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@@ -1,4 +1,17 @@
+Assignment 5
+
Types and OCAML
+---------------
+
+0. Recall that the S combinator is given by \x y z. x z (y z).
+ Give two different typings for this function in OCAML.
+ To get you started, here's one typing for K:
+
+ # let k (y:'a) (n:'b) = y;;
+ val k : 'a -> 'b -> 'a =
+ # k 1 true;;
+ - : int = 1
+
1. Which of the following expressions is well-typed in OCAML?
For those that are, give the type of the expression as a whole.
@@ -108,3 +121,20 @@ or of `match`. That is, you must keep the `let` statements, though
you're allowed to adjust what `b`, `y`, and `n` get assigned to.
[[Hint assignment 5 problem 3]]
+
+4. Baby monads. Read the lecture notes for week 6, then write a
+ function `lift` that generalized the correspondence between + and
+ `add`: that is, `lift` takes any two-place operation on integers
+ and returns a version that takes arguments of type `int option`
+ instead, returning a result of `int option`. In other words,
+ `lift` will have type
+
+ (int -> int -> int) -> (int option) -> (int option) -> (int option)
+
+ so that `lift (+) (Some 3) (Some 4)` will evalute to `Some 7`.
+ Don't worry about why you need to put `+` inside of parentheses.
+ You should make use of `bind` in your definition of `lift`:
+
+ let bind (x: int option) (f: int -> (int option)) =
+ match x with None -> None | Some n -> f n;;
+