{"title":"Reduction Free Normalisation for a proof irrelevant type of propositions","authors":"T. Coquand","doi":"10.46298/lmcs-19(3:5)2023","DOIUrl":null,"url":null,"abstract":"We show normalisation and decidability of convertibility for a type theory\nwith a hierarchy of universes and a proof irrelevant type of propositions,\nclose to the type system used in the proof assistant Lean. Contrary to previous\narguments, the proof does not require explicitly to introduce a notion of\nneutral and normal forms.","PeriodicalId":314387,"journal":{"name":"Log. Methods Comput. Sci.","volume":"53 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2021-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Log. Methods Comput. Sci.","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.46298/lmcs-19(3:5)2023","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 3
Abstract
We show normalisation and decidability of convertibility for a type theory
with a hierarchy of universes and a proof irrelevant type of propositions,
close to the type system used in the proof assistant Lean. Contrary to previous
arguments, the proof does not require explicitly to introduce a notion of
neutral and normal forms.