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Subduing self-application

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Automata, Languages and Programming (ICALP 1989)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 372))

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Abstract

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.

This research has been supported by grants of Ministero della Pubblica Istruzione (Italy), CNR (Italy) and "Projet Stimulation" (EEC).

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Authors and Affiliations

  1. Dip. di Matematica — Istituto "G.Castelnuovo", Università degli Studi di Roma "La Sapienza", P.le A.Moro 5, 1-00185, Roma

    Corrado Böhm

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  1. Corrado Böhm
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Giorgio Ausiello Mariangiola Dezani-Ciancaglini Simonetta Ronchi Della Rocca

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Böhm, C. (1989). Subduing self-application. In: Ausiello, G., Dezani-Ciancaglini, M., Della Rocca, S.R. (eds) Automata, Languages and Programming. ICALP 1989. Lecture Notes in Computer Science, vol 372. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0035755

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  • DOI: https://doi.org/10.1007/BFb0035755

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-51371-1

  • Online ISBN: 978-3-540-46201-9

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