Cables, Trains and Types

  • Simon J. GayEmail author
Part of the Lecture Notes in Computer Science book series (LNCS, volume 12065)


Many concepts of computing science can be illustrated in ways that do not require programming. CS Unplugged is a well-known resource for that purpose. However, the examples in CS Unplugged and elsewhere focus on topics such as algorithmics, cryptography, logic and data representation, to the neglect of topics in programming language foundations, such as semantics and type theory.

This paper begins to redress the balance by illustrating the principles of static type systems in two non-programming scenarios where there are physical constraints on forming connections between components. The first scenario involves serial cables and the ways in which they can be connected. The second example involves model railway layouts and the ways in which they can be constructed from individual pieces of track. In both cases, the physical constraints can be viewed as a type system, such that typable systems satisfy desirable semantic properties.



I am grateful to Ornela Dardha, Conor McBride and Phil Wadler for comments on this paper and the seminar on which it is based; to João Seco for telling me about the Alligator Eggs presentation of untyped \(\lambda \)-calculus; and to an anonymous reviewer for noticing a small error.


  1. 1.
  2. 2.
    CS Unplugged.
  3. 3.
  4. 4.
  5. 5.
    Thomas & Friends.
  6. 6.
    Abramsky, S., Gay, S.J., Nagarajan, R.: Interaction categories and the foundations of typed concurrent programming. In: Broy, M. (ed.) Proceedings of the NATO Advanced Study Institute on Deductive Program Design, pp. 35–113 (1996)Google Scholar
  7. 7.
    Awdrey, W.: Thomas the tank engine (1946)Google Scholar
  8. 8.
    Girard, J.-Y.: Linear logic. Theoret. Comput. Sci. 50, 1–102 (1987)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Joyal, A., Street, R., Verity, D.: Traced monoidal categories. Math. Proc. Cambridge Philos. Soc. 119(3), 447–468 (1996)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Kelly, G.M., Laplaza, M.L.: Coherence for compact closed categories. J. Pure Appl. Algebra 19, 193–213 (1980)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Ştefănescu, G.: Network Algebra. Springer, Heidelberg (2000). Scholar
  12. 12.
    Victor, B.: Alligator eggs.

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.School of Computing ScienceUniversity of GlasgowGlasgowUK

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