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    <p>At first glance, I was going to suggest <code>toList</code> and <code>fromList</code>. It's more code, but it enables elegant composition in the end.</p> <pre><code>toList :: QT a -&gt; [QT a] toList (Q w x y z) = [w,x,y,z] fromList :: [QT a] -&gt; QT a fromList [w,x,y,z] = Q w x y z listOpOnQT :: ([QT a] -&gt; [QT a]) -&gt; QT a -&gt; QT a listOpOnQT _ (C a) = C a listOpOnQT f q = fromList . map (listOpOnQT f) . f . toList $ q flipv :: QT a -&gt; QT a flipv = listOpOnQT reverse </code></pre> <p>Loosely tested in ghci</p> <pre><code>ghci&gt; let q = Q (Q (C 1) (C 2) (C 3) (C 4)) (C 22) (C 33) (C 44) ghci&gt; q Q (Q (C 1) (C 2) (C 3) (C 4)) (C 22) (C 33) (C 44) ghci&gt; flipv q Q (C 44) (C 33) (C 22) (Q (C 4) (C 3) (C 2) (C 1)) </code></pre> <p>You can easily make 'sort' work on your QT structure as well, now.</p> <pre><code>import Data.List (sort) instance (Ord a) =&gt; Ord (QT a) where compare (C x) (C y) = x `compare` y compare (C x) _ = LT compare _ (C x) = GT compare _ _ = EQ sortv :: (Ord a) =&gt; QT a -&gt; QT a sortv = listOpOnQT sort </code></pre> <p>Tested as part of the previous ghci session...</p> <pre><code>ghci&gt; sortv it Q (C 22) (C 33) (C 44) (Q (C 1) (C 2) (C 3) (C 4)) ghci&gt; sortv q Q (C 22) (C 33) (C 44) (Q (C 1) (C 2) (C 3) (C 4)) </code></pre> <p>Notice sorting the flipped q and just plain q both came out with the same result (therefore the sorting probably works! yay). You might want to pick a better implementation of <code>compare</code>, I just threw that one together to see stuff happen.</p> <hr> <p><strong>So how does it work?</strong></p> <p>The magic sauce, as you might have guessed, is <code>listOpOnQT</code>. In the non-trivial case, it turns the QT structure into a list, applies the listy function to the list, maps the <em>lifted</em> listy function on all elements of the list, and then pulls the list back into a QT structure. A better name for <code>listOpOnQT</code> might be <code>liftQT</code>, though it only works for a very special kind of function...</p>
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    1. POApply a function to a list and pass its result to a constructor?
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    1. USDan Burton
    1. USDan Burton
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    1. COthis is actually a nice answer, but not THE answer. I was looking for something concise and in-line, I mean without using any additional function apart from standard prelude.
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    2. CO@Gremo yeah I figured as much. I started out trying to see if something like `fmap` would do the trick, but unless you make QT an instance of a couple classes, then there's not much you can do out of the box (afaik).
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    3. COI object to this ad-hoc `Ord` instance. I would prefer to write a separate compare function, eg. `compareLeaves` and use `sortBy`. This `Ord` instance does not respect the extension of the data type (and, IMO, is hardly natural). Otherwise nice answer.
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