The close family with nonlinear matching does seem simpler. Like I can comfortably read it and understand what it does reasonably well and have uniform expectations of what it means. That said, I'm open to be swayed otherwise. The On Fri, Aug 11, 2017 at 11:44 AM Richard Eisenberg wrote:

tl;dr: I like David's first version, D3835.

There is a fundamental tension in the definition of (==): Should it be reflexive or not? By "reflexive" here, I mean that (a == a) reduces to True, even if you know nothing further about a. The current definition of (==) is reflexive in this way for types of kind Type, but not for any of the other concrete instances (except the one for ()).

We can't currently have our cake and it eat, too: as David points out in this thread, (==) is either reflexive or structurally recursive. It can't do both. Possibly a solution to #4259 ( https://ghc.haskell.org/trac/ghc/ticket/4259) would allow us to have (==) that is both reflexive and structurally recursive, but I have no idea how to do it.

I agree that the current choice of implementation for (==) is inconsistent in this regard and is perhaps foolish. I have no principled argument for why it is the way it is. But I wonder if we're better off embracing the distinction between a reflexive (==) and a structurally recursive (==) and provide both, with different names. Or, we could just decide to go with the structurally recursive one, which seems to be more useful, especially as I have become much more skeptical of non-linear patterns (necessary for the reflexive (==)). In particular, I don't have a good story for how they would work in Dependent Haskell. Section 5.13.2 of my thesis ( http://cs.brynmawr.edu/~rae/papers/2016/thesis/eisenberg-thesis.pdf) contains some technical discussion of the challenges, but that section may not be digestible on its own.

The point of difference between David's two proposed changes is extensibility: that is, could someone decide to have a custom equality operator on a user-defined type? This is indeed a reasonable thing to want -- for example, you could imagine a record system that stores names of fields and their types in a type-level list, but that list should really be regarded as a set. However, worms lurk under this stone. If we have a more flexible notion of equality, how can we be sure that this more inclusive equality is always respected? Specifically, you would want this: if (ty1 == ty2) and ty1 is substituted for ty2 in some context, everything still works. Sadly, there is no way to guarantee such a property. If (==) is to be useful in a type system, we would need such a guarantee. (By "useful", I mean that this is implementable: reifyEq :: ((a == b) ~ True, Typeable a, Typeable b) => a :~: b.) This brings us to the doorstep of higher inductive types -- a door that might be fun to enter, but is a long long way off.

In sum, I argue for David's first, inextensible version.

By the way, nothing about this requires TypeInType. If I had thought of David's version (that splits apart type applications) in 2013, I probably would have implemented (==) that way.

Richard

On Aug 10, 2017, at 9:00 PM, David Feuer wrote:

I tend to agree with you, although I don't think () is a compelling argument. Rather, it reuses the name == that Haskellers are accustomed to defining flexibly. But for that same reason, as well as the convenience, I do think we should consider using a kind class. That way things at the type level look pretty much like they do at the term level.

On Aug 10, 2017 10:59 AM, "Ryan Scott" wrote:

...

Personally, I'd be more inclined towards latter approach (in https://phabricator.haskell.org/D3837). After all, one of the key properties of (==) (for which the Haddocks even make a special note) is that it does not attempt to provide an instance that works for every possible kind. Indeed, as you've discovered, there are cases when it doesn't make sense to use DefaultEq, such as for ().

I'll tentatively give my support for D3837, although I'd be curious to hear what Richard has to say about this (since I'm reasonably confident he gave (==) its current implementation).

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On Aug 11, 2017 9:39 AM, "Richard Eisenberg" wrote: But I wonder if we're better off dxaa aembracing the distinction between a reflexive (==) and a structurally recursive (==) and provide both, with different names. I don't think it would be bad to offer a canonical reflexive equality test. There are probably situations where having such a thing would be marginally useful. In particular, MyEqual a b ~ 'False isn't quite the same ass Alaska YourEqual a b ~ 'False even if the two type families are defined the same. Or, we could just decide to go with the structurally recursive one, which seems to be more useful, especially as I have become much more skeptical of non-linear patterns (necessary Aziz a a add as ad ahs asf as s for the reflexive (==)). I'm a bit fuzzy on this. Don't *both* of my versions rely essentially on nonlinear patterns to compare constructors? I suppose it might c always xd Hz In particular, I don't have a good story for how they would work in Dependent Haskell. Section 5.13.2 of my thesis (http://cs.brynmawr.edu/~rae/ papers/2016/thesis/eisenberg-thesis.pdf) contains some technical discussion of the challenges, but that section may not be digestible on its own. The point of difference between David's two proposed changes is extensibility: that is, could someone decide to have a custom equality operator on a user-defined type? This is indeed a reasonable thing to want -- for example, you could imagine a record system that stores names of fields and their types in a type-level list, but that list should really be regarded as a set. However, worms lurk under this stone. If we have a more flexible notion of equality, how can we be sure that this more inclusive equality is always respected? Specifically, you would want this: if (ty1 == ty2) and ty1 is substituted for ty2 in some context, everything still works. Sadly, there is no way to guarantee such a property. If (==) is to be useful in a type system, we would need such a guarantee. (By "useful", I mean that this is implementable: reifyEq :: ((a == b) ~ True, Typeable a, Typeable b) => a :~: b.) This brings us to the doorstep of higher inductive types -- a door that might be fun to enter, but is a long long way off. In sum, I argue for David's first, inextensible version. By the way, nothing about this requires TypeInType. If I had thought of David's version (that splits apart type applications) in 2013, I probably would have implemented (==) that way. Richard On Aug 10, 2017, at 9:00 PM, David Feuer wrote: I tend to agree with you, although I don't think () is a compelling argument. Rather, it reuses the name == that Haskellers are accustomed to defining flexibly. But for that same reason, as well as the convenience, I do think we should consider using a kind class. That way things at the type level look pretty much like they do at the term level. On Aug 10, 2017 10:59 AM, "Ryan Scott" wrote:

Personally, I'd be more inclined towards latter approach (in https://phabricator.haskell.org/D3837). After all, one of the key properties of (==) (for which the Haddocks even make a special note) is that it does not attempt to provide an instance that works for every possible kind. Indeed, as you've discovered, there are cases when it doesn't make sense to use DefaultEq, such as for ().

I'll tentatively give my support for D3837, although I'd be curious to hear what Richard has to say about this (since I'm reasonably confident he gave (==) its current implementation).

Ryan S. _______________________________________________ Libraries mailing list Libraries@haskell.org http://mail.haskell.org/cgi-bin/mailman/listinfo/libraries

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If we have a more flexible notion of equality, how can we be sure that

Wow, that email really got garbled. I was in the process of drafting it when I sent it accidentally and then went off into the mountains and forgot about it. Sorry about that! I had a few more things to say. First, it might be possible to get away from the non-linear pattern using a version of generics. In particular, if we derive Rep and From type families for each type, we can define (==) by comparing generic representations. Or we could derive (==) directly. Moreover, the non-linear pattern approach won't help us define type-level Ord; for that we need either direct or generic-mediated derivation. Related: it's a bit annoying that when the case ((f :: j -> k) (a :: j)) is rejected, we *know* that the type being matched must be a constructor, but we can't really do anything directly with that information. Second, you write this more inclusive equality is always respected?

[...] Specifically, you would want this: if (ty1 == ty2) and ty1 is substituted for ty2 in some context, everything still works.

How is this really different from the situation on the term level? User code must always take care to respect the quotient. You say (==) is only "useful" if we can produce reifyEq :: ((a == b) ~ True, Typeable a, Typeable b) => a :~: b. I'm not convinced that this is the only measure of utility, although it's an important one. That said, I suspect that the version of (==) in Data.Type.Equality should be the simple polykinded one; others would probably fit better elsewhere. Feel free to accept D3835 if you think we should just do that. On Aug 11, 2017 6:28 PM, "David Feuer" wrote: On Aug 11, 2017 9:39 AM, "Richard Eisenberg" wrote: But I wonder if we're better off dxaa aembracing the distinction between a reflexive (==) and a structurally recursive (==) and provide both, with different names. I don't think it would be bad to offer a canonical reflexive equality test. There are probably situations where having such a thing would be marginally useful. In particular, MyEqual a b ~ 'False isn't quite the same ass Alaska YourEqual a b ~ 'False even if the two type families are defined the same. Or, we could just decide to go with the structurally recursive one, which seems to be more useful, especially as I have become much more skeptical of non-linear patterns (necessary Aziz a a add as ad ahs asf as s for the reflexive (==)). I'm a bit fuzzy on this. Don't *both* of my versions rely essentially on nonlinear patterns to compare constructors? I suppose it might c always xd Hz In particular, I don't have a good story for how they would work in Dependent Haskell. Section 5.13.2 of my thesis ( http://cs.brynmawr.edu/~rae/papers/2016/thesis/eisenberg-thesis.pdf) contains some technical discussion of the challenges, but that section may not be digestible on its own. The point of difference between David's two proposed changes is extensibility: that is, could someone decide to have a custom equality operator on a user-defined type? This is indeed a reasonable thing to want -- for example, you could imagine a record system that stores names of fields and their types in a type-level list, but that list should really be regarded as a set. However, worms lurk under this stone. If we have a more flexible notion of equality, how can we be sure that this more inclusive equality is always respected? Specifically, you would want this: if (ty1 == ty2) and ty1 is substituted for ty2 in some context, everything still works. Sadly, there is no way to guarantee such a property. If (==) is to be useful in a type system, we would need such a guarantee. (By "useful", I mean that this is implementable: reifyEq :: ((a == b) ~ True, Typeable a, Typeable b) => a :~: b.) This brings us to the doorstep of higher inductive types -- a door that might be fun to enter, but is a long long way off. In sum, I argue for David's first, inextensible version. By the way, nothing about this requires TypeInType. If I had thought of David's version (that splits apart type applications) in 2013, I probably would have implemented (==) that way. Richard On Aug 10, 2017, at 9:00 PM, David Feuer wrote: I tend to agree with you, although I don't think () is a compelling argument. Rather, it reuses the name == that Haskellers are accustomed to defining flexibly. But for that same reason, as well as the convenience, I do think we should consider using a kind class. That way things at the type level look pretty much like they do at the term level. On Aug 10, 2017 10:59 AM, "Ryan Scott" wrote:

Personally, I'd be more inclined towards latter approach (in https://phabricator.haskell.org/D3837). After all, one of the key properties of (==) (for which the Haddocks even make a special note) is that it does not attempt to provide an instance that works for every possible kind. Indeed, as you've discovered, there are cases when it doesn't make sense to use DefaultEq, such as for ().

I'll tentatively give my support for D3837, although I'd be curious to hear what Richard has to say about this (since I'm reasonably confident he gave (==) its current implementation).

Ryan S. _______________________________________________ Libraries mailing list Libraries@haskell.org http://mail.haskell.org/cgi-bin/mailman/listinfo/libraries

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