Journal of Automated Reasoning

, Volume 49, Issue 2, pp 275–300 | Cite as

On Explicit Substitution with Names

  • Kristoffer H. RoseEmail author
  • Roel Bloo
  • Frédéric Lang


This paper recounts the origins of the λx family of calculi of explicit substitution with proper variable names, including the original result of preservation of strong β-normalization based on the use of synthetic reductions for garbage collection. We then discuss the properties of a variant of the calculus which is also confluent for “open” terms (with meta-variables), and verify that a version with garbage collection preserves strong β-normalization (as is the state of the art), and we summarize the relationship with other efforts on using names and garbage collection rules in explicit substitution.


Explicit substitution Preservation of strong normalization Confluence Open terms 


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Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  • Kristoffer H. Rose
    • 1
    Email author
  • Roel Bloo
    • 2
  • Frédéric Lang
    • 3
  1. 1.IBM Thomas J. Watson Research CenterYorktown HeightsUSA
  2. 2.Eindhoven University of TechnologyEindhovenThe Netherlands
  3. 3.INRIA Grenoble Rhône-Alpes/LIGSaint-Ismier CedexFrance

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