From 569249692e41ed627bf7b0a3f7d8bb6c26248878 Mon Sep 17 00:00:00 2001 From: barker Date: Sat, 18 Sep 2010 16:30:20 -0400 Subject: [PATCH] --- week2.mdwn | 6 ++++++ 1 file changed, 6 insertions(+) diff --git a/week2.mdwn b/week2.mdwn index b23d1a74..53e86eeb 100644 --- a/week2.mdwn +++ b/week2.mdwn @@ -154,6 +154,12 @@ The orginal lambda term lifts its first argument (think of it as reversing the o Viola: the combinator takes any X and Y as arguments, and returns Y applied to X. +One very nice property of combinatory logic is that there is no need to worry about alphabetic variance, or +variable collision---since there are no (bound) variables, there is no possibility of accidental variable capture, +and so reduction can be performed without any fear of variable collision. We haven't mentioned the intricacies of +alpha equivalence or safe variable substitution, but they are in fact quite intricate. (The best way to gain +an appreciation of that intricacy is to write a program that performs lambda reduction.) + Back to linguistic applications: one consequence of the equivalence between the lambda calculus and combinatory logic is that anything that can be done by binding variables can just as well be done with combinators. This has given rise to a style of semantic analysis called Variable Free Semantics (in addition to -- 2.11.0