X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=blobdiff_plain;f=assignment1.mdwn;h=6fd29ee206bea5daf066f60fdef5b70da0c3b196;hp=e6fe829a235857ae77cb78a733a280ca064d8eae;hb=ec7e61a11b6cbbfe9c6c90e6c077c430424317d0;hpb=1e997f71620b8c4a5d5ca6ee9df1d616ff74fae6 diff --git a/assignment1.mdwn b/assignment1.mdwn index e6fe829a..6fd29ee2 100644 --- a/assignment1.mdwn +++ b/assignment1.mdwn @@ -1,18 +1,18 @@ -*Reduction* +**Reduction** Find "normal forms" for the following (that is, reduce them as far as it's possible to reduce them): - 1. (\x \y. y x) z - 2. (\x (x x)) z - 3. (\x (\x x)) z - 4. (\x (\z x)) z - 5. (\x (x (\y y))) (\z (z z)) - 6. (\x (x x)) (\x (x x)) - 7. (\x (x x x)) (\x (x x x)) + 1. (\x \y. y x) z + 2. (\x (x x)) z + 3. (\x (\x x)) z + 4. (\x (\z x)) z + 5. (\x (x (\y y))) (\z (z z)) + 6. (\x (x x)) (\x (x x)) + 7. (\x (x x x)) (\x (x x x)) -*Booleans* +**Booleans** Recall our definitions of true and false. @@ -26,7 +26,7 @@ In Racket, these can be defined like this: 8. Define a "neg" operator that negates "true" and "false". -Expeceted behavior: (((neg true) 10) 20) evaluates to 20, +Expected behavior: (((neg true) 10) 20) evaluates to 20, (((neg false) 10) 20) evaluates to 10. 9. Define an "and" operator. @@ -44,6 +44,7 @@ one of those values, call it a black-or-white-value, we should be able to write: the-black-or-white-value if-black if-white + (where if-black and if-white are anything), and get back one of if-black or if-white, depending on which of the black-or-white values we started with. Give a definition for each of "black" and "white". (Do it in both lambda calculus