X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?a=blobdiff_plain;f=assignment2.mdwn;h=ff600cc71e8107653cd31bdd0b42c78f0a16f579;hb=8a17989a3112b0bdecfaaf7855f6b41f8f033476;hp=648ef2107c290522b8916b95c411a116be8476e5;hpb=d63b0d0e1c52b50a383e419345a54e2bc6339a77;p=lambda.git
diff --git a/assignment2.mdwn b/assignment2.mdwn
index 648ef210..ff600cc7 100644
--- a/assignment2.mdwn
+++ b/assignment2.mdwn
@@ -33,6 +33,36 @@ Reduce to beta-normal forms:
`(\x y z. x z (y z)) (\u v. u)`
+Combinatory Logic
+-----------------
+
+Reduce the following forms, if possible:
+
+
+- `Kxy`
+
- `KKxy`
+
- `KKKxy`
+
- `SKKxy`
+
- `SIII`
+
- `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:
+
+
+- `\x.x`
+
- `\xy.x`
+
- `\xy.y`
+
- `\xy.yx`
+
- `\x.xx`
+
- `\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
-----------------