From 7bb54cf783a20dd6f8ff464f5be97e72b87f4045 Mon Sep 17 00:00:00 2001 From: Jim Pryor Date: Mon, 20 Sep 2010 07:10:43 -0400 Subject: [PATCH] assignment 2 formatting Signed-off-by: Jim Pryor --- assignment2.mdwn | 42 ++++++++++++++++++++++-------------------- 1 file changed, 22 insertions(+), 20 deletions(-) diff --git a/assignment2.mdwn b/assignment2.mdwn index ba4e1b4a..4f806206 100644 --- a/assignment2.mdwn +++ b/assignment2.mdwn @@ -72,35 +72,37 @@ For these exercises, assume that `LIST` is the result of evaluating: (make-list a (make-list b (make-list c (make-list d (make-list e empty))))) -16. What would be the result of evaluating (see [[Assignment 2 hint 1]] for a hint): +
    +
  1. What would be the result of evaluating (see [[Assignment 2 hint 1]] for a hint): - LIST make-list empty + LIST make-list empty -17. Based on your answer to question 1, how might you implement the **map** function? Expected behavior: +
  2. Based on your answer to question 16, how might you implement the **map** function? Expected behavior: - 
    map f LIST <~~> (make-list (f a) (make-list (f b) (make-list (f c) (make-list (f d) (make-list (f e) empty)))))
    + map f LIST <~~> (make-list (f a) (make-list (f b) (make-list (f c) (make-list (f d) (make-list (f e) empty))))) -18. Based on your answer to question 1, how might you implement the **filter** function? The expected behavior is that: +
  3. Based on your answer to question 16, how might you implement the **filter** function? The expected behavior is that: - filter f LIST + filter f LIST - should evaluate to a list containing just those of `a`, `b`, `c`, `d`, and `e` such that `f` applied to them evaluates to `true`. +should evaluate to a list containing just those of `a`, `b`, `c`, `d`, and `e` such that `f` applied to them evaluates to `true`. -4. How would you implement map using the either the version 1 or the version 2 implementation of lists? +
  4. How would you implement map using the either the version 1 or the version 2 implementation of lists? -5. Our version 3 implementation of the numbers are usually called "Church numerals". If `m` is a Church numeral, then `m s z` applies the function `s` to the result of applying `s` to ... to `z`, for a total of *m* applications of `s`, where *m* is the number that `m` represents or encodes. +
  5. Our version 3 implementation of the numbers are usually called "Church numerals". If `m` is a Church numeral, then `m s z` applies the function `s` to the result of applying `s` to ... to `z`, for a total of *m* applications of `s`, where *m* is the number that `m` represents or encodes. - Given the primitive arithmetic functions above, how would you implement the less-than-or-equal function? Here is the expected behavior, where `one` abbreviates `succ zero`, and `two` abbreviates `succ (succ zero)`. +Given the primitive arithmetic functions above, how would you implement the less-than-or-equal function? Here is the expected behavior, where `one` abbreviates `succ zero`, and `two` abbreviates `succ (succ zero)`. - less-than-or-equal zero zero ~~> true - less-than-or-equal zero one ~~> true - less-than-or-equal zero two ~~> true - less-than-or-equal one zero ~~> false - less-than-or-equal one one ~~> true - less-than-or-equal one two ~~> true - less-than-or-equal two zero ~~> false - less-than-or-equal two one ~~> false - less-than-or-equal two two ~~> true + less-than-or-equal zero zero ~~> true + less-than-or-equal zero one ~~> true + less-than-or-equal zero two ~~> true + less-than-or-equal one zero ~~> false + less-than-or-equal one one ~~> true + less-than-or-equal one two ~~> true + less-than-or-equal two zero ~~> false + less-than-or-equal two one ~~> false + less-than-or-equal two two ~~> true - You'll need to make use of the predecessor function, but it's not important to understand how the implementation we gave above works. You can treat it as a black box. +You'll need to make use of the predecessor function, but it's not important to understand how the implementation we gave above works. You can treat it as a black box. +
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