Subduing self-application

  • Corrado Böhm
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 372)


Recursive equational schemes, defining total functions on natural numbers, are embedded into a combinatory algebra producing an equation system having the following shape:
$$f(0) = b,f(s(x)) = H(a,f,x).$$
Two methods are described to derive the combinator representing f by means of a generalized morphism, avoiding the use of fixed point combinators and preserving strong normalizability, i.e. the same feature warranted by most type disciplines.

Can a given combinator s represent a successor of some adequate algebraic numeral system? Answers to this question are exemplified and assembled to solve the problem of embedding the infinite cyclic group ℤ of integers into a combinatory algebra.


Self-application recursive schemes combinatory and lambda-algebras typability strong normalizability iterator recursor permutator 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • Corrado Böhm
    • 1
  1. 1.Dip. di Matematica — Istituto "G.Castelnuovo"Università degli Studi di Roma "La Sapienza"Roma

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