Autosubst: Reasoning with de Bruijn Terms and Parallel Substitutions

  • Steven SchäferEmail author
  • Tobias Tebbi
  • Gert Smolka
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9236)


Reasoning about syntax with binders plays an essential role in the formalization of the metatheory of programming languages. While the intricacies of binders can be ignored in paper proofs, formalizations involving binders tend to be heavyweight. We present a discipline for syntax with binders based on de Bruijn terms and parallel substitutions, with a decision procedure covering all assumption-free equational substitution lemmas. The approach is implemented in the Coq library Autosubst, which additionally derives substitution operations and proofs of substitution lemmas for custom term types. We demonstrate the effectiveness of the approach with several case studies, including part A of the POPLmark challenge.


Decision Procedure Strong Normalization Term Language Identity Substitution Parallel Substitution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Saarland UniversitySaarbrückenGermany

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