X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=blobdiff_plain;f=assignment2.mdwn;h=3e932561960bbc7792c34d868ea008aee1b2fb25;hp=648ef2107c290522b8916b95c411a116be8476e5;hb=ce6877027e00cdb159651cddba03addb5208e875;hpb=d63b0d0e1c52b50a383e419345a54e2bc6339a77 diff --git a/assignment2.mdwn b/assignment2.mdwn index 648ef210..3e932561 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 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). +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: + +
+
1. `Kxy` +
2. `KKxy` +
3. `KKKxy` +
4. `SKKxy` +
5. `SIII` +
6. `SII(SII)` + +
7. 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)` +
7. 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 -----------------