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POMaking (a, a) a Functor
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copied!<p>How can I make <code>(a, a)</code> a <code>Functor</code> without resorting to a <code>newtype</code>?</p> <p>Basically I want it to work like this:</p> <pre><code>instance Functor (a, a) where fmap f (x, y) = (f x, f y) </code></pre> <p>But of course that's not a legal way to express it:</p> <pre><code>Kind mis-match The first argument of `Functor' should have kind `* -> *', but `(a, a)' has kind `*' In the instance declaration for `Functor (a, a)' </code></pre> <p>What I really want is a type-level function like this: <code>\a -> (a, a)</code> (invalid syntax). So a type alias, perhaps?</p> <pre><code>type V2 a = (a, a) instance Functor V2 where fmap f (x, y) = (f x, f y) </code></pre> <p>I would think this would work, but it doesn't. First I get this complaint:</p> <pre><code>Illegal instance declaration for `Functor V2' (All instance types must be of the form (T t1 ... tn) where T is not a synonym. Use -XTypeSynonymInstances if you want to disable this.) In the instance declaration for `Functor V2' </code></pre> <p>If I follow the advice and add the <code>TypeSynonymInstances</code> extension, I get a new error:</p> <pre><code>Type synonym `V2' should have 1 argument, but has been given 0 In the instance declaration for `Functor V2' </code></pre> <p>Well, duh, that's the point! <code>V2</code> has kind <code>* -> *</code> which is what is required of a <code>Functor</code> instance. Well, ok, I can use a <code>newtype</code> like this:</p> <pre><code>newtype V2 a = V2 (a, a) instance Functor V2 where fmap f (V2 (x, y)) = V2 (f x, f y) </code></pre> <p>But now I've got to sprinkle <code>V2</code>s liberally throughout my code instead of just being able to deal with simple tuples, which kind of defeats the point of making it a <code>Functor</code>; at that point I might as well make my own function <code>vmap :: (a -> b) -> (a, a) -> (b, b)</code>.</p> <p>So is there any way to do this nicely, i.e. without a <code>newtype</code>?</p>

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