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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 Sch枚nfinkel, 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.</p> <div class="buttons"> <a href="https://www.amazon.com/dp/1579550436" target="_blank" class="button" data-walid="WM-SW-Combinators-Amazon">Buy from Amazon</a> <a href="https://www.barnesandnoble.com/w/combinators-stephen-wolfram/1139432064" target="_blank" class="button" data-walid="WM-SW-Combinators-BarnesNoble">Buy from Barnes & Noble</a> </div> </section> <section id="product-info"> <h3 class="basic-h3">Information and Media Inquiries</h3> <p>June 17, 2021 Publication<br>Publicity and Interviews: <a href="mailto:sw-media@wolfram.com">sw-media@wolfram.com</a><br>Trim Size: 7.44" x 9.69"<br>Non-Fiction</p> <p>Distribution by Ingram, Amazon and Baker & Taylor</p> <p>UK Distribution: <a href="https://books.turnaround-uk.com/combinators.html" target="_blank">Turnaround Publisher Services</a></p> </section> <section id="product-toc"> <h3 class="basic-h3">Contents</h3> <ul class="nested-list"> <li>Preface</li> <li class="sections">Combinators: A Centennial View</li> <li class="chapters">Ultimate Symbolic Abstraction 路 Computing with Combinators 路 A Hundred Years Later... 路 Combinators in the Wild: Some Zoology 路 Visualizing Combinators 路 Updating Schemes and Multiway Systems 路 The Question of Evaluation Order 路 The World of the S Combinator 路 Causal Graphs and the Physicalization of Combinators 路 Combinator Expressions as Dynamical Systems 路 Equality and Theorem Proving for Combinators 路 Lemmas and the Structure of Combinator Space 路 Empirical Computation Theory with Combinators 路 The Future of Combinators</li> <li class="sections">Combinators and the Story of Computation</li> <li class="chapters">The Abstract Representation of Things 路 What Is Mathematics鈥攁nd Logic鈥擬ade Of? 路 Combinators Arrive 路 What Is Their Mathematics? 路 G枚del's Theorem and Computability 路 Lambda Calculus 路 Practical Computation 路 Combinators in Culture 路 Designing Symbolic Language 路 Combinators in the Computational Universe 路 Combinators All the Way Down?</li> <li class="sections">Where Did Combinators Come From? Hunting the Story of Moses Sch枚n铿乶kel</li> <li class="chapters">December 7, 1920 路 Who Was Moses Sch枚n铿乶kel? 路 The Beginning of the Story 路 Going to College in Odessa 路 G枚ttingen, Center of the Mathematical Universe 路 Problems Are Brewing 路 The 1924 Paper 路 The "1927" Paper 路 To Moscow and Beyond... 路 Other Sch枚n铿乶kels... 路 Haskell Curry 路 Sch枚n铿乶kel Rediscovered 路 What Should We Make of Sch枚n铿乶kel?</li> <li class="sections">A Little Closer to Finding What Became of Moses Sch枚nfinkel, Inventor of Combinators</li> <li class="sections">1920, 2020 and a $20,000 Prize: Announcing the S Combinator Challenge</li> <li class="chapters">Hiding in Plain Sight for a Century? 路 The Basic Setup 路 The Operation of the S Combinator Challenge</li> <li class="sections">Excerpts from <em>A New Kind of Science</em> (2002)</li> <li class="chapters">Section 10: Symbolic Systems 路 Notes 路 Section 12: Universality in Turing Machines and Other Systems 路 Notes</li> <li class="sections">A Bibliography of Combinators</li> <li class="chapters">Foundational Documents 路 Books 路 Surveys & Summaries 路 Combinators as Symbolic Expressions 路 Combinators as Mathematical Constructs 路 Combinator Computation 路 Extensions & Applications 路 Confusing Issues</li> <li>Index</li> </ul> </section> <section id="product-author"> <h3 class="basic-h3">About the Author</h3> <p><a href="//www.stephenwolfram.com/">Stephen Wolfram</a> 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.</p> <h3 class="basic-h3">Other Books by Stephen Wolfram</h3> <ul> <li><a href="/products/the-second-law-resolving-the-mystery-of-the-second-law-of-thermodynamics/"><em>The Second Law: Resolving the Mystery of the Second Law of Thermodynamics</em></a></li> <li><a href="/products/what-is-chatgpt-doing-and-why-does-it-work/"><em>What Is ChatGPT Doing ... and Why Does It Work?</em></a></li> <li><a href="/products/metamathematics-foundations-and-physicalization/"><em>Metamathematics: Foundations & Physicalization</em></a></li> <li><a href="/products/twenty-years-of-a-new-kind-of-science/"><em>Twenty Years of A New Kind of Science</em></a></li> <li><a href="/products/a-project-to-find-the-fundamental-theory-of-physics/"><em>A Project to Find the Fundamental Theory of Physics</em></a></li> <li><a href="/products/adventures-of-a-computational-explorer/"><em>Adventures of a Computational Explorer</em></a></li> <li><a href="/products/idea-makers/"><em>Idea Makers: Personal Perspectives on the Lives & Ideas of Some Notable People</em></a></li> <li><a href="https://www.wolfram.com/language/elementary-introduction/2nd-ed"><em>An Elementary Introduction to the Wolfram Language</em></a></li> <li><a href="https://www.wolfram-media.com/products/nks/"><em>A New Kind of Science</em></a></li> </ul> </section> </div> <div class="margin-t-3 margin-t-0__900 order-0__900"> <section id="product-cover"> <figure><img src="/products/img/combinators-a-centennial-view.png" alt="" width="324" height="422" class="fill-and-center"></figure> </section> <section id="product-details"> <ul> <li><span class="label">Title:</span> <span class="indent no-widows">Combinators: A Centennial View</span></li> <li><span class="label">Author:</span> Stephen Wolfram</li> <li><span class="label">Hardcover:</span> $39.95  362 pages</li> <li><span class="label">eBook:</span> $16.95  362 pages</li> <li><span class="label">Publisher:</span> Wolfram Media, Inc.</li> <li><span class="label">Publication Date:</span> June 17, 2021</li> <li><span class="label">ISBN-13:</span> 978-1-57955-043-1 (hardcover)</li> <li><span class="label">ISBN-13:</span> 978-1-57955-044-8 (eBook)</li> </ul> </section> </div> </div> </div> </main>  <footer id="shared-footer"> <div class="width"> <p class="copyright">漏 2024 Wolfram Media, Inc. 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