one more exercise

[lambda.git] / exercises / assignment5.mdwn

diff --git a/exercises/assignment5.mdwn b/exercises/assignment5.mdwn
index c72ce6d..5dd1cbb 100644 (file)
--- a/exercises/assignment5.mdwn
+++ b/exercises/assignment5.mdwn
@@ -252,6 +252,8 @@ Again, we've left some gaps. (The use of `type` for the first line in Haskell an
 
 15. Choose one of these languages and fill in the gaps to complete the definition.
 
 
 15. Choose one of these languages and fill in the gaps to complete the definition.
 

+<a id="occurs_free"></a>
+

 16. Write a function `occurs_free` that has the following type:
 
         occurs_free : identifier -> lambda_term -> bool
 16. Write a function `occurs_free` that has the following type:
 
         occurs_free : identifier -> lambda_term -> bool


@@ -329,7 +331,7 @@ any type `α`, as long as your function is of type `α -> α` and you have a bas
         -- Or this:
         let sysf_true = (\y n -> y) :: Sysf_bool a
 
         -- 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; ... }
 
         :set -XExplicitForAll
         let { sysf_true :: forall a. Sysf_bool a; ... }


@@ -384,6 +386,8 @@ Yet we haven't given ourselves the capacity to talk about `list [S]` and so on a
     = λf:T -> S. λxs:list. xs [T] [list [S]] (λx:T. λys:list [S]. cons [S] (f x) ys) (nil [S])
 -->
 
     = 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 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`.)
 
 20. Also give us the type and definition for a `sysf_head` function. Think about what value to give back if its argument is the empty list. It might be cleanest to use the `option`/`Maybe` technique explored in questions 1--2, but for this assignment, just pick a strategy, no matter how clunky. 
 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`.)
 
 20. Also give us the type and definition for a `sysf_head` function. Think about what value to give back if its argument is the empty list. It might be cleanest to use the `option`/`Maybe` technique explored in questions 1--2, but for this assignment, just pick a strategy, no matter how clunky. 


@@ -406,7 +410,7 @@ Be sure to test your proposals with simple lists. (You'll have to `sysf_cons` up
         # k 1 true ;;
         - : int = 1
 
         # 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".