# Combinators: A Centennial View

arXiv: https://arxiv.org/abs/2103.12811 · HTML: https://mlsanity.com/paper/2103.12811/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Mar 2021.

## Built on by (most cited first, 2 of 2)

- [Generating Compressed Combinatory Proof Structures -- An Approach to Automated First-Order Theorem Proving](https://mlsanity.com/paper/2209.12592/) (2022)
- [Mobile Sequencers](https://mlsanity.com/paper/2405.06710/) (2024)

## Abstract (arXiv)

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.