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

[Daniel Fischer]

Am Dienstag 15 September 2009 23:13:59 schrieb Cristiano Paris:
> On Wed, Sep 2, 2009 at 7:16 AM, zaxis <z_axis at 163.com> wrote:
> > Isnot it clear without the 'forall' ?
> > data Branch tok st a = Branch (PermParser tok st (b -> a)) (GenParser tok
> > st b)
> >
> > thanks!
>
> I elaborated on this and I wish to add my personal way of figuring out
> what the "forall" keyword means.
>
> When you define:
>
> foo :: a -> a
>
> you are actually defining a _function for every type of a_, which can
> be read: for every a there exists a function foo which can operate on
> it (universal quantification).
>
> When you define something like:
>
> foo :: forall a. a -> a

This is exactly the same type as

foo :: a -> a

(unless you're using ScopedTypeVariables and there's a type variable a in scope), since 
type signatures are implicitly forall'd.

>
> you are actually defining a _single_ function which must work for
> every a (that's why we use the "forall" keyword). The difference is
> subtle but the direct consequences of this are: a) that one function
> can't use any information about a apart from the fact that it
> eventually belongs to the type classes specified in the context, b) in
> the case of [a] (or any other type of higher kind, * -> *, * -> * -> *
> and so on) you can mix values of different types.
>
> I hope I haven't written anything wrong :)
>
> Cristiano