Acta Informatica

, Volume 28, Issue 6, pp 559–574 | Cite as

On the expansion of non-linear functions

  • Peter G. Harrison


Expansion theorems are obtained for classes of non-linear functions. From these, properties of some complex recursive functions are derived by finding equivalent non-recursive definitions, and a combinator-based formulation facilitates a simpler analysis than is typical of the applicative calculus approach.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [Ba 78] Backus, J.W.: Can programming be liberate from the von Neumann style? A functional style and its algebra of programs. CACM 21(8), 613–641 (1978)Google Scholar
  2. [Ba 81] Backus, J.W.: The algebra of functional programs: Function level reasoning, linear equations and extended definitions. (Lect. Notes Comput. Sci., vol 107, pp. 1–43) Berlin, Heidelberg, New York: Springer 1981Google Scholar
  3. [BM 87] Bird, R.S., Meertens, L.G.L.T.: Two exercises found in a book on Algorithmics. In: Meertens L.G.L.T. (ed) Program specification and transformation, pp. 451–457. Amsterdam: North-Holland 1987Google Scholar
  4. [Cu 86] Curien, P.-L.: Categorical combinators, sequential algorithms and functional programming: San Francisco: Pitman 1986Google Scholar
  5. [FH 88] Field, A.J., Harrison, P.G.: Functional programming. Reading, MA: Addison-Wesley 1988Google Scholar
  6. [Ha 88] Harrison, P.G.: Linearisation: an optimisation for non-linear functional programs. Sci. Comput. Programm. 10: 281–318 (1988)Google Scholar
  7. Harrison, P.G., Khoshnevisan, H.: A new approach to recursion removal. Theoret. Comput. Sci. (to appear 1992)Google Scholar
  8. STOP Summer School on Construcitve Algorithmics. Ameland, Holland, September, 1989Google Scholar
  9. [Wa 80] Continuation-based program transformation strategies. JACM27, 1 (1980)Google Scholar
  10. [Wi 82] Williams, J.H.: On the development of the algebra of functional programs. ACM Trans. Programm. Lang. Syst.4, 733–757 (1982)Google Scholar

Copyright information

© Springer-Verlag 1991

Authors and Affiliations

  • Peter G. Harrison
    • 1
  1. 1.Department of ComputingImperial College of Science, Technology and MedicineLondonEngland

Personalised recommendations