Re: TypeLits and type families wrt. equality

On 7/27/15, Richard Eisenberg wrote:

On Jul 27, 2015, at 10:36 AM, Gabor Greif wrote:

...

When saying "Big Deal" did you mean - highly desirable and somebody should go for it - or a terrible amount of work, and who tackles it is probably a fool on a hubris trip?

(I still have my problems deciphering British irony.)

My use of Big Deal here is more your second option, but without so much negativity. :) I'm sure the person who tackled this problem would learn a ton and contribute to programming language research. It's just that we haven't yet found a great motivation for doing so.

Okay, agreed.

...

I guess a full-blown solution is too much work for now (also considering previous comments from Richard). But what about a simpler construct

decideRefl :: Proxy (a :: Symbol) -> Proxy b -> Proxy (Equal a b :~: 'False) -> Either (Equal a b :~: 'False) (a :~: b)

I believe that this function could be written only with the help of unsafeCoerce. Indeed, the `singletons` package provides an `SDecide` instance for the type-lits (which accomplishes a similar, though not identical, goal) via unsafeCoerce.

I doubt it could even be written with unsafeCoerce. It would need some magic sauce from the compiler, tapping into the type family normalizer. Consider:

decideRefl (Proxy :: Proxy "a") (Proxy :: Proxy "b") (Proxy :: Proxy (Equal a b :~: 'True)

This should give a type error (we shouldn't fabricate false evidence!), while

decideRefl (Proxy :: Proxy "a") (Proxy :: Proxy "b") (Proxy :: Proxy (Equal a b :~: 'False)

should pass the type checker and give Left Refl. Cheers, Gabor

Richard