[Haskell-cafe] GADTs and Exponentiated Functors
Daniel Filonik
d.filonik at hdr.qut.edu.au
Tue Mar 8 21:34:53 UTC 2016
I have managed to pinpoint where my problems with GHC TypeLits came about. The following fails (btw. are there any guidelines for posting code on this mailing list?):
type family NFunctorF f (n :: Nat) a where
NFunctorF f 0 a = a
NFunctorF f n a = f (NFunctorF f (n-1) a)
data MkNFunctor f (n :: Nat) a where
ZF :: a -> MkNFunctor f 0 a
SF :: f (MkNFunctor f (n-1) a) -> MkNFunctor f n a
class NConvertable f (n :: Nat) where
fromNFunctor :: MkNFunctor f n a -> NFunctorF f n a
toNFunctor :: NFunctorF f n a -> MkNFunctor f n a
instance NConvertable f 0 where
fromNFunctor (ZF x) = x
toNFunctor x = ZF x
instance (Functor f, NConvertable f (n-1)) => NConvertable f n where
fromNFunctor (SF xs) = fmap fromNFunctor xs
toNFunctor xs = SF (fmap toNFunctor xs)
type NMaybe = MkNFunctor Maybe
type NList = MkNFunctor []
With error:
Couldn't match expected type `f (NFunctorF f (n - 1) a)'
with actual type `NFunctorF f n a'
Whereas this happily succeeds.
type family NFunctorF f (n :: Peano) a where
NFunctorF f Zero a = a
NFunctorF f (Succ n) a = f (NFunctorF f n a)
data MkNFunctor f (n :: Peano) a where
ZF :: a -> MkNFunctor f Zero a
SF :: f (MkNFunctor f n a) -> MkNFunctor f (Succ n) a
class NConvertable f (n :: Peano) where
fromNFunctor :: MkNFunctor f n a -> NFunctorF f n a
toNFunctor :: NFunctorF f n a -> MkNFunctor f n a
instance NConvertable f Zero where
fromNFunctor (ZF x) = x
toNFunctor x = ZF x
instance (Functor f, NConvertable f n) => NConvertable f (Succ n) where
fromNFunctor (SF xs) = fmap fromNFunctor xs
toNFunctor xs = SF (fmap toNFunctor xs)
type NMaybe = MkNFunctor Maybe
type NList = MkNFunctor []
Is there any way to fix the first version?
Cheers,
Daniel
________________________________
From: Haskell-Cafe <haskell-cafe-bounces at haskell.org> on behalf of Daniel Filonik <d.filonik at hdr.qut.edu.au>
Sent: Monday, March 7, 2016 5:53 PM
To: amindfv at gmail.com
Cc: haskell-cafe at haskell.org
Subject: Re: [Haskell-cafe] GADTs and Exponentiated Functors
Just a quick follow up to this, unless I am mistaken GHC TypeLits does not actually export constructors (Zero, Succ) for the Nat kind, does it? If it did that, of course I could just use those...
FYI, I have cleaned up the example a bit, adding some applicative magic, it now looks like:
data Person = Person { name :: String, age :: Integer, gender :: String, status :: String } deriving Show
persons = fromList' [Person {name="Alice", age=20, gender="F", status="Good"}, Person {name="Bob", age=18, gender="M", status="Good"}, Person {name="Chuck", age=16, gender="M", status="Bad"}] :: NList N1 Person
persons <$$> groupby (gender) <$$> orderby (age) <$$> select (age + 1) <$$> reduce (sum)
-- [21,36]
Or, if you are feeling more adventurous, you can do thing like:
let abg = persons <$$> groupby (gender) <$$> select (age) in ((/) <$> (abg <$$> select(realToFrac)) <***> (abg <$$> reduce(mean)))
[[1.0],[1.0588235294117647,0.9411764705882353]]
All operations select/reduce/produce/filterby/orderby/groupby work on arbitrarily nested lists, making this very composable.
Cheers,
Daniel
________________________________
From: Daniel Filonik
Sent: Monday, March 7, 2016 3:13 AM
To: amindfv at gmail.com
Cc: haskell-cafe at haskell.org
Subject: Re: [Haskell-cafe] GADTs and Exponentiated Functors
I started out using TypeLits, but I was running into problems with GHC's solver along these lines:
http://stackoverflow.com/questions/24734704/append-for-type-level-numbered-lists-with-typelits
However, I would not rule out the possibility that this was due to misuse my behalf. If you know a way to make it work, that would be exactly the kind of feedback I am looking for!
Also, I'd be curious if it is possible to write an instance of the general NFunctor for NList (which does not require explicit type annotations to work):
class NFunctor t (m :: Peano) (n :: Peano) where
pmap' :: (t (Succ m) a -> t m b) -> t (Succ n) a -> t n b
zmap' :: (t m a -> t m b) -> t n a -> t n b
smap' :: (t m a -> t (Succ m) b) -> t n a -> t (Succ n) b
Cheers,
Daniel
________________________________
From: amindfv at gmail.com <amindfv at gmail.com>
Sent: Monday, March 7, 2016 2:38 AM
To: Daniel Filonik
Cc: haskell-cafe at haskell.org
Subject: Re: [Haskell-cafe] GADTs and Exponentiated Functors
Interesting! What's the reason you redefine the Piano numbers and hide the import of the ones from GHC. TypeLits?
Tom
El 6 mar 2016, a las 07:11, Daniel Filonik <d.filonik at hdr.qut.edu.au<mailto:d.filonik at hdr.qut.edu.au>> escribió:
Hi,
I have been recently playing around with GADTs, using them to keep track of how many times a functor has been applied. This provides a solution to what seems to be a long standing problem, summarized here:
https://byorgey.wordpress.com/2007/08/16/mapping-over-a-nested-functor/
If the nesting depth is part of the type, it is possible to apply fmap automatically as needed. This allows you to write fairly elegant expressions like:
data Person = Person { name :: String, age :: Integer, gender :: String, status :: String } deriving Show
let persons = fromList' [Person {name="Alice", age=20, gender="F", status="Good"}, Person {name="Bob", age=18, gender="M", status="Good"}, Person {name="Chuck", age=16, gender="M", status="Bad"}] :: NList N1 Person
persons `select` age
-- [20,18,16]
persons `groupby` gender `select` age
-- [[20],[18,16]]
persons `groupby` gender `groupby` status `select` age
-- [[[20]],[[18],[16]]]
Note that "`select` age" works regardless of nesting depth. You can also append or remove nesting levels:
persons `groupby` gender `select` age `produce` (\x -> [0..x])
-- [[[0..20]],[[0..18],[0..16]]]
persons `groupby` gender `reduce` (sumof age)
-- [20, 34]
Would this kind of thing be of interest? The code is here:
https://github.com/filonik/nlists
Please feel free to suggest improvements.
Cheers,
Daniel
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