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A mathematical modeling of pure, recursive algorithms

  • Yiannis. N. Moschovakis
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 363)

Abstract

This paper follows previous work on the Formal Language of Recursion FLR and develops intensional (algorithmic) semantics for it: the intension of a term t on a structure A is a recursor, a set-theoretic object which represents the (abstract, recursive) algorithm defined by t on A. Main results are the soundness of the reduction calculus of FLR (which models faithful, algorithm-preserving compilation) for this semantics, and the robustness of the class of algorithms assigned to a structure under algorithm adjunction.

Keywords

Normal Form Turing Machine Free Variable Finite Type Functional Structure 
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References

  1. [1]
    J. Backus, Can programming be liberated from the von Neumann style? A functional style and its algebra of programs, Comm. of the ACM, 21 (1978), 613–641.Google Scholar
  2. [2]
    J. Barwise J., R. O. Gandy and Y. N. Moschovakis, The next admissible set, J. of Symbolic Logic, 36 (1971), 108–120.Google Scholar
  3. [3]
    S. Feferman, Inductive schemata and recursively continuous functionals, in: Colloquium '76, R. O. Gandy, J. M. E. Hyland eds., Studies in Logic, North Holland, Amsterdam (1977), 373–392.Google Scholar
  4. [4]
    R. O. Gandy, General recursive functionals of finite type and hierarchies of functionals, Ann. Fac. Sci. Univ. Clermont-Ferrand, 35 (1967), 5–24.Google Scholar
  5. [5]
    A. S. Kechris and Y. N. Moschovakis, Recursion in higher types, in: Handbook of Logic, J. Barwise ed., Studies in Logic, North Holland, Amsterdam (1976), 681–737.Google Scholar
  6. [6]
    S. C. Kleene, Introduction to metamathematics, van Nostrand, Princeton (1952).Google Scholar
  7. [7]
    S. C. Kleene, Recursive functionals and quantifiers of finite types, I, Trans. Amer. Math. Soc., 91 (1959), 1–52.Google Scholar
  8. [8]
    S. C. Kleene, Recursive functionals and quantifiers of finite types, II, Trans. Amer. Math. Soc., 108 (1963), 106–142.Google Scholar
  9. [9]
    P. J. Landin, The mechanical evaluation of expressions, Computer J., 6 (1964), 308–320.Google Scholar
  10. [10]
    J. McCarthy, Recursive functions of symbolic expressions and their computation by machine, Part I, Comm. of the ACM, 3 (1960), 184–195.Google Scholar
  11. [11]
    Y. N. Moschovakis, Abstract first order computability I, II, Trans. Amer. Math. Soc., 138 (1969), 427–504.Google Scholar
  12. [12]
    Y. N. Moschovakis, Axioms for computation theories-first draft, in: Logic Colloquium '69, R. Gandy, C. E. M. Yates eds., Studies in Logic, North Holland, Amsterdam (1971), 199–255.Google Scholar
  13. [13]
    Y. N. Moschovakis, Elementary induction on Abstract Structures, Studies in Logic, North Holland, Amsterdam (1974).Google Scholar
  14. [14]
    Y. N. Moschovakis, On the basic notions in the theory of induction, in: Logic, Foundations of Mathematics and Computability, R. E. Butts, J. Hintikka eds., Reidel, Dordrecht-Boston (1977), 207–236.Google Scholar
  15. [15]
    Y. N. Moschovakis, Abstract recursion as a foundation of the theory of algorithms, in: Computation and Proof Theory, M. M. Richter et al eds., Lecture Notes in Mathematics (1104), Springer, Berlin (1984), 289–364.Google Scholar
  16. [16]
    Y. N. Moschovakis, The formal language of recursion, to appear in J. Symbolic Logic.Google Scholar
  17. [17]
    D. Normann, Set recursion, in: Generalized Recursion Theory II, J. E. Fenstad, R. O. Gandy, G. E. Sacks eds., Studies in Logic, North Holland, Amsterdam (1978), 303–320.Google Scholar
  18. [18]
    D. Park, On the semantics of fair parallelism, Proc. Copenhagen Winter School, Lecture Notes in Computer Science (86), Springer (1980), 504–526.Google Scholar
  19. [19]
    R. Platek, Foundations of recursion theory, Ph. D. Thesis, Stanford Univ., 1966.Google Scholar
  20. [20]
    D. S. Scott and C. Strachey, Towards a mathematical semantics for computer languages, in: Proc. of the Symposium on Computers and Automata, Polytechnic Institute of Brooklyn Press, New York (1971), 19–46.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • Yiannis. N. Moschovakis
    • 1
  1. 1.Department of MathematicsUCLAUSA

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