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2021-06-18 07:05:38 <dminuoso> I have a tree in which each branch (top-to-bottom) alternates between "NwD" and "UsDC". Is there a reasonable way to encode this ontop of a plain rose tree?
2021-06-18 07:06:24 ← Franciman parts (~francesco@openglass.it) (WeeChat 3.0.1)
2021-06-18 07:06:32 <dminuoso> I almost feel like this should be encodable as a fixed point type, but I cant figure out how
2021-06-18 07:06:54 <dminuoso> (i.e. the children of NwD must be UsDC, and the children of UsDC must be NwD)
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2021-06-18 07:20:17 <hololeap> dminuoso: I don't see a way to do that, unless you want to get into type families and a type-level tag
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2021-06-18 07:26:32 <hololeap> even then, it doesn't seem reasonable
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2021-06-18 07:30:20 <kuribas> it's easy if you don't want to enforce the invariant
2021-06-18 07:30:39 <dminuoso> Sure, I can just encode it as `Tree (Either NwD UsDC)` then.
2021-06-18 07:31:07 <hololeap> the mutually-recursive method seems best to me
2021-06-18 07:31:36 <dminuoso> hololeap: Yeah I began to suspect as much.
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2021-06-18 07:33:25 <kuribas> otherwise not possible. You want to constrain the types on value level, which implies some kind of dependent types.
2021-06-18 07:35:47 <hololeap> it might be possible with a GADT holding a type level list of tags and some kind of constraint that makes sure it's in the proper order, but that's way too much complexity
2021-06-18 07:36:45 tomsmeding thinks of a red-black tree
2021-06-18 07:37:47 <dminuoso> tomsmeding: Without the balancing. ;)
2021-06-18 07:37:51 <kuribas> hololeap: how can a GADT check value level information? The "levels" information is not available on type level.
2021-06-18 07:37:52 <tomsmeding> :p
2021-06-18 07:38:01 → chele joins (~chele@user/chele)
2021-06-18 07:39:15 <dminuoso> hololeap: Mmm, what about a non-regular data type?
2021-06-18 07:39:23 <dminuoso> Naively something like:
2021-06-18 07:39:31 <kuribas> perhaps it could have worked if the tree was in recursion-scheme style.
2021-06-18 07:40:36 <dminuoso> data Tree n a = Node a [Tree (Succ n) a]
2021-06-18 07:41:13 <kuribas> data Tree a b = Node { rootLabel :: a, subForest :: [b a] }
2021-06-18 07:41:14 <dminuoso> Or rather a type family that just flips between lifted 'L and 'R `data D = L | R`
2021-06-18 07:41:41 <dminuoso> kuribas: that's what I was wondering about initially
2021-06-18 07:42:03 <dminuoso> but this is not trivial recursion anymore
2021-06-18 07:43:23 <tomsmeding> note that for `type family Flip d where Flip 'L = 'R ; Flip 'R = 'L` GHC cannot prove that `Flip (Flip d) ~ d`
2021-06-18 07:44:33 <tomsmeding> re fixed point type: yes if you take the fixed point of `data Node2 f = Node2 NwD [(UsDC, [f])]` :p
2021-06-18 07:44:44 <dminuoso> tomsmeding: Mmm, I guess Id need an SMT plugged into the type checker for that?
2021-06-18 07:44:51 <dminuoso> *SMT solver
2021-06-18 07:45:13 <tomsmeding> or `believeme :: Flip (Flip d) :~: d ; believeme = unsafeCoerce Refl` ;)
2021-06-18 07:45:19 <tomsmeding> which is what I did
2021-06-18 07:45:28 <dminuoso> tomsmeding: interesting, re Node2: I think I can actually do that!
2021-06-18 07:45:39 <dminuoso> Each tree ends with UsDC, so this seems even better.
2021-06-18 07:45:46 <tomsmeding> it's a kind of weird representation of such a tree though, in my opinion
2021-06-18 07:45:48 <tomsmeding> but it works
2021-06-18 07:46:00 → hughjfchen joins (~hughjfche@vmi556545.contaboserver.net)
2021-06-18 07:46:00 <hololeap> kuribas: it wouldn't be checking value level info. it would be pushing the NwD and UsDC tags to the type level, which would mean that you would be checking a tree of tags to ensure proper order using a type family and a constraint. it would be ugly
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2021-06-18 07:46:55 <kuribas> dminuoso: newtype Even a = Even (Tree Odd a); newtype Odd a = Odd (Tree Even a);
2021-06-18 07:48:43 <kuribas> dminuoso: not sure what you get out of this though...
2021-06-18 07:48:49 <dminuoso> Yeah that's what hololeap suggested with a mutually recursive data type
2021-06-18 07:49:13 <kuribas> but this requires a functorial encoding
2021-06-18 07:49:27 <dminuoso> Though tomsmeding's encoding that cute advantage of being uniform as well as guaranteeding that each branch ends with UsDC (a condition I didnt mention because it didnt occur to me to encode this too)
2021-06-18 07:49:44 <dminuoso> guaranteeding.
2021-06-18 07:49:44 <tomsmeding> yeah I would go either with the plain, simple, mutually recursive approach, or if I really wanted the node constructor to be the same always, perhaps use that Succ trick with a type family that defines the tag on each level (and even whether the tree can terminate there)
2021-06-18 07:49:57 <tomsmeding> yes
2021-06-18 07:50:06 <kuribas> simple is always better IMO
2021-06-18 07:50:37 <tomsmeding> you can also encode the ends-with-UsDC requirement using the simple mutually recursive approach
2021-06-18 07:50:44 × ukari quits (~ukari@user/ukari) (Remote host closed the connection)
2021-06-18 07:50:56 <hololeap> well, not exactly. I was suggesting `data Even a = Even a [Odd a]` and `data Odd a = Odd a [Even a]`
2021-06-18 07:51:08 <tomsmeding> data A = A NwD (NonEmpty B) ; data B = B UsDC [A]
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