A linear algebra approach to linear metatheory

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Linear typed λ-calculi are more delicate than their simply typed siblings when it comes to metatheoretic results like preservation of typing under renaming and substitution. Tracking the usage of variables in contexts places more constraints on how variables may be renamed or substituted. We present a methodology based on linear algebra over semirings, extending McBride's kits and traversals approach for the metatheory of syntax with binding to linear usage-annotated terms. Our approach is readily formalisable, and we have done so in Agda.
Original languageEnglish
Pages (from-to)195-212
Number of pages8
JournalElectronic Proceedings in Theoretical Computer Science, EPTCS
Issue number2021
Early online date29 Jun 2020
Publication statusPublished - 30 Dec 2021
EventLinearity & Trends in Linear Logic and its Application 2020 - Online
Duration: 29 Jun 202030 Jun 2020
Conference number: 2


  • linear algebra
  • renaming
  • variables


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