X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=blobdiff_plain;f=assignment2.mdwn;h=3e932561960bbc7792c34d868ea008aee1b2fb25;hp=066f1b1f60b6863e8738e2604bd2d8748b53a7ed;hb=f2662f133c25062dc28261f655bb9daf9c2bbb9c;hpb=7bffcdc79c27f459cb7d451f23b4ce8e5b39b125 diff --git a/assignment2.mdwn b/assignment2.mdwn index 066f1b1f..3e932561 100644 --- a/assignment2.mdwn +++ b/assignment2.mdwn @@ -1,3 +1,6 @@ +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 -------------------- @@ -30,6 +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 -----------------