A linear linear lambda-calculus - Díaz-Caro, Alejandro; Dowek, Gilles (Mathematical structures in computer science, 2024)
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.