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.
-Edward
Sent from my iPad
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
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 aspecial kind of value and as such very similar to sym, trans, andfriends. The similarity of Refl to the ordinary functions of theHeterogeneous module becomes even more obvious when considering thatRefl is a proof, like sym, trans, and so on.All the best,WolfgangAm 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@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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