Skip to main content
Springer Nature Link
Log in

The Laws of Programming Unify Process Calculi

  • Conference paper
Mathematics of Program Construction (MPC 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7342))

Included in the following conference series:

  • 626 Accesses

Abstract

We survey the well-known algebraic laws of sequential programming, and propose some less familiar laws for concurrent programming. On the basis of these laws, we derive the rules of a number of classical programming and process calculi, for example, those due to Hoare, Milner, and Kahn. The algebra is simpler than each of the calculi derived from it, and stronger than all the calculi put together. We end with a section describing the role of unification in Science and Engineering.

This paper is dedicated in friendship and admiration to the memory of Robin Milner and Gilles Kahn.

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

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

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.

Similar content being viewed by others

References

  1. Hoare, C.A.R., Hayes, I.J., Jifeng, H., Morgan, C.C., Roscoe, A.W., Sanders, J.W., Sorensen, I.H., Spivey, J.M., Sufrin, B.A.: Laws of programming. Commun. ACM 30, 672–686 (1987)

    Article  MATH  Google Scholar 

  2. Hoare, C.A.R.: An axiomatic basis for computer programming. Commun. ACM 12, 576–580 (1969)

    Article  MATH  Google Scholar 

  3. Milner, R.: A Calculus of Communication Systems. LNCS, vol. 92. Springer, Heidelberg (1980)

    Book  Google Scholar 

  4. Kahn, G.: Natural Semantics. In: Brandenburg, F.J., Wirsing, M., Vidal-Naquet, G. (eds.) STACS 1987. LNCS, vol. 247, pp. 22–39. Springer, Heidelberg (1987)

    Chapter  Google Scholar 

  5. Dijkstra, E.W.: A Discipline of Programming. Prentice-Hall, Englewood Cliffs (1976)

    MATH  Google Scholar 

  6. Back, R.J., von Wright, J.: Refinement Calculus: A Systematic Introduction. Graduate Texts in Computer Science. Springer (1998)

    Google Scholar 

  7. Morgan, C.: Programming from specifications, 2nd edn. Prentice Hall International (UK) Ltd., Hertfordshire (1994)

    MATH  Google Scholar 

  8. Plotkin, G.D.: A structural approach to operational semantics. Technical Report DAIMI FN-19, Computer Science Department, Aarhus University, Aarhus, Denmark (September 1981)

    Google Scholar 

  9. Jones, C.B.: Development Methods for Computer Programs including a Notion of Interference. PhD thesis, Oxford University (June 1981); printed as: Programming Research Group, Technical Monograph 25

    Google Scholar 

  10. Isabelle/HOL proofs (2012), http://se.inf.ethz.ch/people/vanstaden/LawsOfProgrammingUnifyProcessCalculi.thy

  11. Kozen, D.: A completeness theorem for Kleene algebras and the algebra of regular events. Inf. Comput. 110, 366–390 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  12. Kozen, D.: On Hoare logic and Kleene algebra with tests. ACM Trans. Comput. Logic 1(1), 60–76 (2000)

    Article  MathSciNet  Google Scholar 

  13. O’Hearn, P.W., Reynolds, J.C., Yang, H.: Local Reasoning about Programs that Alter Data Structures. In: Fribourg, L. (ed.) CSL 2001 and EACSL 2001. LNCS, vol. 2142, pp. 1–19. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  14. O’Hearn, P.W.: Resources, Concurrency and Local Reasoning. In: Gardner, P., Yoshida, N. (eds.) CONCUR 2004. LNCS, vol. 3170, pp. 49–67. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  15. Nielson, H.R., Nielson, F.: Semantics with Applications: A Formal Introduction, revised edn. (July 1999), http://www.daimi.au.dk/~bra8130/Wiley_book/wiley.html , original edition published 1992 by John Wiley & Sons

  16. Hoare, T., Wickerson, J.: Unifying models of data flow. In: Broy, M., Leuxner, C., Hoare, T. (eds.) Proceedings of the 2010 Marktoberdorf Summer School on Software and Systems Safety. IOS Press (2011)

    Google Scholar 

  17. Dinsdale-Young, T., Dodds, M., Gardner, P., Parkinson, M.J., Vafeiadis, V.: Concurrent Abstract Predicates. In: D’Hondt, T. (ed.) ECOOP 2010. LNCS, vol. 6183, pp. 504–528. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  18. Godefroid, P., Levin, M.Y., Molnar, D.: SAGE: Whitebox fuzzing for security testing. Queue 10(1), 20:20–20:27 (2012)

    Google Scholar 

  19. Kleene, S.C.: Representation of events in nerve nets and finite automata. Automata Studies, pp. 3–41. Princeton University Press (1956)

    Google Scholar 

  20. Tarski, A.: On the calculus of relations. J. Symb. Log. 6(3), 73–89 (1941)

    Article  MathSciNet  MATH  Google Scholar 

  21. Gischer, J.L.: The equational theory of pomsets. Theor. Comput. Sci. 61, 199–224 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  22. Hoare, C.A.R.T., Möller, B., Struth, G., Wehrman, I.: Concurrent Kleene Algebra. In: Bravetti, M., Zavattaro, G. (eds.) CONCUR 2009. LNCS, vol. 5710, pp. 399–414. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  23. Wehrman, I., Hoare, C.A.R., O’Hearn, P.W.: Graphical models of separation logic. Inf. Process. Lett. 109(17), 1001–1004 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  24. Hoare, C.A.R., Hussain, A., Möller, B., O’Hearn, P.W., Petersen, R.L., Struth, G.: On Locality and the Exchange Law for Concurrent Processes. In: Katoen, J.-P., König, B. (eds.) CONCUR 2011. LNCS, vol. 6901, pp. 250–264. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Microsoft Research, Cambridge, United Kingdom

    Tony Hoare

  2. ETH Zurich, Switzerland

    Stephan van Staden

Authors
  1. Tony Hoare
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Stephan van Staden
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Computer Science, Oxford University, Wolfson Building, Parks Road, OX1 3QD, Oxford, UK

    Jeremy Gibbons

  2. Facultad de Informática, Universidad Politécnica de Madrid, Campus de Montegancedo s/n, 28660, Boadilla del Monte, Madrid, Spain

    Pablo Nogueira

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Hoare, T., van Staden, S. (2012). The Laws of Programming Unify Process Calculi. In: Gibbons, J., Nogueira, P. (eds) Mathematics of Program Construction. MPC 2012. Lecture Notes in Computer Science, vol 7342. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31113-0_2

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-31113-0_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-31112-3

  • Online ISBN: 978-3-642-31113-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics