X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=blobdiff_plain;f=assignment2.mdwn;h=f0e8a0989cfaf28919d7b03ead3ce51529a969e7;hp=85f63f3678a315f45e11dbd904c3c2f3ed98b3d2;hb=4c0fb46d0cb9dcbfa5687140afeca2fdb48f668c;hpb=af16a855a4b8fd730bbd58a2a546e2bd8affbc21 diff --git a/assignment2.mdwn b/assignment2.mdwn index 85f63f36..f0e8a098 100644 --- a/assignment2.mdwn +++ b/assignment2.mdwn @@ -33,6 +33,33 @@ 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) + +* 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) + +* 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 -----------------