On Thu, Jan 29, 2009 at 01:38, nanothief <nanothief@gmail.com> wrote:

Cory Knapp wrote:

Hello, so, I'm having a simple problem with monads: I have no idea how to actually use them. I understand the category theory (or, at least well enough to be able to explain "what is a monad"); I understand the way to declare something as a monad instance, but I just don't get how to program with them. Can anyone provide me with, or direct me towards, some simple monads and some ways of using (for example) the monadic properties of lists?

Thanks,
Cory
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I found that http://www.haskell.org/all_about_monads/html/index.html gave a lot of nice examples of using list and maybe monads. The list monad is particularly useful for finding possible solutions given available input values.
For example, with the problem
x + 8y = 114
3x - 8y + 4z = 182
x < y < z < 100
Find solutions for x,y,z

The program:
res :: [(Int,Int,Int)]
res = do
x <- [1..100]
y <- [1..100]
z <- [1..100]
guard $ x + 8 * y == 114
guard $ 3*x - 8*y + 4*z == 182
guard $ x < y
guard $ y < z
return (x,y,z)

will output all the possible solutions. Note how close the program is to the actual problem. The values of x,y, and z are chosen from the value [1..100], but if a guard statement fails, the (x,y,z) choice is abandoned.

Another example (taken from http://www.mathsisfun.com/puzzles/sum-of-digits-is-43-solution.html )
*The Puzzle:* I am thinking of a 6-digit number. The sum of the digits is 43.

And only two of the following three statements about the number are true:

(1) it's a square number,
(2) it's a cube number, and
(3) the number is under 500000.

the program
answer = do
d1 <- [0..9]
d2 <- [0..9]
d3 <- [0..9]
d4 <- [0..9]
d5 <- [0..9]
d6 <- [0..9]
let digitSum = d1 + d2 + d3 + d4 + d5 + d6
let value = d1 + d2*10 + d3*100 + d4*1000 + d5*10000 + d6*100000
guard $ digitSum == 43
let lessThan500000 = digitSum < 500000
let isSquare = (round $ sqrt (fromIntegral value)) ^ 2 == value
let isCube = (round $ (fromIntegral value) ** (1/3)) ^ 3 == value
guard $ length (filter id [lessThan500000,isSquare,isCube]) == 2
return value

will output the three answers (not that the author only found one solution!).

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