The dagger lambda calculus

We present a novel lambda calculus that casts the categorical approach to the study of quantum protocols into the rich and well established tradition of type theory. Our construction extends the linear typed lambda calculus with a linear negation of "trivialised" De Morgan duality. Reducti...

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Bibliographic Details
Published inElectronic proceedings in theoretical computer science Vol. 172; no. Proc. QPL 2014; pp. 217 - 235
Main Author Atzemoglou, Philip
Format Journal Article
LanguageEnglish
Published Open Publishing Association 28.12.2014
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Summary:We present a novel lambda calculus that casts the categorical approach to the study of quantum protocols into the rich and well established tradition of type theory. Our construction extends the linear typed lambda calculus with a linear negation of "trivialised" De Morgan duality. Reduction is realised through explicit substitution, based on a symmetric notion of binding of global scope, with rules acting on the entire typing judgement instead of on a specific subterm. Proofs of subject reduction, confluence, strong normalisation and consistency are provided, and the language is shown to be an internal language for dagger compact categories.
ISSN:2075-2180
2075-2180
DOI:10.4204/EPTCS.172.15