X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=blobdiff_plain;f=assignment6.mdwn;h=a31cbf8a8b2ac51ea3a27701892f37d6be423db9;hp=f1a892aa440f9e2b4cf6dfb254ebca7a1fd8d585;hb=74e31ab49f7da7666c6b95130b0abb2b8e557b7a;hpb=b6d91e7ba6477182b6f830b80a61be9b21a18a86 diff --git a/assignment6.mdwn b/assignment6.mdwn index f1a892aa..a31cbf8a 100644 --- a/assignment6.mdwn +++ b/assignment6.mdwn @@ -1,18 +1,18 @@ -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). @@ -21,8 +21,11 @@ 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. -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]]. + + 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