A rarely-used GHC type system extension that allows quantifiers to appear anywhere in a type.
Questions tagged [impredicativetypes]
20 questions
59
votes
2 answers
Impredicative types vs. plain old subtyping
A friend of mine posed a seemingly innocuous Scala language question last week that I didn't have a good answer to: whether there's an easy way to declare a collection of things belonging to some common typeclass. Of course there's no first-class…
mergeconflict
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29
votes
3 answers
Why can't the type of id be specialised to (forall a. a -> a) -> (forall b. b -> b)?
Take the humble identity function in Haskell,
id :: forall a. a -> a
Given that Haskell supposedly supports impredicative polymorphism, it seems reasonable that I should be able to "restrict" id to the type (forall a. a -> a) -> (forall b. b -> b)…
Tom Crockett
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12
votes
1 answer
Why is impredicative polymorphism allowed only for functions in Haskell?
In Haskell I can't write
f :: [forall a. a -> a]
f = [id]
because
• Illegal polymorphic type: forall a. a -> a
GHC doesn't yet support impredicative polymorphism
But I can happily do
f :: (forall a. a -> a) -> (a, b) -> (a, b)
f i (x, y) = (i x,…
radrow
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12
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1 answer
Impredicative polymorphism in F#
OCaml's Hindley-Milner type system does not allow for impredicative polymorphism (à la System-F), except through a somewhat recent extension for record types. The same applies to F#.
It however is sometimes desirable to translate programs written…
David Monniaux
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12
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3 answers
Simple example for ImpredicativeTypes
The GHC user's guide describes the impredicative polymorphism extension with reference to the following example:
f :: Maybe (forall a. [a] -> [a]) -> Maybe ([Int], [Char])
f (Just g) = Just (g [3], g "hello")
f Nothing = Nothing
However, when I…
Ben Millwood
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9
votes
2 answers
Row polymorphism in Haskell: trouble writing Forth DSL with "transformations"
I've been inspired by the recent Haskell blog activity1 to try my hand at writing a Forth-like DSL in Haskell. The approach I have taken is simultaneously straightforward and confusing:
{-# LANGUAGE TypeOperators, RankNTypes, ImpredicativeTypes…
Dan Burton
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9
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2 answers
Why are higher rank types so fragile in Haskell
I was messing around with the runST function. Which has type (forall s. ST s a) -> a and it seems like trying to use it in any way that isn't directly applying without any indirection breaks it in pretty nasty ways.
runST :: (forall s. ST s a) ->…
semicolon
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8
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Why does this equivalent program not compile?
This program:
{-# LANGUAGE RankNTypes, ImpredicativeTypes #-}
import qualified Data.Vector.Mutable as MV
import qualified Data.Vector as V
import Control.Monad.ST
import Control.Monad.Primitive
unsafeModify :: [(forall s . MV.MVector s Int -> ST s…
MaiaVictor
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8
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1 answer
How does let interact with higher rank types in Haskell?
I ran in to a puzzling situation with a higher rank type. I figured out how to make it work, but I don't understand the difference between the working and non-working versions.
With these background definitions:
{-# LANGUAGE RankNTypes #-}
data…
Doug McClean
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7
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1 answer
Practical Implications of runST vs unsafePerformIO
I want something like
f :: [forall m. (Mutable v) (PrimState m) r -> m ()] -> v r -> v r -- illegal signature
f gs x = runST $ do
y <- thaw x
foldM_ (\_ g -> g y) undefined gs -- you get the idea
unsafeFreeze y
I'm essentially in the same…
crockeea
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6
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1 answer
How to non-impredicatively return `Maybe` a lens?
A type like Maybe (Lens' a b) doesn't work because Lens' is under the hood a Rank-2 type, that can't be wrapped in a type constructor without the -XImpredicativeTypes extension (which is not really supported in GHC).
What is thus the best type to…
leftaroundabout
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5
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1 answer
Why doesn't this typecheck?
This is toy-example.hs:
{-# LANGUAGE ImpredicativeTypes #-}
import Control.Arrow
data From = From (forall a. Arrow a => a Int Char -> a [Int] String)
data Fine = Fine (forall a. Arrow a => a Int Char -> a () String)
data Broken = Broken (Maybe…
dave4420
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4
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1 answer
"case" operator for System-F natural numbers coded with RankNTypes fails to typecheck
In Haskell, if one enables the RankNTypes extension
{-# Language RankNTypes #-}
then one can define the natural numbers as they are encoded in System-F:
type Nat = forall a. a -> ((a -> a) -> a)
zero :: Nat
zero = \z s -> z
succ ::…
Jonathan Gallagher
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4
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What is the relationship between polymorphism's rank and (im)predicativity?
What is the relationship between polymorphism's rank and (im)predicativity?
Can rank-1 polymorphism be either predicative or impredicative?
Can rank-k polymorphism with k > 1 be either predicative or impredicative?
My confusions come from:
Why does…
Tim
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Hold a lens in a record
I have a record MyRecord for which I create lenses with makeLenses.
I would like to have a field in that record which holds itself a lens but that is also accessible with a lens like the other fields.
This is my code to achieve this:
{-# LANGUAGE…
F. Böller
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