X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=blobdiff_plain;f=assignment2.mdwn;h=5d75a855a5a09ef187dcdd9b6e4e22bb11b6ee7a;hp=85f63f3678a315f45e11dbd904c3c2f3ed98b3d2;hb=8851b9a8232b479f166c711beae3cc6a665b047c;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: + +
+
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 ----------------- @@ -77,7 +107,7 @@ For these exercises, assume that `LIST` is the result of evaluating:
-
1. What would be the result of evaluating (see [[Assignment 2 hint 1]] for a hint): +
2. What would be the result of evaluating (see [[hints/Assignment 2 hint]] for a hint): LIST make-list empty