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Minimal forms in λ-cakulus computations

Published online by Cambridge University Press:  12 March 2014

Corrado Böhm  and
Silvio Micali
Corrado Böhm
Affiliation:
Università Di Roma, 00100 Roma, Italy
Silvio Micali
Affiliation:
Università Di Roma, 00100 Roma, Italy
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Abstract

The notion of a minimal form is defined as an extension of the notion of a normal form in λ-β-calculus and its meaning is discussed in a computational environment. The features of the Knuth-Gross reduction strategy are used to prove that to possess a minimal form, for a generic term, is a semidecidable predicate.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 45 , Issue 1 , March 1980 , pp. 165 - 171
Copyright
Copyright © Association for Symbolic Logic 1980

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References

REFERENCES

[1]Barendregt, H.P., Open problems, λ-calculus and computer science theory (Böhm, C., Editor), Lecture Notes in Computer Science, vol. 37, Springer-Verlag, Berlin and New York, 1975, pp. 367–370.Google Scholar
[2]Barendregt, H.P., Bergstra, J., Klop, J.W. and Volken, H., Degrees, reductions and representability, preprint, no. 22, Utrecht University, Department of Mathematics, 02 1976.Google Scholar
[3]Church, A., The calculi of lambda conversion, Annals of Mathematical Studies, no. 6, Princeton University Press, Princeton, N.J., 1941.Google Scholar
[4]Curry, H.B. and Feys, R., Combinatory logic, vol. 1, North-Holland, Amsterdam, 1958.Google Scholar
[5]Hindley, J.R., Standard and normal reductions, Preprint, Swansea, 1975.Google Scholar
[6]Knuth, D.E., Examples of formal semantics, Symposium on semantics of algorithmic languages, Lecture Notes in Mathematics, vol. 188 (Engeler, E., Editor), Springer-Verlag, Berlin and New York, 1970, pp. 212–235.CrossRefGoogle Scholar
[7]Lesmo, L. and Zacchi, M., A strong version of Church-Rosser theorem and its relation with formal semantics, paper presented to the Journées des Mathématiques de la Compilations, Marseille, 1973.Google Scholar
[8]Scott, D., Continuous lattices, Toposes, algebraic geometry and logic, Lecture Notes in Mathematics, no. 274, Springer-Verlag, Berlin and New York, 1972.Google Scholar
[9]Schroer, D.E., Doctoral Thesis, Cornell University, Ithaca, New York.Google Scholar
[10]Turing, A.M., Computahility and λ-definability, this Journal, vol. 2 (1937), pp. 153–163.Google Scholar
[11]Turing, A.M., The p-function in λ-K-conversion, this Journal, vol. 2 (1937), p. 164.Google Scholar
[12]Venturini-Zilli, M., Head recurrent terms in combinatory logic: a generalization of the notion of head-normal form, Proceedings of the Sth International Colloquium on Automata, Languages and Programming, Lecture Notes in Computer Science, no. 62, Springer-Verlag, Berlin and New York, 1978, pp. 477–493.Google Scholar