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Reflections on reflections

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Programming Languages: Implementations, Logics, and Programs (PLILP 1997)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1292))

Abstract

In the functional programming literature, compiling is often expressed as a translation between source and target program calculi. In recent work, Sabry and Wadler proposed the notion of a reflection as a basis for relating the source and target calculi. A reflection elegantly describes the situation where there is a kernel of the source language that is isomorphic to the target language. However, we believe that the reflection criteria is so strong that it often excludes the usual situation in compiling where one is compiling from a higher-level to a lower-level language.

We give a detailed analysis of several translations commonly used in compiling that fail to be reflections. We conclude that, in addition to the notion of reflection, there are several relations weaker a reflection that are useful for characterizing translations. We show that several familiar translations (that are not naturally reflections) form what we call a reduction correspondence. We introduce the more general notion of a (R1, R2, R3, R4)-correspondence as a framework for describing relations between source and target calculi.

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Author information

Authors and Affiliations

  1. Centrum voor Wiskunde en Informatica (CWI), PO Box 94079, 1090, GB Amsterdam, The Netherlands

    Gilles Barthel

  2. Computer Science Department, Oklahoma State University, 219 Math Sciences, 74078, Stillwater, OK, USA

    John Hatcliff

  3. Department of Computer Science, University of Copenhagen (DIKU), Universitetsparken 1, DK-2100, Copenhagen, Denmark

    Morten Heine Sørensen

Authors
  1. Gilles Barthel
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  2. John Hatcliff
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  3. Morten Heine Sørensen
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Editor information

Hugh Glaser Pieter Hartel Herbert Kuchen

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© 1997 Springer-Verlag Berlin Heidelberg

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Barthel, G., Hatcliff, J., Sørensen, M.H. (1997). Reflections on reflections. In: Glaser, H., Hartel, P., Kuchen, H. (eds) Programming Languages: Implementations, Logics, and Programs. PLILP 1997. Lecture Notes in Computer Science, vol 1292. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0033848

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  • DOI: https://doi.org/10.1007/BFb0033848

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  • Print ISBN: 978-3-540-63398-3

  • Online ISBN: 978-3-540-69537-0

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