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Reflections on reflections

  • Gilles Barthel
  • John Hatcliff
  • Morten Heine Sørensen
Compilation
Part of the Lecture Notes in Computer Science book series (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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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Gilles Barthel
    • 1
  • John Hatcliff
    • 2
  • Morten Heine Sørensen
    • 3
  1. 1.Centrum voor Wiskunde en Informatica (CWI)GB AmsterdamThe Netherlands
  2. 2.Computer Science DepartmentOklahoma State UniversityStillwaterUSA
  3. 3.Department of Computer ScienceUniversity of Copenhagen (DIKU)CopenhagenDenmark

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