On 09/23/08 01:01, Jake Mcarthur wrote:
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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
According to: cata :: Functor f => Algebra f a -> FixF f -> a from: http://comonad.com/reader/2008/catamorphism ident must be: Algebra f a for some Functor f; however, I don't see any declaration of ident as an Algebra f a. Could you please elaborate. I'm trying to apply this to a simple boolean simplifier shown in the attachement. As near as I can figure, maybe the f could be the ArityN in the attachment and maybe the a would be (Arity0 ConBool var). The output of the last line of attachment is: bool_eval:f+f+v0=(:+) (Op0 (OpCon BoolFalse)) (Op0 (OpVar V0)) however, what I want is a complete reduction to: (OpVar V0) How can this be done using catamorphisms?