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International Symposium on Theoretical Aspects of Computer Software

TACS 1991: Theoretical Aspects of Computer Software pp 290–310Cite as

On abstraction and the expressive power of programming languages

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 526))

Abstract

We present a tentative theory of programming language expressiveness based on reductions (language translations) that preserve observational equivalence. These are called “abstraction-preserving” because of a connection with a definition of “abstraction” or “information-hiding” mechanism. If there is an abstraction-preserving reduction from one language to another, then essentially every function on natural numbers that is definable in the first is also definable in the second. Moreover, regardless of the set of first-order functions definable in either language, no programming language with an abstraction mechanism can be reduced to a language without. Since Lisp with user-defined special forms does not have an abstraction mechanism, it is therefore not “universal” in this theory, in spite of the ability to define every partial recursive function on the natural numbers. Several examples and counter-examples to abstraction-preserving reductions are given. We do not know whether there is a natural universal language with respect to abstraction-preserving reduction.

Supported in part by an NSF PYI Award, matching funds from Digital Equipment Corporation, the Powell Foundation, and Xerox Corporation; NSF grant CCR-8814921 and the Wallace F. and Lucille M. Davis Faculty Scholarship.

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Authors and Affiliations

  1. Department of Computer Science, Stanford University, 94305, Stanford, CA

    John C. Mitchell

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  1. John C. Mitchell
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Takayasu Ito Albert R. Meyer

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© 1991 Springer-Verlag Berlin Heidelberg

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Mitchell, J.C. (1991). On abstraction and the expressive power of programming languages. In: Ito, T., Meyer, A.R. (eds) Theoretical Aspects of Computer Software. TACS 1991. Lecture Notes in Computer Science, vol 526. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-54415-1_51

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  • DOI: https://doi.org/10.1007/3-540-54415-1_51

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-54415-9

  • Online ISBN: 978-3-540-47617-7

  • eBook Packages: Springer Book Archive

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