Combinators : A Centennial View

Combinators have inspired ideas about computation ever since they were first invented in 1920, and in this innovative book, Stephen Wolfram provides a modern view of combinators and their significance. Informed by his work on the computational universe of possible programs and on computational language design, Wolfram explains new and existing ideas about combinators with unique clarity and stunning visualizations, as well as provides insights on their historical connections and the curious story of Moses Schönfinkel, inventor of combinators. Though invented well before Turing machines, combinators have often been viewed as an inaccessibly abstract approach to computation. This book brings them to life as never before in a thought-provoking and broadly accessible exposition of interest across mathematics and computer science, as well as to those concerned with the foundations of formal and computational thinking, and with the history of ideas.
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

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