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

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Pursuit of the Universal (CiE 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9709))

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Abstract

The 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.

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Notes

  1. 1.

    The very first use of the term “type” in programming is probably Curry’s [7], to distinguish between memory words containing instructions (“orders”) and those containing data (“quantities”). These reports by Curry, as reconstructed by [10], contain a surprising, non-trivial mathematical theory of programs, up to a theorem analogous to the “well-typed expressions do not go wrong” of [23]! Despite G.W. Patterson’s review on JSL 22(01), 1957, 102–103, we do not know of any influence of this theory on subsequent developments of programming languages.

  2. 2.

    “A type is a class of values. Associated with each type there are a number of operations which apply to such values”.

  3. 3.

    “Class” is, however, the terminology of Simula 67; in Simula I they are called activities.

  4. 4.

    Under this term Priestly refers to the “coherent and comprehensive research programme within which the Algol 60 report had the status of a paradigmatic achievement, in the sense defined by the historian of science Thomas Kuhn. This research programme established the first theoretical framework for studying not only the design of programming languages, but also the process of software development.” Therefore, are grouped under this broad term the developments of structured programming, of software engineering à la Dijkstra, of the formal description of programming language semantics, etc.

  5. 5.

    A language provides representation independence if two correct implementations of a single specification of an ADT are observationally indistinguishable by the clients of these types.

  6. 6.

    For a pedagogical discussion, see [11], Chap. 10.

  7. 7.

    An expression of Vladimir Voevodsky.

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Authors and Affiliations

  1. Dipartimento di Informatica–Scienza e Ingegneria, Università di Bologna and INRIA, Bologna, Italy

    Simone Martini

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  1. Simone Martini
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Correspondence to Simone Martini .

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Editors and Affiliations

  1. Swansea University, Swansea, United Kingdom

    Arnold Beckmann

  2. Université Paris-Diderot - Paris 7, Paris, France

    Laurent Bienvenu

  3. University of South Florida, Tampa, Florida, USA

    Nataša Jonoska

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Martini, S. (2016). Types in Programming Languages, Between Modelling, Abstraction, and Correctness. In: Beckmann, A., Bienvenu, L., Jonoska, N. (eds) Pursuit of the Universal. CiE 2016. Lecture Notes in Computer Science(), vol 9709. Springer, Cham. https://doi.org/10.1007/978-3-319-40189-8_17

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  • DOI: https://doi.org/10.1007/978-3-319-40189-8_17

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