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International Symposium on Mathematical Foundations of Computer Science

MFCS 1993: Mathematical Foundations of Computer Science 1993 pp 122–141Cite as

Observable properties of higher order functions that dynamically create local names, or: What's new?

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 711))

Abstract

The research reported in this paper is concerned with the problem of reasoning about properties of higher order functions involving state. It is motivated by the desire to identify what, if any, are the difficulties created purely by locality of state, independent of other properties such as side-effects, exceptional termination and non-termination due to recursion. We consider a simple language (equivalent to a fragment of Standard ML) of typed, higher order functions that can dynamically create fresh names; names are created with local scope, can be tested for equality and can be passed around via function application, but that is all. Despite the extreme simplicity of the language and its operational semantics, the observable properties of such functions are shown to be very subtle. A notion of ‘logical relation’ is introduced which incorporates a version of representation independence for local names. We show how to use it to establish observational equivalences. The method is shown to be complete (and decidable) for expressions of first order types, but incomplete at higher types.

Supported by UK SERC grant GR/G53279 and CEC ESPRIT project CLICS-II

Supported by UK SERC studentship 91307943 and CEC SCIENCE project PL910296

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Authors and Affiliations

  1. Computer Laboratory, University of Cambridge, Pembroke Street, CB2 3QG, Cambridge, England

    Andrew M. Pitts & Ian D. B. Stark

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  1. Andrew M. Pitts
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  2. Ian D. B. Stark
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Andrzej M. Borzyszkowski Stefan Sokołowski

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© 1993 Springer-Verlag Berlin Heidelberg

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Pitts, A.M., Stark, I.D.B. (1993). Observable properties of higher order functions that dynamically create local names, or: What's new?. In: Borzyszkowski, A.M., Sokołowski, S. (eds) Mathematical Foundations of Computer Science 1993. MFCS 1993. Lecture Notes in Computer Science, vol 711. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57182-5_8

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  • DOI: https://doi.org/10.1007/3-540-57182-5_8

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-57182-7

  • Online ISBN: 978-3-540-47927-7

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