| Preface |
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vii | |
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Combinators: A Centennial View |
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3 | (162) |
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Ultimate Symbolic Abstraction |
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3 | (3) |
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Computing with Combinators |
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6 | (6) |
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12 | (5) |
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Combinators in the Wild: Some Zoology |
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17 | (17) |
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34 | (20) |
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Updating Schemes and Multiway Systems |
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54 | (18) |
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The Question of Evaluation Order |
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72 | (15) |
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The World of the S Combinator |
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87 | (15) |
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Causal Graphs and the Physicalization of Combinators |
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102 | (18) |
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Combinator Expressions as Dynamical Systems |
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120 | (5) |
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Equality and Theorem Proving for Combinators |
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125 | (8) |
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Lemmas and the Structure of Combinator Space |
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133 | (12) |
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Empirical Computation Theory with Combinators |
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145 | (12) |
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The Future of Combinators |
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157 | (2) |
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159 | (6) |
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Combinators and the Story of Computation |
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165 | (48) |
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The Abstract Representation of Things |
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165 | (2) |
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What Is Mathematics-and Logic-Made Of? |
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167 | (4) |
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171 | (10) |
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What Is Their Mathematics? |
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181 | (2) |
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Godel's Theorem and Computability |
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183 | (3) |
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186 | (5) |
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191 | (4) |
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195 | (3) |
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Designing Symbolic Language |
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198 | (5) |
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Combinators in the Computational Universe |
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203 | (5) |
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Combinators All the Way Down? |
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208 | (5) |
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Where Did Combinators Come From? Hunting the Story of Moses Schdnfinkel |
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213 | (68) |
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213 | (2) |
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Who Was Moses Schonfinkel? |
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215 | (2) |
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The Beginning of the Story |
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217 | (5) |
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Going to College in Odessa |
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222 | (6) |
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Gottingen, Center of the Mathematical Universe |
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228 | (6) |
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234 | (7) |
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241 | (6) |
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247 | (10) |
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257 | (5) |
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262 | (3) |
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265 | (9) |
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274 | (1) |
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What Should We Make of Schonfinkel? |
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275 | (6) |
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A Little Closer to Finding What Became of Moses Schonfinkel, Inventor of Combinators |
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281 | (16) |
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1920 2020 and a $20,000 Prize: Announcing the S Combinator Challenge |
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297 | (10) |
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Hiding in Plain Sight for a Century? |
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297 | (3) |
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300 | (3) |
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The Operation of the S Combinator Challenge |
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303 | (4) |
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Excerpts from A New Kind of Science (2002) |
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307 | (18) |
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Section 10: Symbolic Systems |
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307 | (3) |
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310 | (5) |
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Section 12: Universality in Turing Machines and Other Systems |
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315 | (4) |
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319 | (6) |
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A Bibliography of Combinators |
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325 | (32) |
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325 | (1) |
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325 | (1) |
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326 | (1) |
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Combinators as Symbolic Expressions |
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327 | (7) |
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Combinators as Mathematical Constructs |
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334 | (7) |
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341 | (9) |
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Extensions & Applications |
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350 | (2) |
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352 | (5) |
| Index |
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357 | |
