Skip to main content
SpringerLink
Log in

An FP domain with infinite objects

  • Conference paper
  • First Online:
Mathematical Foundations of Programming Semantics (MFPS 1985)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 239))

  • 150 Accesses

Abstract

We describe a basis for extending Backus's FP languages to apply to infinite data objects, including streams, using data objects called prefixes, which can be viewed as approximations of either finite or infinite sequences. The resulting set of data objects, together with its limit points, admits not only an infinite number of entries in a sequence, but also infinitely nested expressions. Elements in this domain include arbitrarily good finite approximations to any of the infinite objects of the domain.

We also describe a mechanism for extending the primitive functions of an FP language over its domain to a corresponding stream FP language (or SFP language) capable of handling both finite and infinite elements over the extended domain. Extensions of the common functional forms are described. The algebra of FP programs is preserved nearly unchanged. Example programs are given.

This work was supported in part by ARO grant number DAAG29-83-K-0090 and NSF grant number MCS- 8313312

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

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography

  1. Backus, J. Can programming be liberated from the von Neumann style? A functional style and its algebra of programs. Communications of the ACM, 21, No. 8, Aug 1978, pp. 613–641.

    Google Scholar 

  2. Broy, M. A fixed point approach to applicative multiprogramming, in Theoretical Foundations of Programming Methodology. D. Reidel, 1982. pp. 565–622. Ed. by M. Broy & G. Schmidt.

    Google Scholar 

  3. Burge, W.H. Recursive programming techniques. Reading, Mass: Addison-Wesley, 1975.

    Google Scholar 

  4. Dosch, W. & Moller, B. Busy and lazy FP with infinite objects. In Conference Record of the 1984 ACM Symposium on LISP and Functional Programming, 1984. pp. 282–292.

    Google Scholar 

  5. Feldman, G. Functional Specifications of a Text Editor. In Conference Record of the 1982 ACM Symposium on LISP and Functional Programming, 1982. pp. 37–46.

    Google Scholar 

  6. Halpern, J., J. Williams, E. Wimmers & T. Winkler. In Conference Record of the Twelfth Annual ACM Symposium on Principles of Programming Languages, 1985. pp. 108–120.

    Google Scholar 

  7. Henderson, P. Purely Functional Operating Systems in Functional Programming and its Applications. Cambridge University Press, 1982. pp. 177–192.

    Google Scholar 

  8. Ida, T. & Tanaka, J. Functional programming with streams, in Information Processing. North-Holland, 1983. pp. 265–270.

    Google Scholar 

  9. Jacobson, N. Basic Algebra I. San Francisco: W.H.Freeman & Co., 1974.

    Google Scholar 

  10. Kahn, G. The semantics of a simple language for parallel programming. In Proceedings, IFIP Congress 74, 1974 pp. 471–475.

    Google Scholar 

  11. Kahn, G. & Macqueen, D.B. Coroutines and networks of parallel processes. In Proceedings, IFIP Congress 77, North-Holland, Jan 1977.

    Google Scholar 

  12. Keller, R.M. Semantics of parallel program graphs. Technical Report UUCS-77-110, University of Utah, July 22, 1977.

    Google Scholar 

  13. Keller, R.M. Denotational models for parallel programs with indeterminate operators, in Formal Description of Programming Concepts. North-Holland, 1978. pp. 337–366.

    Google Scholar 

  14. Nakata, I. & Sassa, M. Programming with streams. Technical Report RJ3751(43317). IBM. Jan 1983.

    Google Scholar 

  15. Scott, D.S. Lectures on a mathematical theory of computation, in Theoretical Foundations of Programming Methodology. D. Reidel, 1982. pp. 146–292. Ed. by M. Broy & G. Schmidt.

    Google Scholar 

  16. Stoy, J.E. Some Mathematical Aspects of Functional Programming, in Functional Programming and its Applications. Cambridge University Press, 1982. pp. 217–252.

    Google Scholar 

  17. Tanaka, J. & Ida, T. Stream extension for fp-like language. 1981. (Unpublished paper.)

    Google Scholar 

  18. Thomas, T.A. An fp domain with infinite objects. Technical Report TR 83-009. University of North Carolina at Chapel Hill. 1983.

    Google Scholar 

  19. Turner, D.A. Recursion Equations as a Programming Language, in Functional Programming and its Applications. Cambridge University Press, 1982. pp. 1–28.

    Google Scholar 

  20. Wadler, P. Applicative style of programming, program transformation and list operators. In ACM-MIT Proceedings of the 1981 Conference on Functional Programming Languages and Computer Architecture., Oct 1981. pp. 25–32.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, University of North Carolina at Chapel Hill, 27514, Chapel Hill, NC

    Teresa A. Thomas & Donald F. Stanat

Authors
  1. Teresa A. Thomas
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Donald F. Stanat
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Austin Melton

Rights and permissions

Reprints and permissions

Copyright information

© 1986 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Thomas, T.A., Stanat, D.F. (1986). An FP domain with infinite objects. In: Melton, A. (eds) Mathematical Foundations of Programming Semantics. MFPS 1985. Lecture Notes in Computer Science, vol 239. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-16816-8_40

Download citation

  • DOI: https://doi.org/10.1007/3-540-16816-8_40

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-16816-4

  • Online ISBN: 978-3-540-44861-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation