We introduce $\mathsf{LAM}$, a subsystem of $\mathsf{IMALL}_2$ with restricted additive rules able to manage duplication linearly, called \textit{linear additive rules}. $\mathsf{LAM}$ is presented as the type assignment system for a calculus endowed with copy constructors, which deal with substitution in a linear fashion. As opposed to the standard additive rules, the linear additive rules do not affect the complexity of term reduction: typable terms of $\mathsf{LAM}$ enjoy linear strong normalization. Moreover, a mildly weakened version of cut-elimination for this system is proven which takes a cubic number of steps. Finally, we define a sound translation from $\mathsf{LAM}$'s proofs into $\mathsf{IMLL}_2$'s linear lambda terms, and we study its complexity.
翻译：我们引入了 $mathsf{LAM} $\ mathsf{IMAL} $($mathsf{IMALL}) $($mathsf{LAM}) $($mathsffs{LAM) $) 的子系统, 这个子系统有限制的添加规则, 可以直线管理重复, 叫做\ textit{线性添加规则。 $\ mathsf{LAM} $( mathsf{IMall} $($) 。 $( mathsfsf{LAM} ) $($) 。 。 $\ mathsf{LAM} $($) 的缩写系统稍微变弱的切除法化版本需要立方步骤。 最后, 我们定义了一个音译法, 从 $mathsf{LAM} ($($maths) {IMLLL=2$($) 线性羊da) 条款, 我们研究其复杂性 。
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