From: Chris Barker Date: Sat, 18 Sep 2010 13:43:54 +0000 (-0400) Subject: Merge branch 'master' of ssh://server.philosophy.fas.nyu.edu/Users/lambda/lambda X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=commitdiff_plain;h=ec88fb91f1b5d87fe9d4636d7a0b29bda7146142;hp=1cb24c454b4bb50427859def6b3727f59cc88a33 Merge branch 'master' of ssh://server.philosophy.fas.nyu.edu/Users/lambda/lambda --- diff --git a/week2.mdwn b/week2.mdwn index ac2a7c32..54a5ebdf 100644 --- a/week2.mdwn +++ b/week2.mdwn @@ -39,7 +39,7 @@ Lambda expressions that have no free variables are known as **combinators**. Her > **get-second** was our function for extracting the second element of an ordered pair: `\fst snd. snd`. Compare this to our definition of **false**. -> **ω** is defined to be: `\x. x x (\x. x x)` +> **ω** is defined to be: `\x. x x` It's possible to build a logical system equally powerful as the lambda calculus (and readily intertranslatable with it) using just combinators, considered as atomic operations. Such a language doesn't have any variables in it: not just no free variables, but no variables at all. @@ -58,8 +58,9 @@ combinators: For instance, Szabolcsi argues that reflexive pronouns are argument duplicators. +![test](http://lambda.jimpryor.net/szabolcsi-reflexive.jpg) -![Szabolcsi's analysis of *himself* as the duplicator combinator](szabolcsi-reflexive.png) +![Szabolcsi's analysis of *himself* as the duplicator combinator](szabolcsi-reflexive.jpg) These systems are Turing complete. In other words: every computation we know how to describe can be represented in a logical system consisting of only a single primitive operation!