Bag Equivalence via a Proof-Relevant Membership Relation

  • Nils Anders Danielsson
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7406)


Two lists are bag equivalent if they are permutations of each other, i.e. if they contain the same elements, with the same multiplicity, but perhaps not in the same order. This paper describes how one can define bag equivalence as the presence of bijections between sets of membership proofs. This definition has some desirable properties:
  • Many bag equivalences can be proved using a flexible form of equational reasoning.

  • The definition generalises easily to arbitrary unary containers, including types with infinite values, such as streams.

  • By using a slight variation of the definition one gets set equivalence instead, i.e. equality up to order and multiplicity. Other variations give the subset and subbag preorders.

  • The definition works well in mechanised proofs.


Type Theory Implicit Argument Container Type List Membership Mechanise Proof 
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-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Nils Anders Danielsson
    • 1
    • 2
  1. 1.Chalmers University of TechnologySweden
  2. 2.University of GothenburgSweden

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