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There's no completely standard class that does this, but it's pretty easy to make one yourself. I'll sketch one way of doing this: <pre><code>data P = A | B Q deriving Show data Q = C | D R | E deriving Show data R = F | G deriving Show class Finite a where allValues :: [a] instance Finite P where allValues = [A] ++ map B allValues instance Finite Q where allValues = [C] ++ map D allValues ++ [E] instance Finite R where allValues = [F] ++ [G] </code></pre> I've written the instances this way to show that it's very easy and mechanical and could be done by a program (e.g. with generic programming or with Template Haskell). You could also add an instance to do some legwork for you, provided the type is <code>Bounded</code> and <code>Enum</code>erable: <pre><code>instance (Bounded a, Enum a) => Finite a where allValues = [minBound..maxBound] </code></pre> If you now add <code>deriving (Bounded, Show)</code> to <code>R</code>, that's one less instance to write! Anyway, now we can evaluate <code>allValues :: [P]</code> and get back <code>[A,B C,B (D F),B (D G),B E]</code> - which you can then <code>zip</code> with <code>[0..]</code> to get your encoding and so on. <hr> But surely this has been done before! I'm not using serialization much (if ever), but a quick search shows that <a href="http://hackage.haskell.org/package/binary">the binary package</a> and <a href="http://hackage.haskell.org/package/binary-derive">the binary-derive package</a> can do something similar for you, without having to write the instances yourself. I would see if those do what you want first.
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1. POWhat's the most efficient way to represent finite (non-recursive) algebraic type values?
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