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    <p>Actually, your first idea (return the counts with each value) is not a bad one, and can be expressed more abstractly by the Writer monad (in <code>Control.Monad.Writer</code> from the mtl package or <code>Control.Monad.Trans.Writer</code> from the transformers package). Essentially, the writer monad allows each computation to have an associated "output", which can be anything as long as it's an instance of <code>Monoid</code> - a class which defines:</p> <ul> <li>The empty output (<code>mempty</code>), which is the output assigned to 'return'</li> <li>An associative function (`mappend') that combines outputs, which is used when sequencing operations</li> </ul> <p>In this case, your output is a count of operations, the 'empty' value is zero, and the combining operation is addition. For example, if you're tracking operations separately:</p> <pre><code>data Counts = Counts { additions: Int, multiplications: Int } </code></pre> <p>Make that type an instance of <code>Monoid</code> (which is in the module <code>Data.Monoid</code>), and define your operations as something like:</p> <pre><code>add :: Num a =&gt; a -&gt; a -&gt; Writer Counts a add x y = do tell (Counts {additions = 1, multiplications = 0}) return (x + y) </code></pre> <p>The writer monad, together with your Monoid instance, then takes care of propagating all the 'tells' to the top level. If you wanted, you could even implement a <code>Num</code> instance for <code>Num a =&gt; Writer Counts a</code> (or, preferably, for a newtype so you're not creating an orphan instance), so that you can just use the normal numerical operators.</p>
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    1. POUsing functors for global variables?
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    1. COThanks! Can you take a look at my edit? I think this will work well, but I'm wondering if there's a more clever way (since I'm really doing this to learn Haskell rather than have a clear/efficient solution).
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    2. CO@Xodarap: If your functions are more general, you can get what you're looking for by creating a Num instance as I mentioned. For example, if `f:: Num a => a -> a`, then `f` will work for `Double` or for `Writer Counts Double`, assuming such an instance is available. Beware, though, that in doing this you end up counting things in odd ways, as @chrisdb described in a comment on his answer. In fact, I realize that the code I have given here suffers exactly the same problem, and @luqui's below does not. I'll edit mine, and hopefully if you look at the edit you'll see the problem.
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    3. COWow, look at the comments. We are thinking in three point surround sound.
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