(((neg true) 10) 20)
- evaluates to 20, and
+ evaluates to `20`, and
(((neg false) 10) 20)
- evaluates to 10.
+ evaluates to `10`.
16. Define an `or` operator.
Recall our definitions of ordered triples.
-> the triple **(**a**,**b**, **c**)** is defined to be `\f. f a b c`
+> the triple **(**a**, **b**, **c**)** is defined to be `\f. f a b c`
-To extract the first element of a triple t, you write:
+To extract the first element of a triple `t`, you write:
t (\fst snd trd. fst)
21. Using Kapulet syntax, define `fold_left`.
-22. Using Kapulet syntax, define `filter` (problem 7 in last week's homework) in terms of `fold_right`.
+22. Using Kapulet syntax, define `filter` (problem 7 in last week's homework) in terms of `fold_right` and other primitive syntax like `lambda`, `&`, and `[]`. Don't use `letrec`!
23. Using Kapulet syntax, define `&&` in terms of `fold_right`. (To avoid trickiness about the infix syntax, just call it `append`.)
24. Using Kapulet syntax, define `head` in terms of `fold_right`. When applied to a non-empty list, it should give us the first element of that list. When applied to an empty list, let's say it should give us `'error`.
-25. We mentioned in the Encoding notes that `fold_left (flipped_cons, []) xs` would give us the elements of `xs` but in the reverse order. That is, this is how we can express `reverse` in terms of `fold_left`. How would you express `reverse` in terms of `fold_right`?
+25. We mentioned in the Encoding notes that `fold_left (flipped_cons, []) xs` would give us the elements of `xs` but in the reverse order. So that's how we can express `reverse` in terms of `fold_left`. How would you express `reverse` in terms of `fold_right`?
This problem does have an elegant and concise solution, but it may be hard for you to figure it out. We think it will a useful exercise for you to try, anyway. We'll give a [[hint|assignment2 hint]]. Don't look at the hint until you've gotten really worked up about the problem. Before that, it probably will just be baffling. If your mind has really gotten its talons into the problem, though, the hint might be just what you need to break it open.
- Even if you don't get the answer, we think the experience of working on the problem, and then understanding the answer when we reveal it, will be satisfying and worhtwhile. It also fits our pedagogical purposes for one of the recurring themes of the class.
+ Even if you don't get the answer, we think the experience of working on the problem, and then understanding the answer when we reveal it, will be satisfying and worthwhile. It also fits our pedagogical purposes for some of the recurring themes of the class.
Numbers