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    <p>So, in general, the code:</p> <pre><code>a `f` b </code></pre> <p>is just syntactic sugar for:</p> <pre><code>f a b </code></pre> <p>Therefore your code became:</p> <pre><code>mempty PQ.singleton [start] </code></pre> <p>So the type-checker inferred the type for that particular mempty:</p> <pre><code>mempty :: (k -&gt; a -&gt; PQ.MinPQueue k a) -&gt; [Node] -&gt; PQ.MinPQueue b [Node] </code></pre> <p>You correctly found the right instance that is the problem. Anything of type <code>a -&gt; b</code> is a <code>Monoid</code>, provided that <code>b</code> is. So let's bracket that type above:</p> <pre><code>mempty :: (k -&gt; a -&gt; PQ.MinPQueue k a) -&gt; ([Node] -&gt; PQ.MinPQueue b [Node]) </code></pre> <p>So, that type can be a <code>Monoid</code> if <code>[Node] -&gt; PQ.MinPQueue b [Node]</code> is a <code>Monoid</code>. And by the same logic, <code>[Node] -&gt; PQ.MinPQueue b [Node]</code> can be a <code>Monoid</code> if <code>PQ.MinPQueue b [Node]</code> is one. Which it is. So the type-checker is fine with this code.</p> <p>Presumably the implementation of our troublesome instance is:</p> <pre><code>instance Monoid =&gt; Monoid (a -&gt; b) where mempty = const mempty </code></pre> <p>So overall, you get an empty priority queue. So really, I think it comes down to a question of whether it was wise for the designers to include this instance at all. Its net effect is that any function returning a monoid can be a monoid, which should allow you to combine the results. The more useful case here is mappend, which can append two <code>a -&gt; b</code> functions by applying them both and using <code>mappend</code> to combine the results. For example:</p> <pre><code>extremes = (return . minimum) `mappend` (return . maximum) </code></pre> <p>rather than:</p> <pre><code>extremes xs = [minimum xs, maximum xs] </code></pre> <p>Hmmm, maybe someone else can produce a sensible terser example.</p>
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    1. POAccidentally backticking a non-binary function creates bizarre behaviour
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    1. USNeil Brown
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    1. COThanks for the explanation! I actually hadn't realized that PQ.MinPQueue b [Node] was a Monoid.
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    2. COSo do you think anything could have been done to prevent this kind of strangeness from occurring, or was this just a rare, unavoidable perfect storm of types perfectly re-aligning unexpectedly? You hinted at possibly pointing blame at the Monoid instance of (a -> b); would we really lose anything useful by removing that? Or maybe just hiding that instance behind a newtype?
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    3. COA use of this `Monoid (a -> b)` instance is `sortBy (comparing foo \`mappend\` comparing bar)`.
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      1. USReid Barton
 

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