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Acceptable functional programming systems

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In this paper we present a self-contained treatment of the theory of computable functions using acceptable functional programming systems. We construct a particular acceptable functional programming system. Within the framework of this system we prove two main theorems to show that, when working with substitution operators, the fixed point function defined by the mechanism of the system and the fixed point function defined by the recursion theorem are both equal to the least fixed point. Furthermore we show that the programs defined by the mechanism of the system are easier and faster than the ones defined by the recursion theorem. We make some suggestions about how to implement the system using a suitable environment. We also formulate a natural question: what is the relationship between substitution operators and computable operators?

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References

  1. Allen, J.: Anatomy of Lisp. New York: McGraw-Hill 1978

    Google Scholar 

  2. Backus, J.: Can programming be liberated from the von Neumann style? A functional style and its algebra of programs. CACM, 21-8, 613–641 (1978)

    MathSciNet  Google Scholar 

  3. Backus, J.: The algebra of functional programs: Function level reasoning, linear equations and extended definitions. Proc., April 81, International Colloquium on the Formalization of Programming Concepts. Lect. Notes Comput. Sci. 107, 1–43 (1981)

  4. Broy, M., Wirsing, M.: Partial Abstract Types. Acta Inf. 18, 47–64 (1982)

    MathSciNet  Google Scholar 

  5. Broy, M., Wirsing, M.: Algebraic Definition of a Functional Programming Language and its Semantic Models. RAIRO, 17, 137–161 (1983)

    MathSciNet  Google Scholar 

  6. Cutland, N.: Computability. Cambridge: Cambridge University Press 1980

    Google Scholar 

  7. Duponcheel, L., Duponcheel, M.: Elementary Operators and Least Fixed Point Functions. (To appear)

  8. Goguen, J.A., Tatcher, J.W., Wagner, E.G.: An initial algebra approach to the specification, correctness and implementation of abstract data types. In: Current trends in programming methodology, Vol. IV (Yeh ed.). London: Prentice-Hall 1979

    Google Scholar 

  9. Machtey, M., Young, P.: An introduction to the General Theory of Algorithms. New York: Elsevier 1978

    Google Scholar 

  10. Manna, Z.: Mathematical theory of Computation. New York: McGraw-Hill 1974

    Google Scholar 

  11. Manna, Z., Ness, S., Vuillemin, J.: Inductive methods for proving properties of programs. CACM, 16-8, 491–502 (1973)

    MathSciNet  Google Scholar 

  12. Williams, J.H.: On the development of the algebra of functional programs. Tech. Report RJ 2983. San Jose, CA: IBM Research Lab., 1980

    Google Scholar 

  13. Williams, J.H.: Formal representations of recursively defined functional programs. Proc., April 81, International Colloquium on the Formalization of Programming Concepts. Lect. Notes Comput. Sci. 107, 460–470 (1981)

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Duponcheel, L., Duponcheel, M. Acceptable functional programming systems. Acta Informatica 23, 67–98 (1986). https://doi.org/10.1007/BF00268076

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