[Haskell-cafe] GADTs and Exponentiated Functors

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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