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    <p>Have you looked at Chris Okasaki's <a href="http://www.cs.tufts.edu/~nr/cs257/archive/chris-okasaki/breadth-first.pdf" rel="nofollow noreferrer">"Breadth-First Numbering: Lessons from a Small Exercise in Algorithm Design"</a>? The <code>Data.Tree</code> module includes a monadic tree builder named <code>unfoldTreeM_BF</code> that uses an algorithm adapted from that paper.</p> <p>Here's an example that I think corresponds to what you're doing:</p> <p>Suppose I want to search an infinite binary tree of strings where all the left children are the parent string plus "a", and the right children are the parent plus "bb". I could use <code>unfoldTreeM_BF</code> to search the tree breadth-first and return the searched tree up to the solution:</p> <pre><code>import Control.Monad.State import Data.Tree children :: String -&gt; [String] children x = [x ++ "a", x ++ "bb"] expand query x = do found &lt;- get if found then return (x, []) else do let (before, after) = break (==query) $ children x if null after then return (x, before) else do put True return (x, before ++ [head after]) searchBF query = (evalState $ unfoldTreeM_BF (expand query) []) False printSearchBF = drawTree . searchBF </code></pre> <p>This isn't terribly pretty, but it works. If I search for "aabb" I get exactly what I want:</p> <pre><code>| +- a | | | +- aa | | | | | +- aaa | | | | | `- aabb | | | `- abb | `- bb | +- bba | `- bbbb </code></pre> <p>If this is the kind of thing you're describing, it shouldn't be hard to adapt for your tree type.</p> <p>UPDATE: Here's a do-free version of <code>expand</code>, in case you're into this kind of thing:</p> <pre><code>expand q x = liftM ((,) x) $ get &gt;&gt;= expandChildren where checkChildren (before, []) = return before checkChildren (before, t:_) = put True &gt;&gt; return (before ++ [t]) expandChildren True = return [] expandChildren _ = checkChildren $ break (==q) $ children x </code></pre> <p>(Thanks to camccann for prodding me away from old control structure habits. I hope this version is more acceptable.)</p>
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    1. POHow to functionally generate a tree breadth-first. (With Haskell)
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    1. POHow to functionally generate a tree breadth-first. (With Haskell)
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    1. CODear god, that code, it... I... but... what are you *doing* to that poor State monad? You monster!
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    2. COYeah, it's ugly, but it was off the top of my head. How would you do it? I'll admit that I'm a beginner, but I don't see a way to tell unfoldTreeM_BF to stop expanding children without State.
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    3. COOkay I fixed the silly thing I was doing with the query in State, but I still think I need it for knowing when to stop. Isn't this exactly why the tree builder is monadic in the first place?
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