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copied!<p>My preferred implementation for this is</p> <pre><code>fmap . fmap :: (Functor f, Functor f1) => (a -> b) -> f (f1 a) -> f (f1 b) </code></pre> <p>If only because it is fairly easy to remember.</p> <p>When instantiating f and f1 to <code>(->) c</code> and <code>(->) d</code> respectively you get the type</p> <pre><code>(a -> b) -> (c -> d -> a) -> c -> d -> b </code></pre> <p>which is the type of </p> <pre><code>(.) . (.) :: (b -> c) -> (a -> a1 -> b) -> a -> a1 -> c </code></pre> <p>but it is a bit easier to rattle off the <code>fmap . fmap</code> version and it generalizes to other functors.</p> <p>Sometimes this is written <code>fmap fmap fmap</code>, but written as <code>fmap . fmap</code> it can be more readily expanded to allow more arguments.</p> <pre><code>fmap . fmap . fmap :: (Functor f, Functor g, Functor h) => (a -> b) -> f (g (h a)) -> f (g (h b)) fmap . fmap . fmap . fmap :: (Functor f, Functor g, Functor h, Functor i) => (a -> b) -> f (g (h (i a))) -> f (g (h (i b)) </code></pre> <p>etc.</p> <p>In general <code>fmap</code> composed with itself <em>n</em> times can be used to <code>fmap</code> <em>n</em> levels deep! </p> <p>And since functions form a <code>Functor</code>, this provides plumbing for <em>n</em> arguments.</p> <p>For more information, see Conal Elliott's <a href="http://conal.net/blog/posts/semantic-editor-combinators/">Semantic Editor Combinators</a>.</p>

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