Several types of types in programming languages

Types are an important part of any modern programming language, but we often forget that the concept of type we understand nowadays is not the same it was perceived in the sixties. Moreover, we conflate the concept of "type" in programming languages with the concept of the same name in mathematical logic, an identification that is only the result of the convergence of two different paths, which started apart with different aims. The paper will present several remarks (some historical, some of more conceptual character) on the subject, as a basis for a further investigation. The thesis we will argue is that there are three different characters at play in programming languages, all of them now called types: the technical concept used in language design to guide implementation; the general abstraction mechanism used as a modelling tool; the classifying tool inherited from mathematical logic. We will suggest three possible dates ad quem for their presence in the programming language literature, suggesting that the emergence of the concept of type in computer science is relatively independent from the logical tradition, until the Curry-Howard isomorphism will make an explicit bridge between them.Comment: History and Philosophy of Computing, HAPOC 2015. To appear in LNC

The Standard Model for Programming Languages: The Birth of a Mathematical Theory of Computation

International audienceDespite the insight of some of the pioneers (Turing, von Neumann, Curry, Böhm), programming the early computers was a matter of fiddling with small architecture-dependent details. Only in the sixties some form of "mathematical program development" will be in the agenda of some of the most influential players of that time. A "Mathematical Theory of Computation" is the name chosen by John McCarthy for his approach, which uses a class of recursively computable functions as an (extensional) model of a class of programs. It is the beginning of that grand endeavour to present programming as a mathematical activity, and reasoning on programs as a form of mathematical logic. An important part of this process is the standard model of programming languages-the informal assumption that the meaning of programs should be understood on an abstract machine with unbounded resources, and with true arithmetic. We present some crucial moments of this story, concluding with the emergence, in the seventies, of the need of more "intensional" semantics, like the sequential algorithms on concrete data structures. The paper is a small step of a larger project-reflecting and tracing the interaction between mathematical logic and programming (languages), identifying some of the driving forces of this process. To Maurizio Gabbrielli, on his 60th birthda

Types in Programming Languages, between Modelling, Abstraction, and Correctness

International audienceThe notion of type to designate a class of values, and the operations on those values, is a central feature of any modern programming language. In fact, we keep calling them programming languages, but the part of a modern language devoted to the actual specification of the control flow (that is, programming stricto sensu) is only a fraction of the language itself, and two different languages are not much apart under that perspective. What ``makes a language'' are much more its modelling capabilities to describe complex relations between portions of code and between data. In a word, the central part of a language is made by the abstraction mechanisms it provides to model its application domain(s), all issues the language theorist may well group together in the type chapter of a language definition.The conquest of the summit by the notion of type is the result of a rather slow process in the history of programming languages. In a previous paper we have sketched some of the earliest history, observing that the concept of type we understand nowadays is not the same it was perceived in the sixties, and that it was largely absent (as such) in the programming languages of the fifties. While the technical term ``type'' arrives on the scene at the end of the fifties (for sure in the report on Algol 58, the use of types as a modelling tool for the ``objects of the real world'' is the contribution of the sixties (in particular under the influence of McCarthy and Hoare), which will materialize in languages like Algol W or Pascal. Moreover, we observed in that the notion of ``type'' of programming languages, which we now conflate with the concept of the same name of mathematical logic, is instead relatively independent from the logical tradition, until the Curry-Howard isomorphism will make an explicit bridge between them. The connection between these two concepts remains anonymous for a long time---some of the people knew very well the other field, and it is certain that, from mid sixties, the mathematical logic work started influencing programming languages (we think, among other, to Landin, Scott, Strachey, Hoare, McCarthy, Morris etc.). But there is no explicit, mutual recognition---concepts and formal systems are systematically re-discovered in the two fields. The first explicit connection we know of, in a non technical, but explicit, way is.The present paper will elaborate on this story, focusing on that fundamental period covering the seventies and the early eighties. It is there that the types become the cornerstone of the programming language design, passing first from the abstract data type (ADT) movement and blossoming then into the object-oriented paradigm. This will also be the occasion to reflect on how it could have been possible that a concept like ADTs, with its clear mathematical semantics, neat syntax, and straightforward implementation, could have given way to objects, a lot dirtier from any perspective the language theorist may take

What we talk about when we talk about monads

Computer science provides an in-depth understanding of technical aspects of programming concepts, but if we want to understand how programming concepts evolve, how programmers think and talk about them and how they are used in practice, we need to consider a broader perspective that includes historical, philosophical and cognitive aspects. In this paper, we develop such broader understanding of monads, a programming concept that has an infamous formal definition, syntactic support in several programming languages and a reputation for being elegant and powerful, but also intimidating and difficult to grasp. This paper is not a monad tutorial. It will not tell you what a monad is. Instead, it helps you understand how computer scientists and programmers talk about monads and why they do so. To answer these questions, we review the history of monads in the context of programming and study the development through the perspectives of philosophy of science, philosophy of mathematics and cognitive sciences. More generally, we present a framework for understanding programming concepts that considers them at three levels: formal, metaphorical and implementation. We base such observations on established results about the scientific method and mathematical entities - cognitive sciences suggest that the metaphors used when thinking about monads are more important than widely accepted, while philosophy of science explains how the research paradigm from which monads originate influences and restricts their use. Finally, we provide evidence for why a broader philosophical, sociological look at programming concepts should be of interest for programmers. It lets us understand programming concepts better and, fundamentally, choose more appropriate abstractions as illustrated in a number of case studies that conclude the paper

A necessity-driven ride on the abstraction rollercoaster of CS1 programming

International audienceIntroductory programming courses (CS1) are difficult for novices. Inspired by Problem solving followed by instruction and Productive Failure approaches, we define an original "necessity driven" learning design. Students are put in an apparently well-known situation, but this time they miss an essential ingredient (the target concept) to solve the problem. Then, struggling to solve it, they experience the necessity of that concept. A direct instruction phase follows. Finally, students return to the problem with the necessary knowledge to solve it. In a typical CS1 learning path, we recognise a challenging "rollercoaster of abstraction". We provide examples of learning sequences designed with our approach to support students when the abstraction changes (both upward and downward) inside the programming language, for example, when a new construct (and the related syntactical, conceptual, and strategic knowledge) is introduced. Also, we discuss the benefits of our design in light of Informatics education literature

Teaching informatics to novices: big ideas and the necessity of optimal guidance

This thesis reports on the two main areas of our research: introductory programming as the traditional way of accessing informatics and cultural teaching informatics through unconventional pathways. The research on introductory programming aims to overcome challenges in traditional programming education, thus increasing participation in informatics. Improving access to informatics enables individuals to pursue more and better professional opportunities and contribute to informatics advancements. We aimed to balance active, student-centered activities and provide optimal support to novices at their level. Inspired by Productive Failure and exploring the concept of notional machine, our work focused on developing Necessity Learning Design, a design to help novices tackle new programming concepts. Using this design, we implemented a learning sequence to introduce arrays and evaluated it in a real high-school context. The subsequent chapters discuss our experiences teaching CS1 in a remote-only scenario during the COVID-19 pandemic and our collaborative effort with primary school teachers to develop a learning module for teaching iteration using a visual programming environment. The research on teaching informatics principles through unconventional pathways, such as cryptography, aims to introduce informatics to a broader audience, particularly younger individuals that are less technical and professional-oriented. It emphasizes the importance of understanding informatics's cultural and scientific aspects to focus on the informatics societal value and its principles for active citizenship. After reflecting on computational thinking and inspired by the big ideas of science and informatics, we describe our hands-on approach to teaching cryptography in high school, which leverages its key scientific elements to emphasize its social aspects. Additionally, we present an activity for teaching public-key cryptography using graphs to explore fundamental concepts and methods in informatics and mathematics and their interdisciplinarity. In broadening the understanding of informatics, these research initiatives also aim to foster motivation and prime for more professional learning of informatics