<story><title>Closer to finding what became of Moses Schönfinkel, inventor of combinators</title><url>https://writings.stephenwolfram.com/2021/03/a-little-closer-to-finding-what-became-of-moses-schonfinkel-inventor-of-combinators/</url></story><parent_chain></parent_chain><comment><author>crdrost</author><text>If you have never read it before, “On the Building Blocks of Mathematical Logic”[1] is incredibly readable given that it&amp;#x27;s talking pure theory and trying to do something quite remarkable. Basically it teaches you to remove variables from arbitrary logic expressions, including logic expressions that have existential and universal quantification, and just represent them with a couple of fixed symbols (you can get it down to 2, which if you were so inclined you could call 0 and 1).&lt;p&gt;That&amp;#x27;s a pretty lofty goal and Schönfinkel just baby-steps you into it, “you know how NAND gates (the Sheffer stroke) work and can make any other boolean circuit by making AND and NOT and OR the following ways? Cool. Here’s how we can extend that idea to ‘there exists X such that...’ and here is how you curry functions and use the Applicative functor for functions in practice to remove multiple calls of the same argument, and with those you can write anything point-free and do away with arguments and symbols altogether.”&lt;p&gt;At the end of reading it, there is simultaneously a sense of epiphany and a sense of confused scope, like when you&amp;#x27;ve been walking up a mountain all day and you turn around and you don&amp;#x27;t really believe that you have gotten as high as you have gotten, every step was reasonable and the sum total is unreasonable. Well worth the reading time.&lt;p&gt;[1] &lt;a href=&quot;https:&amp;#x2F;&amp;#x2F;writings.stephenwolfram.com&amp;#x2F;data&amp;#x2F;uploads&amp;#x2F;2020&amp;#x2F;12&amp;#x2F;Schonfinkel-OnTheBuildingBlocksOfMathematicalLogic.pdf&quot; rel=&quot;nofollow&quot;&gt;https:&amp;#x2F;&amp;#x2F;writings.stephenwolfram.com&amp;#x2F;data&amp;#x2F;uploads&amp;#x2F;2020&amp;#x2F;12&amp;#x2F;Sch...&lt;/a&gt;</text></comment>
<story><title>Closer to finding what became of Moses Schönfinkel, inventor of combinators</title><url>https://writings.stephenwolfram.com/2021/03/a-little-closer-to-finding-what-became-of-moses-schonfinkel-inventor-of-combinators/</url></story><parent_chain></parent_chain><comment><author>gfaure</author><text>I did my dissertation on an aspect of Combinatory Categorial Grammar, as mentioned in the article as a byproduct of Schönfinkel&amp;#x27;s work.&lt;p&gt;One of the interesting byproducts of considering sequences of words in a natural language sentence as functions, is a solution to analysing a phenomenon in syntax called right node raising: &amp;quot;I washed and you dried the dishes.&amp;quot;&lt;p&gt;In context-free grammars of English, &amp;quot;I washed&amp;quot; and &amp;quot;you dried&amp;quot; do not form constituents (unlike &amp;quot;washed the dishes&amp;quot; or &amp;quot;dried the dishes&amp;quot;, which are VPs — verb phrases). However, in Combinatory Categorial Grammar, this is no problem, as &amp;quot;I washed&amp;quot; is simply a function looking rightward for a noun phrase (NP), and returning a sentence (S). In CCG terms, this function would be notated S&amp;#x2F;NP, corresponding to an interpretation function of type NP -&amp;gt; S.</text></comment>