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On Explicit Substitution with Names


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.

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Correspondence to Kristoffer H. Rose.

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Rose, K.H., Bloo, R. & Lang, F. On Explicit Substitution with Names. J Autom Reasoning 49, 275–300 (2012).

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  • Explicit substitution
  • Preservation of strong normalization
  • Confluence
  • Open terms