Haskell @kbin.social bss03 @infosec.pub 1y ago

Defeating Return Type Polymorphism

philipphagenlocher.de Defeating Return Type Polymorphism

This post is an exploration of a generic technique to effectively circumvent return type polymorphism in Haskell programs using GADTs and existential quantification.

This was already featured in the Weekly News a couple of weeks back, but I think maybe it deserves it's own thread. I've tried to explain this approach to some people before, but I think this article does a much better job than I have.

I do think the "Defeating" in the title might be a little bit negative, it's have preferred something neutral like "When your result type depends on your argument values", but it's still something useful to know from retaining your type safety.

This existentials and GADTs can be converted into a CPS style without type equality constraints (usually, with enough work) so that you can start from this description but use it in languages with less sophisticated type systems -- as long as they have parametricity -- like Haskell 2010.

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This gives a nice practical motivation for GADTs and existential quantification.

This existentials and GADTs can be converted into a CPS style without type equality constraints

That sounds interesting. I can't easily imagine what that would look like. Do you have an example?

@jaror @bss03 Maybe I was wrong, but I think you can do Scott encoding of the GADT underneath the standard codensity representation of existentials via CPS. Still need higher-rank types, not "just" parametricity.

I should write up some code to check myself against GHC.

I put this together this evening.

{-# language GADTs #-}
{-# language RankNTypes #-}

import Data.Functor.Const

-- The GADT
data AGADT a where
    I :: [Integer] -> AGADT Integer
    S :: String -> AGADT String

type Scott_GADT a = forall fr. ([Integer] -> fr Integer) -> (String -> fr String) -> fr a

f :: AGADT a -> String
f (I x) = show x
f (S x) = x

f' :: Scott_GADT a -> String
f' x = getConst $ x (Const . show) Const

-- The Existential
data AnyGADT = forall a. MkAnyGADT (AGADT a)

type Scott_Any =
  forall r.
    (forall a. (forall fr. ([Integer] -> fr Integer) -> (String -> fr String) -> fr a) -> r) ->
    r

g :: String -> AnyGADT
g "foo" = MkAnyGADT (I [42])
g "bar" = MkAnyGADT (I [69])
g x = MkAnyGADT (S x)

g' :: String -> Scott_Any
g' "foo" x = x (\i _s -> i [42])
g' "bar" x = x (\i _s -> i [69])
g' s x = x (\_i s' -> s' s)

main = interact (unlines . fmap x . lines)
 where
  x s = case g s of { MkAnyGADT x -> f x }
  y s = g' s f'

You can swap out x for y to see the behavior is the same.

You can drop the GADT pragma, GADT definition, f, existential, g, and x (but keep all the Scott versions, includeing y) to reveal code that works "simply" with RankNTypes.

Higher-rank types and parametricity is quite powerful.

BTW, this isn't new / doesn't require the bleeding edge compiler. I'm on "The Glorious Glasgow Haskell Compilation System, version 9.0.2" from the Debian repositories.

Ah, that's interesting. Although I can imagine not many people would want to write code in that style. And I also wonder how many languages support higher rank polymorphism in the first place.

The Lemmy->Kbin conversion has inserted a lot of <span> elements into your code making it unreadable. For people reading this from the Kbin side, here's the code:

{-# language GADTs #-}
{-# language RankNTypes #-}

import Data.Functor.Const

-- The GADT
data AGADT a where
    I :: [Integer] -> AGADT Integer
    S :: String -> AGADT String

type Scott_GADT a = forall fr. ([Integer] -> fr Integer) -> (String -> fr String) -> fr a

f :: AGADT a -> String
f (I x) = show x
f (S x) = x

f' :: Scott_GADT a -> String
f' x = getConst $ x (Const . show) Const

-- The Existential
data AnyGADT = forall a. MkAnyGADT (AGADT a)

type Scott_Any =
  forall r.
    (forall a. (forall fr. ([Integer] -> fr Integer) -> (String -> fr String) -> fr a) -> r) ->
    r

g :: String -> AnyGADT
g "foo" = MkAnyGADT (I [42])
g "bar" = MkAnyGADT (I [69])
g x = MkAnyGADT (S x)

g' :: String -> Scott_Any
g' "foo" x = x (\i _s -> i [42])
g' "bar" x = x (\i _s -> i [69])
g' s x = x (\_i s' -> s' s)

main = interact (unlines . fmap x . lines)
 where
  x s = case g s of { MkAnyGADT x -> f x }
  y s = g' s f'

```</span>

This is probably a stupid question, but what does this trickery with GADTs and Existential Types give compared to the "normal" way?

import Data.Int (Int8, Int16) import Data.ByteString (ByteString) data ParsedImage = ParsedAs8 (Int, Int, [Int8]) | ParsedAs16 (Int, Int, [Int16]) deriving Show parseImage :: ByteString -> ParsedImage parseImage = undefined imageDimensions :: ByteString -> (Int, Int) imageDimensions str = case parseImage str of ParsedAs8 (w, h, _) -> (w, h) ParsedAs16 (w, h, _) -> (w, h)

Basically, the same way as a function can return an Either and everyone is happy to pattern-match on the result.
- The GADT allows some constructors to be safely unhandled when the type parameter is known.
  
  The consuming a ParsedImage, you always have to deal with both constructors. When consuming a Image px or an AnyImage, you also have to deal with both Image constructors. When consuming a Image Pixel8Bit the type system proves that it couldn't be constructed with the Image16Bit constructor, so you only have to deal with the Image8Bit constructor.
  
  HTH
  
  But how? Parsing function can return any of the types, we don't know what was in the bytestring. So we'd need to deal with all variations in any case, no?
  
  Is the difference in that it becomes possible to pattern-match on a type of an element inside the structure, rather than on the structure as a whole? So as long as you don't need that element, you can access elements that are common without pattern-matching? I guess it's a marginal benefit...
  
  Or do I still misunderstand?

12 comments