[Haskell-cafe] Fixed point newtype confusion

[Francesco Mazzoli]

Sorry, I think I misunderstood your question, if I understand correctly 
you want some function to convert nested Expr to Fix'ed Exprs.

You can do that with a typeclass, but you have to provide the Fix'ed 
type at the bottom:

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

{-# LANGUAGE FlexibleInstances #-}

data E e = Lit Int | Add e e
data Fix f = Fix {unFix :: f (Fix f)}
type Expr = Fix E

lit :: Int -> Expr
lit = Fix . Lit

add :: Expr -> Expr -> Expr
add e1 e2 = Fix (Add e1 e2)

term :: Expr
term = add (lit 1) (add (lit 2) (lit 3))

class FixE e where
     fix :: e -> Expr

instance FixE Expr where
     fix = id

instance FixE e => FixE (E e) where
     fix (Lit i)     = lit i
     fix (Add e1 e2) = add (fix e1) (fix e2)

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

This is because your `term' works since you don't have any occurrence of 
`expr' at leaves of your Expr tree, and that works because the leaves 
are all literals. However, we can't guarantee this statically.

We can, of course, write an unsafe instance based on the assumption that 
the the values at the leaves of the expression tree will be literals:

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

instance FixE (E e) where
     fix (Lit i) = lit i
     fix _       = error "non-literal!"

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

Francesco.

On 06/05/12 13:59, Sebastien Zany wrote:
> Hi,
>
> Suppose I have the following types:
>
>  > data Expr expr = Lit Nat | Add (expr, expr)
>  > newtype Fix f = Fix {unFix :: f (Fix f)}
>
> I can construct a sample term:
>
>  > term :: Expr (Expr (Expr expr))
>  > term = Add (Lit 1, Add (Lit 2, Lit 3))
>
> But isn't quite what I need. What I really need is:
>
>  > term' :: Fix Expr
>  > term' = Fix . Add $ (Fix . Lit $ 1, Fix . Add $ (Fix . Lit $ 2, Fix .
> Lit $ 3))
>
> I feel like there's a stupidly simple way to automatically produce term'
> from term, but I'm not seeing it.
>
> Any ideas?
>
> Best,
> Sebastien
>
>
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