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$\textit{和}$空间消耗？尽管文献中关于时间已有肯定答案，但有关空间的了解却少得多。本文提出了一种基于Krivine抽象机变体的新型λ-演算合理空间代价模型。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。