type-level definitions naming

[Richard Eisenberg]

On Oct 21, 2013, at 6:06 AM, Gábor Lehel <illissius at gmail.com> wrote:

> Unless there's some issues I'm missing, all of the `liftEq` functions could be replaced by just one:
> 
>     apply :: (f :~: g) -> (a :~: b) -> (f a :~: g b)
> 
> `lower` could be generalized:
> 
>     inner :: (f a :~: g b) -> (a :~: b)
> 
> and this could be added:
> 
>     outer :: (f a :~: g b) -> (f :~: g)
> 

I like these, and prefer them to the existing liftEqN and lower functions. These mirror more accurately what we have in Core (not that that matters much). I should also note that any similar functions are *very* easy for a user to write, so choosing just the right set of combinators is not critical.

> 
> On Mon, Oct 21, 2013 at 6:04 AM, Richard Eisenberg <eir at cis.upenn.edu> wrote:
> - There is a new function (in Data.Type.Equality) gcastWith :: (a :~: b) -> ((a ~ b) => r) -> r. Type inference for this function works well.
> 
> In my experience, for partial application it's convenient to have the arguments the other way around.

I'd be worried about type inference with partial application and reversed parameters. The values of a and b can only be gleaned from the equality witness, so I would think that delaying that parameter would cause some havoc. Is that not what you've seen?

>  
> - I've renamed EqualityT and CoercionT to EqualityType and CoercionType. The T's at the ends of the old names made me think of monad transformers. I don't like the new names, though.
> 
> No radically better ideas, but perhaps marginally: `TypeEq` and `TypeReprEq`? Or `TestEquality` and `TestCoercible`?
>   
> - EqualityType's method is now maybeEquality (instead of equalsT). CoercionType's method is now maybeCoercion (instead of coercionT).
> 
> These seem alright. I suppose they might change to track the class names, if those change.

These names are better than mine.

>  
> - An earlier version of TypeLits had Nat1 as a canonical unary natural number type and conversions to and from. I expect this will be a popular addition, so I restored it. I also added instances of Eq, Ord, Data, Typeable, Read, Show, Num, Integral, Real, Enum, and Ix, in case someone wants to use Nat1 at the term level.
> 
> It seems GHC is on a mission to obsolete my packages :-). First type-eq, now data-nat. But that's good, these things should exist in a central place.

I like your implementation of Nat much more than mine and would be happy to take your definitions wholesale, with your permission. Of course, I should have looked for such a thing before rewriting it myself! But, with all the extra functionality, it feels too big to just be shoehorned into TypeLits.

Perhaps a better solution is to remove Nat1 from TypeLits and then ask that the data-nat package add type-level conversions to and from the TypeLits Nat. Of course, that introduces some naming confusing (two things named Nat!), but there's nothing so special about Nat1 that it needs to live in base. I just thought it would be convenient.

> 
> The name `Nat1` seems a bit unfortunate. If we ever get a term-level `Natural` type to complement `Integer`, will that and the current `Nat` be different concepts (in which case with `Nat1`, there would be 3)? If they would be the same, i.e. only 2 different types, I think calling one of them `Nat` and the other `Natural` would be nice. If all 3 would be different things then I don't have better ideas.
> 
> There's a few useful auxiliary definitions (`nat`, `foldNat`, `unfoldNat`, `infinity`, `diff`) in my version which might be worth lifting:
> 
> http://hackage.haskell.org/package/data-nat-0.1.2/docs/Data-Nat.html
> 
> I also have a `Bounded` instance with `maxBound = infinity`, which I added mostly for kicks, and I'm genuinely not sure whether it meets the implicit expectations for a `Bounded` instance. `n < infinity` will be `True` for any `n` that's not `infinity`, and similarly `[n..infinity]` will be an infinite list (which seems reasonable), but any comparison involving two infinities will be bottom.
> 

Thanks for taking a look!
Richard

> 
> -- 
> Your ship was destroyed in a monadic eruption.

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