X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=blobdiff_plain;f=assignment2.mdwn;h=5d75a855a5a09ef187dcdd9b6e4e22bb11b6ee7a;hp=85f63f3678a315f45e11dbd904c3c2f3ed98b3d2;hb=bf8d964cc93f6b0b44a432bca8c94b1374c05e1f;hpb=85bd77d2f5fc08beca4d2d65ccf9a6cf81b4a658
diff --git a/assignment2.mdwn b/assignment2.mdwn
index 85f63f36..5d75a855 100644
--- a/assignment2.mdwn
+++ b/assignment2.mdwn
@@ -1,4 +1,4 @@
-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.
+For these assignments, you'll probably want to use our [[lambda evaluator]] to check your work. This accepts any grammatical lambda expression and reduces it to normal form, when possible.
More Lambda Practice
@@ -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
-----------------
@@ -77,7 +107,7 @@ For these exercises, assume that `LIST` is the result of evaluating:
-- What would be the result of evaluating (see [[Assignment 2 hint 1]] for a hint):
+
- What would be the result of evaluating (see [[hints/Assignment 2 hint]] for a hint):
LIST make-list empty