[Haskell-cafe] Intanciate data type

[adam vogt]

I'll add that Gautier's Prod has an inverse. When it's included, ghc can
infer the types of x in these expressions:

 \x -> (Foo x :: Foo Int a)

 \x -> (Foo x :: Foo String a)

as String and Maybe String respectively. Prod was unchanged, but the rest
becomes:

type family ProdInv a where
    ProdInv Int = String
    ProdInv a = Maybe a

data Foo e a
where

   Foo :: e ~ ProdInv (Prod e)
          => e -> Foo (Prod e) a


I also thought about using a data family instead of a pair of type
families. But then you still have two constructors.

`class ProdFD e pe | e -> pe, pe -> e` can't work:

  1. FDs don't provide coercions like TFs
  2. the two ProdFD instances are rejected -- they overlap/violate FDs


On Mon, Jul 4, 2016 at 5:31 PM, Gautier DI FOLCO <gautier.difolco at gmail.com>
wrote:

> Hello,
>
> I would say that type families should do the joke:
>
> {-# LANGUAGE TypeFamilies #-}
> {-# LANGUAGE GADTs #-}
> type family Prod a where
>   Prod String    = Int
>   Prod (Maybe a) = a
>
> data Foo e a
> where
>
>    Foo :: e -> Foo (Prod e) a
>
> Regards.
>
> 2016-07-04 22:43 GMT+02:00 Corentin Dupont <corentin.dupont at gmail.com>:
>
>> Hi all,
>> I have a data type looking like this:
>>
>> data Foo e a
>> where
>>
>>    Foo :: e →  Foo e a
>>
>> I would like to instantiate it to make it equivalent to:
>>
>> data Bar a
>> where
>>
>>    A :: String    →  Bar Int
>>    B :: Maybe a     →  Bar a
>>
>> How can I do that? With a functional dependency?
>> I probably need to change the definition of Foo.
>>
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>
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