Sat Oct 18 17:48:06 EDT 2008

```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:

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?

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