-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 calculation. That is, the desired behavior should be like this:
- # lift ( + ) (lift ( / ) (unit 20) (unit 2))
- (lift ( * ) (unit 2) (unit 3)) 0;;
+ # 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).
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.
+ 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]].
+ See our [commentary](/hints/assignment_6_commentary) on your solutions.
+
+
2. Prove that your monad satisfies the monad laws. First, give
examples illustrating specific cases in which the monad laws are
obeyed, then explain (briefly, not exhaustively) why the laws hold in