A linear linear lambda-calculus
Alejandro Díaz-Caro, Gilles Dowek · Mathematical Structures in Computer Science · 2024
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.