A linear linear lambda-calculus

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.

This is the full revised journal version of the FSCD 2022 paper published at LIPIcs 228:21, 2022