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A linear linear lambda-calculus

Published online by Cambridge University Press:  31 May 2024

Alejandro Díaz-Caro Open the ORCID record for Alejandro Díaz-Caro [Opens in a new window]  and
Gilles Dowek
Alejandro Díaz-Caro*
Affiliation:
Departamento de Ciencia y Tecnología, Universidad Nacional de Quilmes, Bernal, Argentina CONICET-Universidad de Buenos Aires, Instituto de Ciencias de la Computación (ICC), Buenos Aires, Argentina Departamento de Computación, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Buenos Aires, Argentina
Gilles Dowek
Affiliation:
Inria & ENS Paris-Saclay, Paris, France
*
Corresponding author: Alejandro Díaz-Caro; Email: adiazcaro@conicet.gov.ar
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Abstract

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.

Keywords

Proof theorylambda calculuslinear logicquantum computing
Type
Special Issue: LSFA 2021 and LSFA 2022
Information
Mathematical Structures in Computer Science , Volume 34 , Special Issue 10: LSFA 2021 and LSFA 2022 , November 2024 , pp. 1103 - 1137
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Copyright
© The Author(s), 2024. Published by Cambridge University Press

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