6. How would you use the function defined in problem 4 to enumerate a tree's fringe? (Don't worry about whether it comes out left-to-right or right-to-left.)
-7. Write a recursive function to make a copy of a `color_tree` with the same structure and inner branch colors, but where the leftmost leaf is now labeled `0`, the second-leftmost leaf is now labeled `1`, and so on. (Here's a [[hint|assignment5 hint4]], if you need one.)
+7. Write a recursive function to make a copy of a `color_tree` with the same structure and inner branch colors, but where the leftmost leaf is now labeled `0`, the second-leftmost leaf is now labeled `1`, and so on. (Here's a [[hint|assignment5 hint3]], if you need one.)
8. (More challenging.) Write a recursive function that makes a copy of a `color_tree` with the same structure and inner branch colors, but replaces each leaf label with the `int` that reports how many of that leaf's ancestors are labeled `Red`. For example, if we give your function a tree:
-- Or this:
let sysf_true = (\y n -> y) :: Sysf_bool a
- Note that in both OCaml and the Haskell code, the generalization `∀'a` on the free type variable `'a` is implicit. If you really want to, you can supply it explicitly in Haskell by saying:
+ Note that in both OCaml and Haskell code, the generalization `∀α` on the free type variable `α` is implicit. If you really want to, you can supply it explicitly in Haskell by saying:
:set -XExplicitForAll
let { sysf_true :: forall a. Sysf_bool a; ... }
= λf:T -> S. λxs:list. xs [T] [list [S]] (λx:T. λys:list [S]. cons [S] (f x) ys) (nil [S])
-->
-*Update: Never mind, don't bother with the next three questions. They proved to be more difficult to implement in OCaml than we expected. Here is [[some explanation|assignment5 hint3]].*
+*Update: Never mind, don't bother with the next three questions. They proved to be more difficult to implement in OCaml than we expected. Here is [[some explanation|assignment5 hint4]].*
19. Convert this list encoding and the `map` function to OCaml or Haskell. Again, call the type `sysf_list`, and the functions `sysf_nil`, `sysf_cons`, and `sysf_map`, to avoid collision with the names for native lists and functions in these languages. (In OCaml and Haskell you *can* say `('t) sysf_list` or `Sysf_list t`.)
# k 1 true ;;
- : int = 1
- If you can't understand how one term can have several types, recall our discussion in this week's notes of "principal types". (WHERE?)
+ If you can't understand how one term can have several types, recall our discussion in this week's notes of "principal types".