Heterogeneous equality into base?

Edward Kmett ekmett at gmail.com
Mon Jul 10 00:31:32 UTC 2017

I for one favor the HRefl constructor name for practical reasons. These types will commonly be used in similar scopes.

Also, there is a theoretical quibble for why this shouldn't just replace :~: directly in any code that would otherwise use both and why both will be used in much the same code going forward:

Heterogenous equality is a form of what Conor McBride calls "John Major" equality. In a more general type theory, HRefl doesn't imply Refl! You can't show HRefl implies Refl in MLTT. This extra power is granted by dependent pattern matching most dependent type theories or in Haskell by the way we implement ~. In Haskell, today, it works out because we have "uniqueness of identity proofs" or "axiom K". This means that anything going on in the world of homotopy type theory today can't be used in Haskell directly as univalence and axiom k are inconsistent. 

Some work has been put into pattern matching in Agda without axiom K. Do I expect that folks are going to run out and implement it in Haskell? No, but in general I want to be very clear in my code when I rely upon this extra power that Haskell grants us kinda by accident or fiat today as those results don't transfer, and could be dangerous to assume if we decide to go in a different direction in the far flung future.


Sent from my iPad

> On Jul 9, 2017, at 5:35 PM, Oleg Grenrus <oleg.grenrus at iki.fi> wrote:
> It's not only a value, it's also a pattern. We have PatternSynonyms, but IMHO it's not a strong argument for having constructors with a same name.
> - Oleg
> Sent from my iPhone
>> On 9 Jul 2017, at 22.47, Wolfgang Jeltsch <wolfgang-it at jeltsch.info> wrote:
>> Hi!
>> I agree with you, Andrew, that types should have different names.
>> However, (H)Refl is not a type. It is a data constructor; so it is a
>> special kind of value and as such very similar to sym, trans, and
>> friends. The similarity of Refl to the ordinary functions of the
>> Heterogeneous module becomes even more obvious when considering that
>> Refl is a proof, like sym, trans, and so on.
>> All the best,
>> Wolfgang
>> Am Samstag, den 08.07.2017, 21:25 -0400 schrieb Andrew Martin:
>>> Just wanted to weigh in with my two cents. I also prefer to use the
>>> module system for the most part rather than prefixing function names
>>> with something that indicates the data type they operate on. However,
>>> when it comes to types, I would much rather they have different names.
>>> I like that the data constructor of :~~: is HRefl. However, for the
>>> functions sym, trans, etc., I would rather have a
>>> Data.Type.Equality.Hetero that exports all of these without any kind
>>> of prefixes on them. Then there's the question of where we export :~~:
>>> from. It could be exported only from the Hetero module, or it could be
>>> exported from both.
>>> Sent from my iPhone
>>>> On Jul 8, 2017, at 7:56 PM, Wolfgang Jeltsch <wolfgang-it at jeltsch.in
>>>> fo> wrote:
>>>> Hi!
>>>> Unfortunately, my wish has not been granted, as I wanted the data
>>>> constructor of (:~~:) to be named Refl and (:~~:) to be defined in a
>>>> separate module. I see that there are no heterogeneous versions of
>>>> sym,
>>>> trans, and so on in base at the moment. If they will be available at
>>>> some time, how will they be called? Will they be named hsym, htrans,
>>>> and
>>>> so on? This would be awful, in my opinion.
>>>> In Haskell, we have the module system for qualification. I very well
>>>> understand the issues Julien Moutinho pointed out. For example, you
>>>> cannot have a module that just reexports all the functions from
>>>> Data.Sequence and Data.Map, because you would get name clashes.
>>>> However, I think that the solution to these kinds of problems is to
>>>> fix
>>>> the module system. An idea would be to allow for exporting qualified
>>>> names. Then a module could import Data.Sequence and Data.Map
>>>> qualified
>>>> as Seq and Map, respectively, and export Seq.empty, Map.empty, and
>>>> so
>>>> on. 
>>>> If we try to work around those issues with the module system by
>>>> putting
>>>> qualification into the actual identifiers in the form of single
>>>> letters
>>>> (like in mappend, HRef, and so on), we will be stuck with this
>>>> workaround forever, even if the module system will be changed at
>>>> some
>>>> time, because identifiers in core libraries are typically not
>>>> changed.
>>>> Just imagine, we would have followed this practice for the
>>>> containers
>>>> package. We would have identifiers like “smap”, “munion”,
>>>> “imintersection”, and so on.
>>>> All the best,
>>>> Wolfgang
>>>> Am Freitag, den 07.07.2017, 08:15 -0700 schrieb Ryan Scott:
>>>>> Sorry for only just discovering this thread now. A lot of this
>>>>> discussion is in fact moot, since (:~~:) already is in base!
>>>>> Specifically, it's landing in Data.Type.Equality [1] in the next
>>>>> version of base (bundled with GHC 8.2). Moreover, it's constructor
>>>>> is
>>>>> named HRefl, so your wish has been granted ;)
>>>>> As for why it's being introduced in base, it ended up being useful
>>>>> for
>>>>> the new Type-indexed Typeable that's also landing in GHC 8.2. In
>>>>> particular, the eqTypeRep function [2] must return heterogeneous
>>>>> equality (:~~:), not homogeneous equality (:~:), since it's
>>>>> possible
>>>>> that you'll compare two TypeReps with different kinds.
>>>>> Ryan S.
>>>>> -----
>>>>> [1] http://git.haskell.org/ghc.git/blob/99adcc8804e91161b35ff1d0e5
>>>>> f718d18fcaa66a:/libraries/base/Data/Type/Equality.hs#l37
>>>>> [2] http://git.haskell.org/ghc.git/blob/99adcc8804e91161b35ff1d0e5
>>>>> f718d18fcaa66a:/libraries/base/Data/Typeable/Internal.hs#l311>; 
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