Can the $\lambda$-calculus be considered a reasonable computational model? Can we use it for measuring the time $\textit{and}$ space consumption of algorithms? While the literature contains positive answers about time, much less is known about space. This paper presents a new reasonable space cost model for the $\lambda$-calculus, based on a variant over the Krivine abstract machine. For the first time, this cost model is able to accommodate logarithmic space. Moreover, we study the time behavior of our machine and show how to transport our results to the call-by-value $\lambda$-calculus.

翻译：λ演算能否被视为合理的计算模型？我们能否用它来衡量算法的时间与空间消耗？尽管文献中已存在关于时间消耗的肯定答案，但对空间消耗的认知却远为有限。本文基于Krivine抽象机的一种变体，提出了一种新的λ演算合理空间成本模型。该成本模型首次实现了对数级空间复杂度的兼容。此外，我们研究了该抽象机的时间特性，并展示了如何将研究结果迁移至按值调用λ演算体系。