-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 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
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.
+<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:
-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
+<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
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