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.
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- 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
- 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?
- 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?
- Hiding in Plain Sight for a Century? · The Basic Setup · The Operation of the S Combinator Challenge
- Section 10: Symbolic Systems · Notes · Section 12: Universality in Turing Machines and Other Systems · Notes
- Foundational Documents · Books · Surveys & Summaries · Combinators as Symbolic Expressions · Combinators as Mathematical Constructs · Combinator Computation · Extensions & Applications · Confusing Issues
Combinators: A Centennial View
Combinators and the Story of Computation
Where Did Combinators Come From? Hunting the Story of Moses 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
Excerpts from A New Kind of Science (2002)
A Bibliography of Combinators
About the Author
Stephen Wolfram is a distinguished scientist and best-selling author, and the creator of some of the world's most respected software systems, including Mathematica, Wolfram|Alpha and the Wolfram Language. For more than 30 years he has been the CEO of the global technology company Wolfram Research.
Other books by Stephen Wolfram
- Title: Combinators: A Centennial View
- Author: Stephen Wolfram
- Hardback: $39.95 362 pages
- Publisher: Wolfram Media, Inc.
- Publication Date: June 17, 2021
- ISBN-13: 978-1-57955-043-1 (hardback)
- ISBN-13: 978-1-57955-044-8 (eBook)