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Axiomatic Extensions

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The Combinatory Programme

Part of the book series: Progress in Theoretical Computer Science ((PTCS))

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Abstract

Combinatory algebras are models of Combinatory Logic (CL); they are algebras that are combinatory complete; i.e., they satisfy the principle of combinatory abstraction.1 As Engeler pointed out in the introductory chapter, suitably rich models of combinatory logic may serve as universes for a big variety of mathematical activities, from algebra to numerical analysis.

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References

  1. Barendregt, H.P., The Lambda Calculus, North-Holland, Amsterdam, 1984.

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  2. Beeson, M.J., Foundations of Constructive Mathematics. Springer-Verlag, Berlin, 1985.

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  3. Bishop, E., Foundations of Constructive Analysis, McGraw-Hill, New York, 1967.

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  4. Engeler, E., Representation of varieties in combinatory algebras, Algebra Universalis, 25: 85–95, 1988.

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  5. Weibel, T. Some Representation Problems in Combinatory Logic, Ph.D. thesis, No. 8903, ETH-ZĂĽrich, 1989.

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  6. Weibel, T., Extension of combinatory logic to a theory of combina- tory representation, Theoret. Comput. Sci 97 (1992), 157–173.

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© 1995 Birkhäuser Boston

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Weibel, T. (1995). Axiomatic Extensions. In: The Combinatory Programme. Progress in Theoretical Computer Science. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-4268-0_2

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  • DOI: https://doi.org/10.1007/978-1-4612-4268-0_2

  • Publisher Name: Birkhäuser Boston

  • Print ISBN: 978-1-4612-8716-2

  • Online ISBN: 978-1-4612-4268-0

  • eBook Packages: Springer Book Archive

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