church Rosser property holds for this extended reduction. Moreover, we show that we can transform generalised redexes into usual ones by a process called ‘term reshuffling’.

This paper argues that the basic problems of nominalization are those of set theory. We shall therefore overview the problems of set theory, the various solutions and assess the influence on nominalization. We shall then discuss Aczel's Frege structures [1] and compare them with Scott domains. Moreover, we shall set the ground for the second part which demonstrates that Frege structures are a suitable framework for dealing with nominalization.

In this paper we shall meet the application of Scott domains to nominalization and explain its problem of predication. We claim that it is possible to find a solution to such a problem within semantic domains without logic. Frege structures are more conclusive than a solution to domain equations and can be used as models for nominalization. Hence we develop a type theory based on Frege structures and use it as a theory of nominalization.