X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=blobdiff_plain;f=assignment2.mdwn;h=ff600cc71e8107653cd31bdd0b42c78f0a16f579;hp=648ef2107c290522b8916b95c411a116be8476e5;hb=98652627403eaa920f51cedc4d0cc68c1103b972;hpb=d63b0d0e1c52b50a383e419345a54e2bc6339a77 diff --git a/assignment2.mdwn b/assignment2.mdwn index 648ef210..ff600cc7 100644 --- a/assignment2.mdwn +++ b/assignment2.mdwn @@ -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 -----------------