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-演算能否被视为一种合理的计算模型？我们能否用它来度量算法的时间和空间消耗？尽管文献中已有关于时间合理性的肯定答案，但关于空间合理性的研究却少得多。本文基于Krivine抽象机的一种变体，为λ-演算提出了一种新的合理空间代价模型。该代价模型首次能够容纳对数空间。此外，我们研究了该机器的时间行为，并展示了如何将我们的结果迁移到按值调用λ-演算中。