Can the $\lambda$-calculus be considered as a reasonable computational model? Can we use it for measuring the time 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's abstract machine. For the first time, this cost model is able to account for 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：$\ lambda$- calculus 是否可被视为合理的计算模型? 我们能否用它来测量算法的时间和空间消耗量? 虽然文献包含对时间的正面答案, 但对空间的认知却少得多。 本文为$\ lambda$- calculus 提出了一个新的合理空间成本模型, 其依据是克里维尼抽象机器的变体。 这个成本模型首次能够计算对数空间。 此外, 我们研究我们的机器的时间行为, 并展示如何将我们的结果传输到调值 $\ lambda$- calculules 。
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