We give a modern computational introduction to the S,K combinators invented by Moses Sch\"onfinkel in 1920, and present a variety of new results and ideas about combinators. We explore the spectrum of behavior obtained with small combinator expressions, showing a variety of approaches to analysis and visualization. We discuss the implications of evaluation strategies, and of multiway systems representing all possible strategies. We show how causal graphs introduced in recent models of fundamental physics can be applied to combinators, as well as describing how combinators introduce a new form of treelike separation. We give a variety of new results on minimal combinator expressions, as well as showing how empirical computation theory and computational complexity theory can be done with combinators. We also suggest that when viewed in terms of ongoing computation, the S combinator alone may be capable of universal computation.

中文翻译：

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结合者：百年观点

我们对Moses Schonfinkel在1920年发明的S，K组合器进行了现代的计算介绍，并给出了有关组合器的各种新结果和新思想。我们探索了用较小组合器表达式获得的行为谱，显示了多种分析和可视化方法；我们讨论了评估策略以及代表所有可能策略的多路系统的含义；展示了如何将最新的基础物理学模型中引入的因果图应用于组合器，并描述了组合器如何引入新的方法我们以最小组合器表达式给出了各种新结果，并展示了如何用组合器完成经验计算理论和计算复杂性理论。我们还建议，从正在进行的计算的角度来看，仅S组合器就可以进行通用计算。