+++ /dev/null
-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;;
- - : int * int = (16, 3)
-
- Here, `lift` 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
-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
-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]].
-
-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
-general for your unit and bind operators.
-
-3. How would you extend your strategy if you wanted to count
-arithmetic operations, but you also wanted to be safe from division by
-zero? This is a deep question: how should you combine two monads into
-a single system? If you don't arrive at working code, you can still
-discuss the issues and design choices.