X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?a=blobdiff_plain;f=week2.mdwn;h=37b717787fa0d2eca16ee42b9fe6c66900a722de;hb=42db6a206c30f67c0693e8b367c46d5c86e65d9b;hp=ac2a7c32f775365eb6233c35c327363153b733f8;hpb=a9e5201a0fefa3602e5d3477bd2d9670aee40515;p=lambda.git diff --git a/week2.mdwn b/week2.mdwn index ac2a7c32..37b71778 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](./szabolcsi-reflexive.png) -![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!