  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.
