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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
-
--------------------------------------------------------------------------------
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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