X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=blobdiff_plain;f=assignment6.mdwn;h=7a2bb0f104245dfd9a9382494a386d13dc068fe9;hp=919ff24f246a565a8c13157d2ed56987b46263ee;hb=5f209baee5d46b2d6b52258bcfa77a35a1995f7d;hpb=11a31a071405f0eb9bc48ea98e5e9ee592fac245 diff --git a/assignment6.mdwn b/assignment6.mdwn index 919ff24f..7a2bb0f1 100644 --- a/assignment6.mdwn +++ b/assignment6.mdwn @@ -2,12 +2,13 @@ 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) + # 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 + 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 @@ -16,12 +17,12 @@ 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 lift. +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