Guarded Impredicativity

[Simon Peyton Jones]

Just to amplify: we are very interested to


  *   Get some idea of whether anyone  cares about impredicativity.  If we added it to GHC, would you use it?  Have you ever bumped up Haskell’s inability to instantiate a polymorphic function at a polytype.



  *   Get some idea of whether the particular form of impredicativity described in the paper would be expressive enough for your application.

Simon

From: ghc-devs <ghc-devs-bounces at haskell.org> On Behalf Of Alejandro Serrano Mena
Sent: 28 June 2019 13:12
To: ghc-devs at haskell.org
Subject: Guarded Impredicativity

Dear all,

We are trying to bring back `ImpredicativeTypes` into GHC by using the ideas in the "Guarded Impredicative Polymorphism" paper [https://www.microsoft.com/en-us/research/publication/guarded-impredicative-polymorphism/<https://nam06.safelinks.protection.outlook.com/?url=https%3A%2F%2Fwww.microsoft.com%2Fen-us%2Fresearch%2Fpublication%2Fguarded-impredicative-polymorphism%2F&data=02%7C01%7Csimonpj%40microsoft.com%7Ca2d42d6134644b3d128a08d6fbc1e36d%7C72f988bf86f141af91ab2d7cd011db47%7C1%7C0%7C636973207496244478&sdata=o8H3dd5tLDRCGpwzsq6BMwNwYepPQgmoKsrXtLbJQdk%3D&reserved=0>].

For now I have produced a first attempt, which lives in https://gitlab.haskell.org/trupill/ghc<https://nam06.safelinks.protection.outlook.com/?url=https%3A%2F%2Fgitlab.haskell.org%2Ftrupill%2Fghc&data=02%7C01%7Csimonpj%40microsoft.com%7Ca2d42d6134644b3d128a08d6fbc1e36d%7C72f988bf86f141af91ab2d7cd011db47%7C1%7C0%7C636973207496244478&sdata=TGegIFjwdjJ7XPdmlVNY3wve385FalfVLaW1YLCiXlM%3D&reserved=0>. It would be great if those interested in impredicative polymorphism could give it a try and see whether it works as expected or not.

The main idea behing "guarded impredicativity" is that you can infer an impredicative instantiation for a type variable in a function call if you have at least one given argument where that type variable appears under a type constructor different from (->).
For example, consider the call `(\x -> x) : ids`, where `ids :: [forall a. a -> a]`. Since in the type of `(:)`, namely `forall a. a -> [a] -> [a]`, the variable `a` appears under the `[]` constructor and that second argument is given, we are allowed to instantiate `a := forall a. a -> a`. On the other hand, if we try to do `ids <> ids`, where `(<>)` is monoid concatenation with type `forall m. Monoid m => m -> m -> m`, we are forced to instantiate `m` with a not-polymorphic type because at no point the variable appears under a type constructor.

Just for reference, the best to get a working clone is to follow these steps:
> git clone --recursive https://gitlab.haskell.org/ghc/ghc<https://nam06.safelinks.protection.outlook.com/?url=https%3A%2F%2Fgitlab.haskell.org%2Fghc%2Fghc&data=02%7C01%7Csimonpj%40microsoft.com%7Ca2d42d6134644b3d128a08d6fbc1e36d%7C72f988bf86f141af91ab2d7cd011db47%7C1%7C0%7C636973207496254471&sdata=hXtR8j0th3U65DW7MvaofVW8tq7pubXUJqlyflGSBPw%3D&reserved=0> impredicative-ghc
> cd impredicative-ghc
> git remote add trupill git at gitlab.haskell.org:trupill/ghc.git<mailto:git at gitlab.haskell.org:trupill/ghc.git>
> git fetch trupill
> git checkout trupill master

Thanks very much in advance,
Alejandro

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