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PODo Traversables really require to be traversed "left-to-right"?
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copied!<p>I have an infinite structure like the following (using the <a href="http://hackage.haskell.org/packages/archive/streams/3.0/doc/html/Data-Stream-Infinite.html">Stream</a> type from the <a href="http://hackage.haskell.org/package/streams">streams</a> package):</p> <pre><code>data U x = U (Stream x) x (Stream x) deriving (Functor,Foldable) </code></pre> <p>I want to provide an instance of Traversable for it, like this:</p> <pre><code>instance Traversable U where traverse f (U lstream focus rstream) = let pairs = liftA unzip . sequenceA . fmap (traversepair f) $ zip lstream rstream traversepair f (a,b) = (,) <$> f a <*> f b rebuild c (u,v) = U u c v in rebuild <$> f focus <*> pairs </code></pre> <p>The <a href="http://www.haskell.org/ghc/docs/latest/html/libraries/base/Data-Traversable.html">documentation for Data.Traversable</a> says that they represent the "class of data structures that can be traversed from left to right". But my definition does not traverse from left to right, it traverses <em>outwardly</em>. I had to define it that way to be able to lazily extract values on both sides after a <a href="http://www.haskell.org/ghc/docs/latest/html/libraries/base/Data-Traversable.html#v%3asequence">sequence</a> operation involving the <a href="http://hackage.haskell.org/packages/archive/MonadRandom/0.1.8/doc/html/Control-Monad-Random.html#t%3aRand">Rand</a> monad.</p> <p>Is it a valid definition nonetheless? I have noticed that the <a href="http://www.haskell.org/haskellwiki/Typeclassopedia#Traversable">Typeclassopedia entry for Traversable</a> doesn't say anything about "left-to-right", it only talks about "commuting two functors".</p>

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