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POimplementing a per-digit counter using the list monad
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copied!<p>So, I was looking at the question <a href="https://stackoverflow.com/questions/1855561/implementing-a-factorisation-method-in-haskell">here</a>, and built a rather ugly solution for the problem. While trying to clean it up, I started investigating list comprehensions and the list monad. What I decided to do was to implement a per-digit counter using the list monad. Given an input sequence of digits, <code>[1, 2]</code>, I wanted to generate an output sequence that looked something like:</p> <pre><code>[ [ 0, 0], [ 0, 1 ], [ 0, 2 ], [ 1, 0 ], [ 1, 1 ], [ 1, 2 ] ] </code></pre> <p>That is, I'd iterate over all possible values of all elements in the list in that range.</p> <p>The haskell.org <a href="http://www.haskell.org/all_about_monads/html/listmonad.html" rel="nofollow noreferrer">list monad documentation</a> says:</p> <blockquote> <p>The bound function is applied to all possible values in the input list and the resulting lists are concatenated to produce a list of all possible results.</p> </blockquote> <p>Great! Looks perfect... Here's the code I wrote to produce the solution:</p> <pre><code>count :: [Integer] -> [[Integer]] count [] = [] count (x:xs) = -- get all possible sequences for the remaining digits let remDigits :: [[Integer]] remDigits = count xs in -- pull out a possible sequence for the remaining digits do nextDigits <- remDigits -- pull out all possible values for the current digit y <- [0..x] -- record that "current digit" : "remaining digits" is -- a valid output. return (y:nextDigits) </code></pre> <p>But calling <code>count</code> with anything produces the empty list, and I don't know why. What am I missing?</p>

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