A linear linear lambda-calculus

We present a linearity theorem for a proof language of intuitionistic multiplicative additive linear logic, incorporating addition and scalar multiplication. The proofs in this language are linear in the algebraic sense. This work is part of a broader research program aiming to define a logic with a...

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Bibliographic Details
Published inMathematical structures in computer science Vol. 34; no. 10; pp. 1103 - 1137
Main Authors Díaz-Caro, Alejandro, Dowek, Gilles
Format Journal Article
LanguageEnglish
Published Cambridge, UK Cambridge University Press 01.11.2024
Subjects
Algebra
Calculus
Linearity
Logic programming
Multiplication
Programming languages
Special Issue: LSFA 2021 and LSFA 2022
lambda calculus
Proof theory
linear logic
quantum computing
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ISSN0960-1295
1469-8072
DOI10.1017/S0960129524000197

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Summary:We present a linearity theorem for a proof language of intuitionistic multiplicative additive linear logic, incorporating addition and scalar multiplication. The proofs in this language are linear in the algebraic sense. This work is part of a broader research program aiming to define a logic with a proof language that forms a quantum programming language.
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ISSN:0960-1295
1469-8072
DOI:10.1017/S0960129524000197