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Compact numeral representation with combinators

Published online by Cambridge University Press:  12 March 2014

E. V. Krishnamurthy
Affiliation:
Computer Science Department, University of Waikato, Hamilton, New Zealand
B. P. Vickers
Affiliation:
Computer Science Department, University of Waikato, Hamilton, New Zealand

Abstract

This paper is concerned with the combinator representation of numeral systems with logarithmic space complexity of symbols. The principle used is based on the lexicographic ordering of words over a finite alphabet.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 1987

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References

REFERENCES

[1]Curry, H. B., Hindley, R. and Seldin, J., Combinatory logic. Vol. 2, North-Holland, Amsterdam, 1972.Google Scholar
[2]Curry, H. B. and Feys, R., Combinatory logic. Vol. 1, North-Holland, Amsterdam, 1958.Google Scholar
[3]Wadsworth, C. P., Some unusual λ-calculus numeral systems, To H. B. Curry: Essays on combinatory logic, lambda calculus and formalism (Seldin, J. P. and Hindley, J. R., editors), Academic Press, New York, 1980, pp. 215230.Google Scholar
[4]Böhm, C., An abstract approach to (hereditary) finite sequences of comhinators, To H. B. Curry: Essays on combinatory logic, lambda calculus and formalism (Seldin, J. P. and Hindley, J. R., editors), Academic Press, New York, 1980, pp. 231242.Google Scholar
[5]McCarthy, J., Recursive functions of symbolic expressions and their computation by machine, Communications of the Association for Computing Machinery, vol. 7 (1960), pp. 184195.CrossRefGoogle Scholar
[6]Krishnamurthy, E. V., Introductory theory of computer science, Macmillan, New York, 1983.CrossRefGoogle Scholar
[7]Corcoran, J., Frank, W. and Maloney, M., String theory, this Journal, vol. 39 (1974), pp. 625637.Google Scholar
[8]Church, A., A set of postulates for the foundation of logic, Annals of Mathematics, ser. 2, vol. 33 (1932), pp. 346366.CrossRefGoogle Scholar