[Haskell-cafe] Is there already an abstraction for this?

[Jake Mcarthur]

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The first thing I thought of was to try to apply one of the recursion  
schemes
in the category-extras package. Here is what I managed using  
catamorphism.

- - Jake

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data Expr' a
   = Quotient a a
   | Product a a
   | Sum a a
   | Difference a a
   | Lit Double
   | Var Char

type Expr = FixF Expr'

instance Functor Expr' where
     fmap f (a `Quotient` b) = f a `Quotient` f b
     fmap f (a `Product` b) = f a `Product` f b
     fmap f (a `Sum` b) = f a `Sum` f b
     fmap f (a `Difference` b) = f a `Difference` f b
     fmap _ (Lit x) = Lit x
     fmap _ (Var x) = Var x

identity = cata ident
     where ident (a `Quotient` InF (Lit 1)) = a
           ident (a `Product` InF (Lit 1)) = a
           ident (InF (Lit 1) `Product` b) = b
           ident (a `Sum` InF (Lit 0)) = a
           ident (InF (Lit 0) `Sum` b) = b
           ident (a `Difference` InF (Lit 0)) = a
           ident (Lit x) = InF $ Lit x
           ident (Var x) = InF $ Var x
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