You probably want to look at this:
http://wadler.blogspot.com/2008/02/data-types-la-carte.html
which refers to a paper about this exact problem.
The main types you want are:
newtype Fix a = In { out :: a (Fix a) }
data (f :+: g) x = Inl (f x) | Inr (g x)
Yes, you end up with a ton of constructors, but you can use typeclass
machinery and "smart constructors" to help with this problem; see, for
example, http://www.haskell.org/pipermail/haskell-cafe/2008-February/040098.html
With (:<:) and inj as defined by that post, you can end up with something like:
and :: (t :<: LogicalConnective) => [Fix t] -> Fix t
and ps = In (inj (And ps))
empty :: (t :<: BasicGoal) => Fix t
empty = In (inj Empty)
type Problem1 = Fix (LogicalConnective :+: BasicGoal)
test :: Problem1
test = and empty empty
-- ryan
On 4/16/08, Ron Alford
Here's the setup: I have a series of problems that use various logical connectives. The problem is that they're not all the same. So instead of creating one giant datatype (or duplicating much code), I'd like to assemble them like toy blocks.
I've boiled down an example here:
data LogicalConnective a = Not a | And [a] | Or [a]
data BasicGoal a = Atomic String [Term] | Empty | Logical (LogicalConnective a) deriving (Show, Eq)
data PreferenceGoal1 = Basic1 PreferenceGoal1 | Prefer1 PreferenceGoal1
This works OK, but PreferenceGoal1 is a dead end. I can't combine it with other connectives. So I try:
data PreferenceGoal2 a = Basic2 (PreferenceGoal2 a) | Prefer2 (PreferenceGoal2 a)
And this works fine, but seems impossible to explicitly type (ie, there is nothing to substitute for 'a' in a type declaration). Or am I wrong?
Also, it could be that this is just an ugly way to represent things (it does require a huge number of constructors). Any suggestions?
-Ron _______________________________________________ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe