From: Jim Pryor <profjim@jimpryor.net>
Date: Mon, 20 Sep 2010 02:28:11 +0000 (-0400)
Subject: expand assignment 2
X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=commitdiff_plain;h=ffe08a8b7b983eb0919882f2a2e9c72aa27394ea;ds=sidebyside

expand assignment 2

Signed-off-by: Jim Pryor <profjim@jimpryor.net>
---

diff --git a/assignment2.mdwn b/assignment2.mdwn
index 04c3a282..f6bde83d 100644
--- a/assignment2.mdwn
+++ b/assignment2.mdwn
@@ -1,3 +1,39 @@
+More Lambda Practice
+--------------------
+
+Insert all the implicit `( )`s and <code>&lambda;</code>s into the following abbreviated expressions:
+
+1.	`x x (x x x) x`
+2.	`v w (\x y. v x)`
+3.	`(\x y. x) u v`
+4.	`w (\x y z. x z (y z)) u v`
+
+Mark all occurrences of `x y` in the following terms:
+
+<OL start=5>
+<LI>`(\x y. x y) x y`
+<LI>`(\x y. x y) (x y)`
+<LI> `\x y. x y (x y)`
+</OL>
+
+Reduce to beta-normal forms:
+
+<OL start=8>
+<LI>`(\x. x (\y. y x)) (v w)`
+<LI>`(\x. x (\x. y x)) (v w)`
+<LI>`(\x. x (\y. y x)) (v x)`
+<LI>`(\x. x (\y. y x)) (v y)`
+
+<LI>`(\x y. x y y) u v`
+<LI>`(\x y. y x) (u v) z w`
+<LI>`(\x y. x) (\u u)`
+<LI>`(\x y z. x z (y z)) (\u v. u)`
+</OL>
+
+
+Lists and Numbers
+-----------------
+
 We'll assume the "Version 3" implementation of lists and numbers throughout. So:
 
 <pre><code>zero &equiv; \s z. z