X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=blobdiff_plain;f=assignment2.mdwn;h=f0e8a0989cfaf28919d7b03ead3ce51529a969e7;hp=c60f50e8892777485e3775fe4d5b30ce0c42edf9;hb=4c0fb46d0cb9dcbfa5687140afeca2fdb48f668c;hpb=2c3b570cee9e45d3a826a38871fbcbd9bf356d46

diff --git a/assignment2.mdwn b/assignment2.mdwn
index c60f50e8..f0e8a098 100644
--- a/assignment2.mdwn
+++ b/assignment2.mdwn
@@ -1,3 +1,6 @@
+For these assignments, you'll probably want to use a "lambda calculator" to check your work. This accepts any grammatical lambda expression and reduces it to normal form, when possible. See the page on [[using the programming languages]] for instructions and links about setting this up.
+
+
 More Lambda Practice
 --------------------
 
@@ -30,6 +33,33 @@ Reduce to beta-normal forms:
 <LI>`(\x y z. x z (y z)) (\u v. u)`
 </OL>
 
+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
 -----------------
@@ -88,7 +118,7 @@ For these exercises, assume that `LIST` is the result of evaluating:
 
 should evaluate to a list containing just those of `a`, `b`, `c`, `d`, and `e` such that `f` applied to them evaluates to `true`.
 
-<LI>How would you implement map using the either the version 1 or the version 2 implementation of lists?
+<LI>What goes wrong when we try to apply these techniques using the version 1 or version 2 implementation of lists?
 
 <LI>Our version 3 implementation of the numbers are usually called "Church numerals". If `m` is a Church numeral, then `m s z` applies the function `s` to the result of applying `s` to ... to `z`, for a total of *m* applications of `s`, where *m* is the number that `m` represents or encodes.