On 2/6/13, Richard Eisenberg wrote:

On Feb 6, 2013, at 1:03 PM, Gabor Greif wrote:

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On 2/5/13, Richard Eisenberg wrote:

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My argument would be not to return Maybe (SameSing kparam a b) but to return Either (SameSing kparam a b) (SameSing kparam a b -> Void) or something similar. (Void is taken from the void package, but it could

I see where you want to get at and recognize the added value. I have two thoughts to add, though.

o most people are comfortable with assembling equality evidence (for example by means of the Maybe monad), but few have done this for its refutations.

o sometimes an equality proof is just what you need to proceed, which is probably a smaller data structure to be created (laziness may help here, but still allocates).

I agree with these points, and I would want a function that returns Maybe … to be available. Essentially, I want what you've written -- a general "decide" function with a "semi-decide" wrapper. Programmers can choose not to implement the "decide" function if they don't want/need to.

Yeah, it is a bit dodgy to say "decideSing = undefined", but it may become just easy to write the proof down.

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I also flipped the type arguments to Either, since 'Right' sounds like "Yep" and should signify positive evidence. I believe the ErrorT monad transformer also uses this convention.

Wholeheartedly agreed.

Cool.

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Also, why generalize the return type with SameSing? Do you have a case where you would want the equality witness type to be other than (:~:)?

This leaves open the possibility of non-constructivistic evidence (is there such a thing?). For example I could imagine an infinite Nat-like type (with different representation) where we have a refutation proof that n < m-1 and a refutation of n > m+1, and this would allow us to construct evidence for n=m. I have seen http://queuea9.wordpress.com/2012/11/05/canonize-this/ (and more recent ones).

This I'm not so sure of. I think that the evidence returned by sameSing needs to be isomorphic to (a ~ b) in some way for sameSing to be useful. While I can imagine more elaborate structures than (:~:) that can be reduced to (~), those structures then could also be reduced to (:~:). So, I think the generality remains even if you remove the associated type.

Okay, I have created a branch "type-reasoning" and pushed it to darcs.haskell.org, just try to fill in the missing stuff and feel free to create the other modules. I'll remove the type SameSing kparam :: k -> k -> * from the class by tomorrow if you haven't done it yet.

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I've thrown together a wiki page at http://hackage.haskell.org/trac/ghc/wiki/TypeLevelReasoning with Gabor's code, my code, and some of my thoughts. Please add your thoughts and any ideas into the mix!

I have commented on PropNot, suggesting alternatives.

+1 for Refuted.

Great, no change here.

To define decideSing for Nat and Symbol, I think we would need to refine eqSingNat and eqSingSymbol to become decideSingNat and decideSingSymbol, using unsafeCoerce for both branches. If Nat and Symbol were real inductive kinds under the hood, the unsafeCoerce would be unnecessary; it is essentially an optimization here.

The only thing that stops me from saying "push" is that I think there is a better organization for all of this. The ideas we're discussing here (things like the Void type) don't seem to belong in TypeLits -- it has nothing to do with literals. Time for a GHC.TypeReasoning module? Does someone have a better name?

Sounds okay. We can wiggle around on the new branch 'till we feel comfortable, but I'd like to land this on master before the v7.8 train leaves the station (i.e. the release branch is created). Cheers, Gabor

Richard

Oi José, this is a library-only issue, the branch is in libraries/base, thus somewhat tied to the 7.8 release. Cheers, Gabor On 2/7/13, José Pedro Magalhães wrote:

On Wed, Feb 6, 2013 at 7:17 PM, Gabor Greif wrote:

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On 2/6/13, Richard Eisenberg wrote:

...

The only thing that stops me from saying "push" is that I think there is a better organization for all of this. The ideas we're discussing here (things like the Void type) don't seem to belong in TypeLits -- it has nothing to do with literals. Time for a GHC.TypeReasoning module? Does someone have a better name?

Sounds okay. We can wiggle around on the new branch 'till we feel comfortable, but I'd like to land this on master before the v7.8 train leaves the station (i.e. the release branch is created).

Can you perhaps summarise exactly what needs to be added to GHC for this to work? It's not immediately clear to me why this is not just a library issue.

Thanks, Pedro

In its current state it is not tied to TypeLits, but when Richard adds his magic it probably will be. It is still an open issue where to put what, and whether a new module would be fitting. Richard surely will comment on this. I'd prefer the new instance definitions in TypeLits to avoid orphans. Thanks for your input though, this is exactly the kind of feedback we were hoping for :-) Cheers, Gabor [looks like I lost a previous version of this response, sorry if you get it twice] On 2/7/13, José Pedro Magalhães wrote:

Hey Gabor,

And why should it be part of base? Don't get me wrong, I'm not saying this is not important/useful. I'm just wondering about the reason to have it in base. Is it tied to TypeLits?

Cheers, Pedro

On Thu, Feb 7, 2013 at 2:21 PM, Gabor Greif wrote:

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Oi José,

this is a library-only issue, the branch is in libraries/base, thus somewhat tied to the 7.8 release.

Cheers,

Gabor

On 2/7/13, José Pedro Magalhães wrote:

...

On Wed, Feb 6, 2013 at 7:17 PM, Gabor Greif wrote:

...

On 2/6/13, Richard Eisenberg wrote:

...

The only thing that stops me from saying "push" is that I think there is a better organization for all of this. The ideas we're discussing here (things like the Void type) don't seem to belong in TypeLits -- it has nothing to do with literals. Time for a GHC.TypeReasoning module? Does someone have a better name?

Sounds okay. We can wiggle around on the new branch 'till we feel comfortable, but I'd like to land this on master before the v7.8 train leaves the station (i.e. the release branch is created).

Can you perhaps summarise exactly what needs to be added to GHC for this to work? It's not immediately clear to me why this is not just a library issue.

Thanks, Pedro

I've just pushed a commit to the type-reasoning branch with a strawman proposal of a reorganization of these definitions. Specifically, this commit breaks TypeLits into the following five files: - GHC.TypeEq, which contains the definitions for (:~:), Void, Refuted, etc. - GHC.Singletons, which contains the definitions about singletons in general, such as SingI and SingEquality - GHC.TypeLits.Unsafe, which contains just unsafeSingNat and unsafeSingSymbol - GHC.TypeLits.Internals, which is necessary to get GHC.TypeLits.Unsafe to have access to the right internals; this module is not exported from the 'base' package and - GHC.TypeLits, which contains the definitions specific to type-level literals. Some thoughts on this design: - First off, why is TypeEq part of GHC?? Because we wish to write eqSingNat and eqSingSym in GHC.TypeLits, and that module rightly deserves to be part of GHC. I'm quite uncomfortable with this decision, and I even created a new git repo at github.com/goldfirere/type-reasoning to hold the definitions that eventually ended up in GHC.TypeEq. (The repo has nothing in it, now.) Perhaps the best resolution is to move eqSingNat and eqSingSym out of GHC.TypeLits and into an external package, but that seems silly in a different direction. (It is fully technically feasible, as those functions don't depend on any internals.) I would love some feedback here. - Why is Singletons broken off? No strong reason here, but it seemed that the singletons-oriented definitions weren't solely related to type-level literals, so it seemed more natural this way. - Making the Unsafe module was a little more principled, because those functions really are unsafe! They are quite useful, though, and should be available somewhere. - Currently, the internals of GHC assign types like "0" the kind GHC.TypeLits.Nat, so Nat and Symbol *must* remain in the GHC.TypeLits module. Unfortunately, the plumbing around GHC.TypeLits.Unsafe want Nat and Symbol to be defined in GHC.TypeLits.Internals. So, I created a TypeLits.hs-boot file to fix the problem. This is highly unsatisfactory, and if something like what I've done here sticks around, we should change the internals of GHC to use GHC.TypeLits.Internals.Nat, getting rid of the import cycle. - I've put in the decideSing function as discussed further up in this thread. Its implementation for Nat and Symbol must use unsafeCoerce, but that shouldn't be a surprise. Unfortunately, the code doesn't compile now. This is because it needs SingI instances for, say, Sing 0. For a reason I have not explored, these instances are not available here, though they seem to be for code written outside of GHC. Iavor, any thoughts on this? Please tear any of these ideas (or my whole commit) to shreds! It really is meant to be a strawman proposal, but committing these changes seemed the best way of communicating on possible set of design decisions. Richard PS: I'm pasting much of this email to the wiki page for posterity. On Feb 7, 2013, at 10:45 AM, Iavor Diatchki wrote:

Hello,

my preference would be to build this kind of functionality (and other related features) in libraries on top of GHC.TypeLits. This modules was intended to contain only a minimal set of the constants that the compiler needs to know about, and it already may have too much in it.

On the concrete issue: orphan instances could be avoided if the type lits instances are defined in the same module as the class.

-Iavor

On Thu, Feb 7, 2013 at 6:50 AM, Gabor Greif wrote: In its current state it is not tied to TypeLits, but when Richard adds his magic it probably will be. It is still an open issue where to put what, and whether a new module would be fitting. Richard surely will comment on this. I'd prefer the new instance definitions in TypeLits to avoid orphans. Thanks for your input though, this is exactly the kind of feedback we were hoping for :-)

Cheers,

Gabor

[looks like I lost a previous version of this response, sorry if you get it twice]

On 2/7/13, José Pedro Magalhães wrote:

...

Hey Gabor,

And why should it be part of base? Don't get me wrong, I'm not saying this is not important/useful. I'm just wondering about the reason to have it in base. Is it tied to TypeLits?

Cheers, Pedro

On Thu, Feb 7, 2013 at 2:21 PM, Gabor Greif wrote:

...

Oi José,

this is a library-only issue, the branch is in libraries/base, thus somewhat tied to the 7.8 release.

Cheers,

Gabor

On 2/7/13, José Pedro Magalhães wrote:

...

On Wed, Feb 6, 2013 at 7:17 PM, Gabor Greif wrote:

...

On 2/6/13, Richard Eisenberg wrote:

...

The only thing that stops me from saying "push" is that I think there is a better organization for all of this. The ideas we're discussing here (things like the Void type) don't seem to belong in TypeLits -- it has nothing to do with literals. Time for a GHC.TypeReasoning module? Does someone have a better name?

Sounds okay. We can wiggle around on the new branch 'till we feel comfortable, but I'd like to land this on master before the v7.8 train leaves the station (i.e. the release branch is created).

Can you perhaps summarise exactly what needs to be added to GHC for this to work? It's not immediately clear to me why this is not just a library issue.

Thanks, Pedro

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Hi Richard, Thanks for pushing on this! The summary of my comments is this: I think that we should have 1 or 2 low-level (not necessarily safe) GHC modules that contain all the bits that GHC needs to know about, and move all other bits into a separate library, which is to be used by the actual users of the system. In this way, this library could evolve independently of GHC releases. Here are some more detailed comments: On Mon, Feb 11, 2013 at 6:40 PM, Richard Eisenberg wrote:

I've just pushed a commit to the type-reasoning branch with a strawman proposal of a reorganization of these definitions. Specifically, this commit breaks TypeLits into the following five files:

- GHC.TypeEq, which contains the definitions for (:~:), Void, Refuted, etc. - GHC.Singletons, which contains the definitions about singletons in general, such as SingI and SingEquality - GHC.TypeLits.Unsafe, which contains just unsafeSingNat and unsafeSingSymbol - GHC.TypeLits.Internals, which is necessary to get GHC.TypeLits.Unsafe to have access to the right internals; this module is not exported from the 'base' package and - GHC.TypeLits, which contains the definitions specific to type-level literals.

Like Simon, I think that there is no need to distinguish between TypeList.Unsafe and TypeLits.Internals.

Some thoughts on this design:

- First off, why is TypeEq part of GHC?? Because we wish to write eqSingNat and eqSingSym in GHC.TypeLits, and that module rightly deserves to be part of GHC. I'm quite uncomfortable with this decision, and I even created a new git repo at github.com/goldfirere/type-reasoning to hold the definitions that eventually ended up in GHC.TypeEq. (The repo has nothing in it, now.) Perhaps the best resolution is to move eqSingNat and eqSingSym out of GHC.TypeLits and into an external package, but that seems silly in a different direction. (It is fully technically feasible, as those functions don't depend on any internals.) I would love some feedback here.

We could move these out of GHC: they are just defined using (a safe use of) `unsafeCoerce`. They just need to know about the equality type (:~:), so I think they should be defined wherever the equality type is defined. Also, an unrelated piece of advice: try to keep down the use of type synonyms---they make libraries seem complex. For example, most programmers would understand the type 'a -> Void', but when I see `Refuted a` I have to go lookup its definition and check if there is something special about it.

- Why is Singletons broken off? No strong reason here, but it seemed that the singletons-oriented definitions weren't solely related to type-level literals, so it seemed more natural this way.

I don't think this matters too much either way, but I would look for things to remove from here and move to the programmer facing library. For example, why should `SingEquality` be there? It is important for `SingI` to be in GHC, because the instances for type-level literals are wired into GHC: it expects the class to be in GHC.TypeLits (this is why moving the class broke the instances, take a look in `compiler/prelude/TysWiredIn.lhs`, indeed, `Nat` and `Symbol` are also wired into GHC in the same module).

- Making the Unsafe module was a little more principled, because those functions really are unsafe! They are quite useful, though, and should be available somewhere.

Yes, I think that we want to export these at least for the use by the programmer facing library---it may choose not to re-export them. -Iavor On Tue, Feb 12, 2013 at 12:38 AM, Simon Peyton-Jones wrote:

- Currently, the internals of GHC assign types like "0" the kind GHC.TypeLits.Nat, so Nat and Symbol *must* remain in the GHC.TypeLits module. Unfortunately, the plumbing around GHC.TypeLits.Unsafe want Nat and Symbol to be defined in GHC.TypeLits.Internals. So, I created a TypeLits.hs-boot file to fix the problem. This is highly unsatisfactory, and if something like what I've done here sticks around, we should change the internals of GHC to use GHC.TypeLits.Internals.Nat, getting rid of the import cycle.****

** **

Let’s NOT have an hs-boot file here. Instead, change PrelNames to tell GHC where Nat and Symbol are defined. It’s ok for them to be in Internals. ****

** **

I’m also unconvinced about the distinction between “Internals” and “Unsafe”. To me the former connotes the latter. Import Internals if you know what you are doing; eg that might let you break important invariants. Import a kosher module like TypeLits if you want the Joe Programmer interface.****

** **

Simon****

** **

On 2/12/13, Richard Eisenberg wrote:

I've just pushed a commit to the type-reasoning branch with a strawman proposal of a reorganization of these definitions. Specifically, this commit breaks TypeLits into the following five files:

- GHC.TypeEq, which contains the definitions for (:~:), Void, Refuted, etc. - GHC.Singletons, which contains the definitions about singletons in general, such as SingI and SingEquality - GHC.TypeLits.Unsafe, which contains just unsafeSingNat and unsafeSingSymbol - GHC.TypeLits.Internals, which is necessary to get GHC.TypeLits.Unsafe to have access to the right internals; this module is not exported from the 'base' package and - GHC.TypeLits, which contains the definitions specific to type-level literals.

As Simon said, having GHC.TypeLits.Unsafe and GHC.TypeLits.Internals sounds like overkill, but it is similar to the other "unsafe" functionality's whereabouts. If we had an "export towards" feature then this division would make perfect sense and users could only ever include GHC.TypeLits.Unsafe, which should make their alarm bells ring. As I understand nobody should include GHC.TypeLits.Internals (other than GHC.TypeLits.Unsafe), but we cannot enforce that now. In light of this I think it is okay to have two modules.

Some thoughts on this design: - First off, why is TypeEq part of GHC?? Because we wish to write eqSingNat and eqSingSym in GHC.TypeLits, and that module rightly deserves to be part of GHC. I'm quite uncomfortable with this decision, and I even created a new git repo at github.com/goldfirere/type-reasoning to hold the definitions that eventually ended up in GHC.TypeEq. (The repo has nothing in it, now.) Perhaps the best resolution is to move eqSingNat and eqSingSym out of GHC.TypeLits and into an external package, but that seems silly in a different direction. (It is fully technically feasible, as those functions don't depend on any internals.) I would love some feedback here.

But doesn't the GHC type system need some inside knowledge of the Nat and Symbol kinds?

- Why is Singletons broken off? No strong reason here, but it seemed that the singletons-oriented definitions weren't solely related to type-level literals, so it seemed more natural this way.

I can understand this.

- Making the Unsafe module was a little more principled, because those functions really are unsafe! They are quite useful, though, and should be available somewhere. - Currently, the internals of GHC assign types like "0" the kind GHC.TypeLits.Nat, so Nat and Symbol *must* remain in the GHC.TypeLits module. Unfortunately, the plumbing around GHC.TypeLits.Unsafe want Nat and Symbol to be defined in GHC.TypeLits.Internals. So, I created a TypeLits.hs-boot file to fix the problem. This is highly unsatisfactory, and if something like what I've done here sticks around, we should change the internals of GHC to use GHC.TypeLits.Internals.Nat, getting rid of the import cycle. - I've put in the decideSing function as discussed further up in this thread. Its implementation for Nat and Symbol must use unsafeCoerce, but that shouldn't be a surprise.

Great, hope to have a look at them soon.

Unfortunately, the code doesn't compile now. This is because it needs SingI instances for, say, Sing 0. For a reason I have not explored, these instances are not available here, though they seem to be for code written outside of GHC. Iavor, any thoughts on this?

Please tear any of these ideas (or my whole commit) to shreds! It really is meant to be a strawman proposal, but committing these changes seemed the best way of communicating on possible set of design decisions.

One thing i think is pretty much important, that I haven't seen spelled out yet, is the "derive SingEquality" feature that can probably be stacked upon all of this. After all, the decidable equality should be rather mechanically derivable from any singleton definition. So overall, I like what I read here, of course the compilability should be restored, but I cannot contribute at that end. Thanks for the hard work, and cheers, Gabor

Richard

PS: I'm pasting much of this email to the wiki page for posterity.

On Feb 7, 2013, at 10:45 AM, Iavor Diatchki wrote:

...

Hello,

my preference would be to build this kind of functionality (and other related features) in libraries on top of GHC.TypeLits. This modules was intended to contain only a minimal set of the constants that the compiler needs to know about, and it already may have too much in it.

On the concrete issue: orphan instances could be avoided if the type lits instances are defined in the same module as the class.

-Iavor

On Thu, Feb 7, 2013 at 6:50 AM, Gabor Greif wrote: In its current state it is not tied to TypeLits, but when Richard adds his magic it probably will be. It is still an open issue where to put what, and whether a new module would be fitting. Richard surely will comment on this. I'd prefer the new instance definitions in TypeLits to avoid orphans. Thanks for your input though, this is exactly the kind of feedback we were hoping for :-)

Cheers,

Gabor

[looks like I lost a previous version of this response, sorry if you get it twice]

On 2/7/13, José Pedro Magalhães wrote:

...

Hey Gabor,

And why should it be part of base? Don't get me wrong, I'm not saying this is not important/useful. I'm just wondering about the reason to have it in base. Is it tied to TypeLits?

Cheers, Pedro

On Thu, Feb 7, 2013 at 2:21 PM, Gabor Greif wrote:

...

Oi José,

this is a library-only issue, the branch is in libraries/base, thus somewhat tied to the 7.8 release.

Cheers,

Gabor

On 2/7/13, José Pedro Magalhães wrote:

...

On Wed, Feb 6, 2013 at 7:17 PM, Gabor Greif wrote:

...

On 2/6/13, Richard Eisenberg wrote: > The only thing that stops me from saying "push" is that I think > there > is a > better organization for all of this. The ideas we're discussing > here (things > like the Void type) don't seem to belong in TypeLits -- it has > nothing to do > with literals. Time for a GHC.TypeReasoning module? Does someone > have a > better name?

Sounds okay. We can wiggle around on the new branch 'till we feel comfortable, but I'd like to land this on master before the v7.8 train leaves the station (i.e. the release branch is created).

Can you perhaps summarise exactly what needs to be added to GHC for this to work? It's not immediately clear to me why this is not just a library issue.

Thanks, Pedro

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