Contents

Preface

Combinators: A Centennial View:
Ultimate Symbolic Abstraction • Computing with Combinators • A Hundred Years Later... • Combinators in the Wild: Some Zoology • Visualizing Combinators • Updating Schemes and Multiway Systems • The Question of Evaluation Order • The World of the S Combinator • Causal Graphs and the Physicalization of Combinators • Combinator Expressions as Dynamical Systems • Equality and Theorem Proving for Combinators • Lemmas and the Structure of Combinator Space • Empirical Computation Theory with Combinators • The Future of Combinators • Historical & Other Notes

Combinators and the Story of Computation
The Abstract Representation of Things • What Is Mathematics―and Logic―Made Of? • Combinators Arrive • What Is Their Mathematics? • Gödel's Theorem and Computability • Lambda Calculus • Practical Computation • Combinators in Culture • Designing Symbolic Language • Combinators in the Computational Universe • Combinators All the Way Down?

Where Did Combinators Come From? Hunting the Story of Moses Schönfinkel
December 7, 1920 • Who Was Moses Schönfinkel? • The Beginning of the Story • Going to College in Odessa • Göttingen, Center of the Mathematical Universe • Problems Are Brewing • The 1924 Paper • The "1927" Paper • To Moscow and Beyond... • Other Schönfinkels... • Haskell Curry • Schönfinkel Rediscovered • What Should We Make of Schönfinkel?

A Little Closer to Finding What Became of Moses Schönfinkel, Inventor of Combinators

1920, 2020 and a $20,000 Prize: Announcing the S Combinator Challenge Hidi...