Skip to main content

Types and Programs from Euler Diagrams

  • Conference paper
  • 1652 Accesses

Part of the Lecture Notes in Computer Science book series (LNAI,volume 5223)


Type theory provides a formal basis for programming languages and can also be used to model reasoning systems such as Euler diagrams. We present part of a simple type theory of Euler diagrams. Expressing a system of reasoning with Euler diagrams as a collection of types and operations on types (which correspond to diagrams and reasoning rules) is a first step towards embedding visually modelled constraints directly into the type system of a programming language.

This is a preview of subscription content, access via your institution.

Buying options

USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions


  1. Altenkirch, T., Mcbride, C., Mckinna, J.: Why dependent types matter (2005) (accessed 01/02/08),

  2. Nordstrom, B., Petersson, K., Smith, J.M.: Programming in Martin-Löf’s Type Theory. OUP (1990)

    Google Scholar 

  3. Stapleton, G., Delaney, A.: Evaluating and generalizing constraint diagrams. Journal of Visual Languages and Computing (JVLC 2008)

    Google Scholar 

  4. Stapleton, G., Masthoff, J., Flower, J., Fish, A., Southern, J.: Automated theorem proving in Euler diagrams systems. Journal of Automated Reasoning 39, 431–470 (2007)

    CrossRef  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations


Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 2008 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Burton, J. (2008). Types and Programs from Euler Diagrams. In: Stapleton, G., Howse, J., Lee, J. (eds) Diagrammatic Representation and Inference. Diagrams 2008. Lecture Notes in Computer Science(), vol 5223. Springer, Berlin, Heidelberg.

Download citation

  • DOI:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-87729-5

  • Online ISBN: 978-3-540-87730-1

  • eBook Packages: Computer ScienceComputer Science (R0)