-1. **Build a state monad.** Based on the division by zero monad,
+1. **Build a State monad.** Based on the division by zero monad,
build a system that will evaluate arithmetic expressions. Instead of
returning a simple integer as a result, it will deliver the correct
answer along with a count of the number of operations performed during
-the calculuation. That is, the desired behavior should be like this:
+the calculation. That is, the desired behavior should be like this:
- # lift ( + ) (lift ( / ) (unit 20) (unit 2)) (lift ( * ) (unit 2) (unit 3)) 0;;
- - : int * int = (16, 3)
+ # lift2 ( + ) (lift2 ( / ) (unit 20) (unit 2))
+ (lift2 ( * ) (unit 2) (unit 3)) 0;;
+ - : int * int = (16, 3)
-Here, `lift` is the function that uses `bind` to prepare an ordinary
+ Here, `lift2` is the function that uses `bind` to prepare an ordinary
arithmetic operator (such as addition `( + )`, division `( / )`, or
multiplication `( * )`) to recieve objects from the counting monad as
arguments. The response of the interpreter says two things: that
-(20/2) + (2*3) = 16, and that the computation took three arithmetic
+(20/2) + (2\*3) = 16, and that the computation took three arithmetic
steps. By the way, that zero at the end provides the monadic object
with a starting point (0 relevant computations have occurred previous
to the current computation).
-Assume for the purposes of this excercise that no one ever tries to
+ Assume for the purposes of this excercise that no one ever tries to
divide by zero (so there should be no int option types anywhere in
your solution).
-You'll need to define a computation monad type, unit, bind, and lift.
-We encourage you to consider this hint: [[Assignment 6 Hint 1]].
+ You'll need to define a computation monad type, unit, bind, and lift2.
+We encourage you to consider this hint: [[hints/Assignment 6 Hint 1]].
2. Prove that your monad satisfies the monad laws. First, give
examples illustrating specific cases in which the monad laws are