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    <p>What you need to express is that <code>f</code>, like <code>reduce</code> used in <code>reduceSig</code>, can be applied to <em>any</em> type that is an instance of <code>C</code>, as opposed to the current type, where <code>f</code> works on a single type that is an instance of <code>C</code>. This can be done like so:</p> <pre><code>mapsig :: (forall a. (C a) =&gt; a -&gt; a) -&gt; Signal -&gt; Signal mapsig f (Signal sig) = Signal (map (second f) sig) </code></pre> <p>You'll need the <code>RankNTypes</code> extension, as you often do when using existential types; note that the <em>implementation</em> of <code>mapsig</code> is the same, the type has just been generalised.</p> <p>Basically, with this type, <code>mapsig</code> gets to decide which <em>a</em> the function is called on; with your previous type, the <em>caller</em> of <code>mapsig</code> gets to decide that, which doesn't work, because only <code>mapsig</code> knows the correct <em>a</em>, i.e. the one inside the <code>Signal</code>.</p> <p>However, <code>mapsig reduce</code> does not work, for the obvious reason that <code>reduce :: (C a) =&gt; a -&gt; Int</code>, and you don't know that <em>a</em> is Int! You need to give <code>mapsig</code> a more general type (with the same implementation):</p> <pre><code>mapsig :: (C b) =&gt; (forall a. (C a) =&gt; a -&gt; b) -&gt; Signal -&gt; Signal </code></pre> <p>i.e., <code>f</code> is a function taking <em>any</em> type that is an instance of <code>C</code>, and producing a type that is an instance of <code>C</code> (that type is fixed at the time of the <code>mapsig</code> call and chosen by the caller; i.e. while the value <code>mapsig f</code> can be called on any Signal, it will always produce a Signal with the same <em>a</em> as a result (not that you can inspect this from outside).)</p> <p>Existentials and rank-N types are very tricky indeed, so this might take a bit of time to digest. :)</p> <hr> <p>As an addendum, it's worth pointing out that if all the functions in <code>C</code> look like <code>a -&gt; r</code> for some r, then you would be better off creating a <em>record</em> instead, i.e. turning</p> <pre><code>class C a where reduce :: a -&gt; Int foo :: a -&gt; (String, Double) bar :: a -&gt; ByteString -&gt; Magic data Signal = forall a. (C a) =&gt; Signal [(Double, a)] mapsig :: (C b) =&gt; (forall a. (C a) =&gt; a -&gt; b) -&gt; Signal -&gt; Signal </code></pre> <p>into</p> <pre><code>data C = C { reduce :: Int , foo :: (String, Double) , bar :: ByteString -&gt; Magic } data Signal = Signal [(Double, C)] mapsig :: (C -&gt; C) -&gt; Signal -&gt; Signal </code></pre> <p>These two Signal types are actually equivalent! The benefits of the former solution only appear when you have other data types that use <code>C</code> <em>without</em> existentially quantifying it, so that you can have code that uses special knowledge and operations of the specific instance of <code>C</code> it's using. If your primary use-cases of this class are through existential quantification, you probably don't want it in the first place. But I don't know what your program looks like :)</p>
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    1. COAha, I thought it would involve RankNTypes somehow, but I didn't know that it would select a type for 'a' to agree with the type hidden inside Signal. That's pretty cool. Actually, it turns out I slightly misstated my problem, 'C a' has various 'a->a' functions, and those are happy with the first mapsig. You're right, the second is a little magical seeming and I'll have to put some more thought into that one. Thanks for the enlightenment!
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    2. COWell, it can pick any *a* it wants, and it *has* to pick a single given *a* it knows nothing about — not a difficult choice for a type-checker :) I'm glad you found it enlightening.
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    3. CO(Note that you can rephrase `a -> a` functions inside the `C` typeclass as `C` fields of a `C` data type. I don't know your design, of course; just throwing that out there.)
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