+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 our [lambda-let page](/lambda-let.html), based on Chris Barker's JavaScript lambda calculator and [Oleg Kiselyov's Haskell lambda calculator](http://okmij.org/ftp/Computation/lambda-calc.html#lambda-calculator-haskell).
+
+
More Lambda Practice
--------------------
<LI>`(\x y z. x z (y z)) (\u v. u)`
</OL>
+Combinatory Logic
+-----------------
+
+Reduce the following forms, if possible:
+
+<OL start=16>
+<LI> `Kxy`
+<LI> `KKxy`
+<LI> `KKKxy`
+<LI> `SKKxy`
+<LI> `SIII`
+<LI> `SII(SII)`
+
+<LI> Give Combinatory Logic combinators that behave like our boolean functions.
+ You'll need combinators for `true`, `false`, `neg`, `and`, `or`, and `xor`.
+</OL>
+
+Using the mapping specified in the lecture notes,
+translate the following lambda terms into combinatory logic:
+
+<OL start=23>
+<LI> `\x.x`
+<LI> `\xy.x`
+<LI> `\xy.y`
+<LI> `\xy.yx`
+<LI> `\x.xx`
+<LI> `\xyz.x(yz)`
+<LI> For each translation, how many I's are there? Give a rule for
+ describing what each I corresponds to in the original lambda term.
+</OL>
Lists and Numbers
-----------------