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copied!<p>Here's a suggestion to solve a more general problem, not yours specifically (I need more detail yet first - I promise to check later). I'm writing it in case other people are searching for a solution to a similar problem to you, I certainly was in the past, before I discovered SO. SO is especially great when it helps you try a radically new approach.</p> <p>I used to have the work habit:</p> <ol> <li>Introduce a multi-parameter type class (Types hanging out all over the place, so...)</li> <li>Introduce functional dependencies (Should tidy it up but then I end up needing...)</li> <li>Add FlexibleInstances (Alarm bells start ringing. There's a reason the compiler has this off by default...)</li> <li>Add UndecidableInstances (GHC is telling you you're on your own, because it's not convinced it's up to the challenge you're setting it.)</li> <li>Everything blows up. Refactor somehow.</li> </ol> <p>Then I discovered the joys of <a href="http://www.haskell.org/haskellwiki/Simonpj/Talk%3aFunWithTypeFuns" rel="nofollow">type families</a> (functional programming for types (hooray) - multi-parameter type classes are (a bit like) logic programming for types). My workflow changed to:</p> <ol> <li><p>Introduce a type class including an associated type, i.e. replace</p> <pre><code>class MyProblematicClass a b | a -> b where thing :: a -> b thang :: b -> a -> b </code></pre> <p>with</p> <pre><code>class MyJustWorksClass a where type Thing a :: * -- Thing a is a type (*), not a type constructor (* -> *) thing :: a -> Thing a thang :: Thing a -> a -> Thing a </code></pre></li> <li><p>Nervously add FlexibleInstances. Nothing goes wrong at all.</p></li> <li>Sometimes fix things by using constraints like <code>(MyJustWorksClass j,j~a)=></code> instead of <code>(MyJustWorksClass a)=></code> or <code>(Show t,t ~ Thing a,...)=></code> instead of <code>(Show (Thing a),...) =></code> to help ghc out. (<code>~</code> essentially means 'is the same type as')</li> <li>Nervously add FlexibleContexts. Nothing goes wrong at all.</li> <li>Everything works.</li> </ol> <p>The reason "Nothing goes wrong at all" is that ghc <em>calculates</em> the type <code>Thing a</code> using my type function <code>Thang</code> rather than trying to <em>deduce</em> it using a merely a bunch of assertions that there's a function there and it ought to be able to work it out. </p> <p>Give it a go! Read <a href="http://www.haskell.org/haskellwiki/Simonpj/Talk%3aFunWithTypeFuns" rel="nofollow">Fun with Type Functions</a> <em>before</em> reading the <a href="http://www.haskell.org/haskellwiki/GHC/Type_families" rel="nofollow">manual</a>!</p>

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