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

[Anthony Clayden]

> It's occurred to me that one could write a class C t which is satisfied

> whenever (A t) or (B t) is satisfied like so:

Hi Clinton, this sounds like you might want "Choosing a type-class
instance based on the context"
https://wiki.haskell.org/GHC/AdvancedOverlap


> ---
>
> data Satisfied
>
> type family IsSatisfiable :: Constraint -> Type

That type family is doing the same job as auxiliary class `ShowPred`
on that wiki page.

Rather than all the machinery you give for the disjunction, you could
use another type family:

type family EitherSatisfied :: Type -> Type -> Type
instance EitherSatisfied Satisfied tb = Satisfied
instance EitherSatisfied ta Satisfied = Satisfied

Those two instances do overlap (as you expected); and they exhibit
confluence, aka coincident overlap (they produce the same result); so
that's fine.

But you haven't given any instances for `IsSatisfiable`. How do you
expect to get from the Constraint to the `Satisfied` type?

You say

> IsSatisfiable c = Satisfied -- (if c is satisfiable)

What are you going to put for `c`? If you follow that wiki page,
you'll need to in effect repeat every instance decl for classes `A,
B`:

instance A Int where ...

type instance IsSatisfiable (A Int) = Satisfied

(The wiki page was written before there were type families, so type
class `ShowPred` has a Functional Dependency giving a type-level
Boolean result.)
Your `C t` class becomes

class EitherSatisfied ( IsSatisfiable (A t)) ( IsSatisfiable (B t)) ~
Satisfied => C t where ...

----

Nowadays there's a better way: make Associated Types for the two
classes, give them a default instance:

class A t where
  type APred t
  type instance APred t = Satisfied
  ...

class B t where
  type BPred t

  type instance BPred t = Satisfied
  ...


Now every instance defined for `A, B` in effect automatically gives you
`APred, BPred` instances. Then

class EitherSatisifed (APred t) (BPred t) ~ Satisfied => C t where ...


AntC
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