[Haskell-cafe] How to understand the 'forall' ?

[Ryan Ingram]

On Thu, Sep 17, 2009 at 6:59 AM, Cristiano Paris <frodo at theshire.org> wrote:

> On Thu, Sep 17, 2009 at 8:36 AM, Ryan Ingram <ryani.spam at gmail.com> wrote:
> > ...
> > Explicitly:
> >
> > Haskell:
> >> test1 :: forall a. a -> Int
> >> test1 _ = 1
> >> test2 :: (forall a. a) -> Int
> >> test2 x = x
> >
> > explicitly in System F:
> >
> > test1 = /\a \(x :: a). 1
> > test2 = \(x :: forall a. a). x @Int
> >
> > /\ is type-level lambda, and @ is type-level application.
>
> Ok. But let me be pedantic: where is the universal quantification in
> test1? It seems to me the a is a free variable in test1 while being
> closed under universal quantification in test2.
>

The universal quantification is right in the extra lambda: it works for all
types "a".

Just like this works on all lists [a]:

length = /\a. \(xs :: [a]). case xs of { [] -> 0 ; (x:ys) -> 1 + length @a
ys }

Here are some uses of test1:

v1 = test1 @Int 0
v2 = test1 @[Char] "hello"
v3 = test1 @() ()

Here's a use of test2:

v4 = test2 (/\a. error @a "broken")

given error :: forall a. String -> a

  -- ryan
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