From: Jim Pryor Date: Sat, 18 Sep 2010 19:07:13 +0000 (-0400) Subject: week2 tweaks X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=commitdiff_plain;h=0f719db1bec7f71732823ba4e558ab1c3edd5792 week2 tweaks Signed-off-by: Jim Pryor --- diff --git a/week2.mdwn b/week2.mdwn index ce21d268..3b4e7eec 100644 --- a/week2.mdwn +++ b/week2.mdwn @@ -49,7 +49,7 @@ Lambda expressions that have no free variables are known as **combinators**. Her 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. -One can do that with a very spare set of basic combinators. These days the standard base is just three combinators: K and I from above, and also one more, **S**, which behaves the same as the lambda expression `\f g x. f x (g x)`. behaves. But it's possible to be even more minimalistic, and get by with only a single combinator. (And there are different single-combinator bases you can choose.) +One can do that with a very spare set of basic combinators. These days the standard base is just three combinators: **K** and **I** from above, and also one more, **S**, which behaves the same as the lambda expression `\f g x. f x (g x)`. behaves. But it's possible to be even more minimalistic, and get by with only a single combinator. (And there are different single-combinator bases you can choose.) There are some well-known linguistic applications of Combinatory Logic, due to Anna Szabolcsi, Mark Steedman, and Pauline Jacobson.