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POhaskell : making a superclass of Num
 

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    <p>I want to make a superclass of Num, called Linear</p> <pre><code>class Linear a where add :: a -&gt; a -&gt; a instance (Num a) =&gt; Linear a where add = (+) </code></pre> <p>I get the error : </p> <pre><code>Illegal instance declaration for `Linear a' (All instance types must be of the form (T a1 ... an) where a1 ... an are *distinct type variables*, and each type variable appears at most once in the instance head. Use -XFlexibleInstances if you want to disable this.) In the instance declaration for `Linear a' </code></pre> <p>From what I understand, something about the line <code>instance (Num a) =&gt; Linear a where</code> is incorrect. (It compiles if I use the flags : <code>-XFlexibleInstances -XUndecidableInstances</code>)</p> <p>Is there a way to achieve this without using those scary flags? (and what in the world is undecidable about the code above??)</p> <p><strong>UPDATE</strong> : Added Polynomial type to Linear.</p> <pre><code>newtype Polynomial a = Polynomial (a,[a]) deriving Show-- list of coeffients instance (Linear a) =&gt; Linear (Polynomial a) where add (Polynomial (c1, l1)) (Polynomial (c2, l2)) = Polynomial (add c1 c2, zipWith (add) l1 l2) p1 = Polynomial (0, [3,4,5]) p2 = Polynomial (0, []) main = putStrLn $ show ((add p1 p2):: Polynomial Int) </code></pre> <p>After adding polynomial, it doesn't compile with even those flags and give the error:</p> <pre><code>Overlapping instances for Linear (Polynomial Int) arising from a use of `add' Matching instances: instance Num a =&gt; Linear a -- Defined at Algebra.hs:22:10-28 instance Linear a =&gt; Linear (Polynomial a) -- Defined at Algebra.hs:25:10-44 In the first argument of `show', namely `((add p1 p2) :: Polynomial Int)' In the second argument of `($)', namely `show ((add p1 p2) :: Polynomial Int)' In the expression: putStrLn $ show ((add p1 p2) :: Polynomial Int) </code></pre>
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    1. COcan you please point out why they are needed; and undecidability is scary :)
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    2. COIn Haskell, many things have scary names that nobody would worry about for a second in other languages.
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