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Recursive Functions

In: Reflexive Structures

Author

Listed:
  • Luis E. Sanchis

    (Syracuse University, School of Computer and Information Science)

Abstract

All the specification rules in the preceding chapter are explicit, in the sense that the function (or predicate) being specified is determined entirely by a procedure involving only the given functions and predicates. Now we consider recursive specifications, in which a function h is specified by a rule involving the function h itself. Such a procedure is essentially ambiguous, because in general there are many functions satisfying the specification. This ambiguity can be disposed of only by elimination of the recursion, and this can be done in several ways. Closure under recursive specifications is used to define recursive functions. The relation with Church’s thesis is discussed in some detail.

Suggested Citation

  • Luis E. Sanchis, 1988. "Recursive Functions," Springer Books, in: Reflexive Structures, chapter 0, pages 36-67, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-3878-2_2
    DOI: 10.1007/978-1-4612-3878-2_2
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