Lens put-put laws: monotonic and mixed

Michael Johnson, Robert Rosebrugh

Research output: Contribution to journalConference paperpeer-review

78 Citations (Scopus)


Many authors have argued, for good reasons, that in a range of applications the lens put-put law is too strong. On the other hand, the present authors have shown that very well behaved lenses, which do satisfy the put-put law by definition, are algebras for a certain monad, and that this viewpoint admits fruitful generalisations of the lens concept to a variety of base categories. In the algebra approach to lenses, the put-put law corresponds to the associativity axiom, and so is fundamentally important. Thus we have a dilemma. The put-put law seems inappropriate for many applications, but is fundamental to the mathematical development that can support an extended range of applications. In this paper we resolve this dilemma. We outline monotonic put-put laws and introduce a new mixed put-put law that appears to be immune to many of the objections to the classical put-put law, and still supports a very satisfactory mathematical foundation.
Original languageEnglish
Pages (from-to)1-13
Number of pages13
JournalProceedings of the First International Workshop on Bidirectional Transformations : BX 2012
Publication statusPublished - 2012
EventInternational Workshop on Bidirectional Transformations (1st : 2012) - Tallinn, Estonia
Duration: 25 Mar 201225 Mar 2012


  • Lens
  • view update
  • algebra
  • monad
  • span

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