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    <p>This is a followup to a previous question: <a href="https://stackoverflow.com/questions/19191348/type-level-map-with-datakinds">Type-level Map with DataKinds</a>, starting with from the two answers it received.</p> <p>My goal is to take a <code>HList</code> of arbitrary types and turn it into a list of related/derived types</p> <pre><code>type family TypeMap (a :: * -&gt; *) (xs :: [*]) :: [*] type instance TypeMap t '[] = '[] type instance TypeMap t (x ': xs) = t x ': TypeMap t xs data HList :: [*] -&gt; * where HNil :: HList '[] HCons :: a -&gt; HList as -&gt; HList (a ': as) </code></pre> <p>When I actually tried to do this with a few types, I ran into a problem. The type-function " argument to TypeMap has to take the <code>HList</code> element type as its last argument and return a new type. This works okay sometimes:</p> <pre><code>test :: HList rqs -&gt; HList (TypeMap ((,) Int) rqs) test HNil = HNil test (HCons x xs) = HCons (3,x) $ test xs </code></pre> <p>But what if I wanted to switch the order of the tuple in the definition of test? My first attempt was to define a type synonym:</p> <pre><code>type RevIntTup b = (b,Int) test2 :: HList rqs -&gt; HList (TypeMap RevIntTup rqs) test2 HNil = HNil test2 (HCons x xs) = HCons (x,3) $ test2 xs </code></pre> <p>But of course, <a href="https://stackoverflow.com/questions/4922560/why-doesnt-typesynonyminstances-allow-partially-applied-type-synonyms-to-be-use">you can't partially apply type synonyms</a>, which would certainly do the trick. Is there any (other) way to achieve this?</p>
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