On 5/7/12 8:55 PM, Sebastien Zany wrote:
To slightly alter the question, is there a way to define a class
class (Functor f) => Fixpoint f x where
...
You can just do that (with MPTCs enabled). Though the usability will be
much better if you use fundeps or associated types in order to constrain
the relation between fs and xs. E.g.:
-- All the following require the laws:
-- > fix . unfix == id
-- > unfix . fix == id
-- With MPTCs and fundeps:
class (Functor f) => Fixpoint f x | f -> x where
fix :: f x -> x
unfix :: x -> f x
class (Functor f) => Fixpoint f x | x -> f where
fix :: f x -> x
unfix :: x -> f x
class (Functor f) => Fixpoint f x | f -> x, x -> f where
fix :: f x -> x
unfix :: x -> f x
-- With associated types:
-- (Add a type/data family if you want both Fix and Pre.)
class (Functor f) => Fixpoint f where
type Fix f :: *
fix :: f (Fix f) -> Fix f
unfix :: Fix f -> f (Fix f)
class (Functor f) => Fixpoint f where
data Fix f :: *
fix :: f (Fix f) -> Fix f
unfix :: Fix f -> f (Fix f)
class (Functor (Pre x)) => Fixpoint x where
type Pre x :: * -> *
fix :: Pre x x -> x
unfix :: x -> Pre x x
class (Functor (Pre x)) => Fixpoint x where
data Pre x :: * -> *
fix :: Pre x x -> x
unfix :: x -> Pre x x
Indeed, that last one is already provided in the fixpoint[1] package,
though the names are slightly different. The differences between using
"x -> f", "f -> x", or both, and between using "data" or "type", are how
it affects inference. That is, implicitly there are two relations on types:
Fix \subseteq * \cross *
Pre \subseteq * \cross *
And we need to know: (1) are these relations functional or not? And, (2)
are they injective or not? The answers to those questions will affect
how you can infer one of the types (f or x) given the other (x or f).
[1] http://hackage.haskell.org/package/fixpoint
--
Live well,
~wren
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