From 4c0fb46d0cb9dcbfa5687140afeca2fdb48f668c Mon Sep 17 00:00:00 2001
From: barker
Date: Mon, 20 Sep 2010 13:43:28 -0400
Subject: [PATCH]
---
assignment2.mdwn | 27 +++++++++++++++++++++++++++
1 file changed, 27 insertions(+)
diff --git a/assignment2.mdwn b/assignment2.mdwn
index 85f63f36..f0e8a098 100644
--- a/assignment2.mdwn
+++ b/assignment2.mdwn
@@ -33,6 +33,33 @@ Reduce to beta-normal forms:
`(\x y z. x z (y z)) (\u v. u)`
+Combinatory Logic
+-----------------
+
+Reduce the following forms, if possible:
+
+1. Kxy
+2. KKxy
+3. KKKxy
+4. SKKxy
+5. SIII
+6. SII(SII)
+
+* Give Combinatory Logic combinators that behave like our boolean functions.
+ You'll need combinators for true, false, neg, and, or, and xor.
+
+Using the mapping specified in the lecture notes,
+translate the following lambda terms into combinatory logic:
+
+1. \x.x
+2. \xy.x
+3. \xy.y
+4. \xy.yx
+5. \x.xx
+6. \xyz.x(yz)
+
+* For each translation, how many I's are there? Give a rule for
+ describing what each I corresponds to in the original lambda term.
Lists and Numbers
-----------------
--
2.11.0