Skip to main content
SpringerLink
Log in

Closed Freyd- and κ-categories

  • Conference paper
  • First Online:
Automata, Languages and Programming

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1644))

Abstract

We give two classes of sound and complete models for the computational λ-calculus, or λc-calculus. For the first, we generalise the notion of cartesian closed category to that of closed Freyd-category. For the second, we generalise simple indexed categories. The former gives a direct semantics for the computational λ-calculus. The latter corresponds to an idealisation of stack-based intermediate languages used in some approaches to compiling.

This work is supported by EPSRC grant GR/J84205: Frameworks for programming language semantics and logic.

Supported by EPSRC grant GR/L54639.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. R. Douence and P. Fradet. A Taxonomy of Functional Language Implementations Part I: Call-by-Value, INRIA Research Report No 2783, 1995.

    Google Scholar 

  2. M. Hasegawa. Decomposing typed lambda calculus into a couple of categorical programming languages, Proc. CTCS, Lect. Notes in Computer Science 953 (1995).

    Google Scholar 

  3. A. Jeffrey. Premonoidal categories and a graphical view of programs. http://www.cogs.susx.ac.uk/users/alanje/premon/paper-title.html.

  4. G.M. Kelly. The basic concepts of enriched categories. CUP (1982).

    Google Scholar 

  5. X. Leroy. The ZINC experiment: an economical implementation of the ML language. Technical Report RT-0117, INRIA, Institut National de Recherche en Informatique et en Automatique, 1990.

    Google Scholar 

  6. P.B. Levy. Call-by-push-value: a subsuming paradigm (extended abstract). In J.-Y Girard, editor, Typed Lambda-Calculi and Applications, Lecture Notes in Computer Science, April 1999.

    Google Scholar 

  7. E. Moggi. Computational Lambda calculus and Monads, Proc. LICS 89, IEEE Press (1989) 14–23.

    Google Scholar 

  8. E. Moggi. Notions of computation and monads, Information and Computation 93 (1991) 55–92.

    Article  MathSciNet  Google Scholar 

  9. A.J. Power. Premonoidal categories as categories with algebraic structure (submitted).

    Google Scholar 

  10. A.J. Power and E.P. Robinson. Premonoidal categories and notions of computation, Proc. LDPL’ 96, Math Structures in Computer Science.

    Google Scholar 

  11. A.J. Power and H. Thielecke. Environments, Continuation Semantics and Indexed Categories, Proc. Theoretical Aspects of Computer Science, Lecture Notes in Computer Science (1997) 391–414.

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of Edinburgh, Edinburgh, EH9 3JZ, Scotland

    John Power

  2. QMW, University of London, London, E1 4NS, UK

    Hayo Thielecke

Authors
  1. John Power
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hayo Thielecke
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Institute for Computer Science, Academy of Sciences of the Czech Republic, Pod vodarenskou vezi 2, 182 07, Prague 8 - Liben, Czech Republic

    Jirí Wiedermann

  2. ILLC-WINS-University of Amsterdam, Plantage Muidergracht 24, 1018, TV, Amsterdam, The Netherlands

    Peter van Emde Boas

  3. BRICS, Department of Computer Science, University of Aarhus, Ny Munkegade, Bldg. 540, DK, 8000, Aarhus C, Denmark

    Mogens Nielsen

Rights and permissions

Reprints and permissions

Copyright information

© 1999 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Power, J., Thielecke, H. (1999). Closed Freyd- and κ-categories. In: Wiedermann, J., van Emde Boas, P., Nielsen, M. (eds) Automata, Languages and Programming. Lecture Notes in Computer Science, vol 1644. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48523-6_59

Download citation

  • DOI: https://doi.org/10.1007/3-540-48523-6_59

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66224-2

  • Online ISBN: 978-3-540-48523-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation