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copied!<p>From what I understand, your layers look like:</p> <pre><code>Maybe [Maybe r] </code></pre> <p>... and you want to <code>join</code> the two <code>Maybe</code>s together, but the list is in the way. This is precisely the problem <code>sequence</code> solves:</p> <pre><code>sequence :: (Monad m) => [m r] -> m [r] </code></pre> <p>Note that if we specialize <code>sequence</code> to the <code>Maybe</code> monad we get:</p> <pre><code>sequence :: [Maybe r] -> Maybe [r] </code></pre> <p>In this particular case, <code>sequence</code> will return a <code>Nothing</code> if there is at least one <code>Nothing</code> in the list, but if they are all <code>Just</code>s, then it will join them all into a single <code>Just</code>.</p> <p>All that remains is to map <code>sequence</code> over the outer <code>Maybe</code>:</p> <pre><code>fmap sequence :: Maybe [Maybe r] -> Maybe (Maybe [r]) </code></pre> <p>Now this is exactly in the form we need for join:</p> <pre><code>join . fmap sequence :: Maybe [Maybe r] -> Maybe [r] </code></pre> <p>So, intuitively, what the above function does is that if all the inner <code>Maybe</code>s are <code>Just</code>s and the outer <code>Maybe</code> is a <code>Just</code>, then it fuses the entire result into a single <code>Just</code> containing the list. However, if any <code>Maybe</code> (either the inner ones or outer one) is a <code>Nothing</code>, the final result is a <code>Nothing</code>.</p> <p>Notice that despite doing a bunch of blind type-chasing, we ended up with a function that intuitively does the right thing. This is the power of abstractions grounded in category theory.</p>

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