Re: [Haskell-cafe] How to expose if a constraint is satisfiable

On Tue, May 8, 2018 at 11:17 AM, Anthony Clayden < anthony_clayden@clear.net.nz> wrote:

On Tue, 8 May 2018 at 12:20 AM, Clinton Mead wrote:

...

Firstly, you refer to https://wiki.haskell.org/GHC/AdvancedOverlap. Unfortunately (unless I've missed something) these involve listing all the instances of parent classes. I'm trying to avoid that. Indeed if I have to explicitly list all the instances I might as well write them the normal way so I'm not sure what the point of any trickery is.

Yes that approach does need declaring instances of `ShowPred` (or in general `XXXPred`), which doubles-up the instances for `Show` (or `XXX`). That approach is making a closed world: for every type `t`, return either `True` or `False` that it has an instance for `Show`.

I'm not sure what you mean by "write them the normal way"? Just declaring `t` an instance of `Show` doesn't expose that in any way you can run type-level functions over it.

By normal way as in if I need to list every instance as "ShowPred", I might as well just scrap "ShowPred" and just write them directly as instances of "Print". i.e. instance Print Int where print = show instance Print Char where print = show Seems not much more work than: instance ShowPred Int = HTrue instance ShowPred Bool = HTrue etc so why use "ShowPred" at all?

I'm puzzled what it is you're trying to do.

I'm trying to select instances based on whether constraints are fulfilled. For example: class Join m where join :: m (m a) -> m a instance Monad m => Join m where join x = x >>= id instance Comonad m => Join m where join = extract Obviously I can't do this, but consider: class Join' m (IsSatisfied m) (IsSatisfied m) => Join m where join :: m (m a) -> m a instance Join' m (IsSatisfied m) (IsSatisfied m) => Join m where join = join' instance Monad m => Join' m Satisfied t2 where join' x = x >>= id instance Comonad m => Join' m t1 Satisfied where join' = extract instance Comonad m => Join' m Satisfied Satisfied where join' = extract If I'm in a room, I can quite correctly assert things do exist if I can see them. But I can't assert things can't exist. Asserting things don't exist would violate the open world assumption, but only asserting when they do exist should not. "IsSatisfied" only needs to assert when the constraint is satisfied, it doesn't need to assert when it isn't, so I don't think it violates the open world assumption. Also GHC has this information to give an answer to IsSatisfied, it simply has to try to solve the constraint and if it succeeds reduce it to Satisfied, and if it doesn't it just does nothing. I just need a way to entice GHC to do that.