2021/03/23 by Stephen Wolfram, Wolfram, Stephen · 1 voice
Computer Science · #Data Visualization and Analytics #Graph Labeling and Dimension Problems #cs.DM #cs.LO
paper · pdf · doi:10.48550/arxiv.2103.12811
openalex publication_date 2021/03/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We give a modern computational introduction to the S,K combinators invented by Moses Schönfinkel 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.