Evaluating higher-order functional programs through abstract machines inspired by the geometry of the interaction is known to induce $\textit{space}$ efficiencies, the price being $\textit{time}$ performances often poorer than those obtainable with traditional, environment-based, abstract machines. Although families of lambda-terms for which the former is exponentially less efficient than the latter do exist, it is currently unknown how \emph{general} this phenomenon is, and how far the inefficiencies can go, in the worst case. We answer these questions formulating four different well-known abstract machines inside a common definitional framework, this way being able to give sharp results about the relative time efficiencies. We also prove that non-idempotent intersection type theories are able to precisely reflect the time performances of the interactive abstract machine, this way showing that its time-inefficiency ultimately descends from the presence of higher-order types.

中文翻译：

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交互的（In）效率

众所周知，通过受交互几何学启发的抽象机器评估高阶功能程序会导致 $\textit{space}$ 效率，代价是 $\textit{time}$ 性能通常比传统的、环境-基于抽象机器。尽管前者的效率比后者低得多的 lambda 项族确实存在，但目前尚不清楚这种现象的程度如何，以及在最坏的情况下效率低下的程度。我们在一个共同的定义框架内制定了四个不同的著名抽象机器来回答这些问题，这样就能够给出关于相对时间效率的清晰结果。