I&#39;m beginning to understand how the `forall` keyword is used in so-called &quot;existential types&quot; like this:

    data ShowBox = forall s. Show s =&gt; SB s

This is only a subset, however, of how `forall` is used and I simply cannot wrap my mind around its use in things like this:

    runST :: forall a. (forall s. ST s a) -&gt; a

Or explaining why these are different:

    foo :: (forall a. a -&gt; a) -&gt; (Char, Bool)
    bar :: forall a. ((a -&gt; a) -&gt; (Char, Bool))

Or the whole `RankNTypes` stuff...

I tend to prefer clear, jargon-free English rather than the kinds of language which are normal in academic environments.  Most of the explanations I attempt to read on this (the ones I can find through search engines) have these problems:

 1. They&#39;re incomplete.  They explain one part of the use of this keyword (like &quot;existential types&quot;) which makes me feel happy until I read code that uses it in a completely different way (like `runST`, `foo` and `bar` above).
 2. They&#39;re densely packed with assumptions that I&#39;ve read the latest in whatever branch of discrete math, category theory or abstract algebra is popular this week.  (If I never read the words &quot;consult the paper *whatever* for details of implementation&quot; again, it will be too soon.)
 3. They&#39;re written in ways that frequently turn even simple concepts into tortuously twisted and fractured grammar and semantics.

So...

On to the actual question.  Can anybody completely explain the `forall` keyword in clear, plain English (or, if it exists somewhere, point to such a clear explanation which I&#39;ve missed) that doesn&#39;t assume I&#39;m a mathematician steeped in the jargon?

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*Edited to add:*

There were two stand-out answers from the higher-quality ones below, but unfortunately I can only choose one as best.  [Norman&#39;s answer](https://stackoverflow.com/questions/3071136/what-does-the-forall-keyword-in-haskell-ghc-do/3071365#3071365) was detailed and useful, explaining things in a way that showed some of the theoretical underpinnings of `forall` and at the same time showing me some of the practical implications of it.  [yairchu&#39;s answer](https://stackoverflow.com/questions/3071136/what-does-the-forall-keyword-in-haskell-ghc-do/3071932#3071932) covered an area nobody else mentioned (scoped type variables) and illustrated all of the concepts with code and a GHCi session.  Were it possible to select both as best, I would.  Unfortunately I can&#39;t and, after looking over both answers closely, I&#39;ve decided that yairchu&#39;s slightly edges out Norman&#39;s because of the illustrative code and attached explanation.  This is a bit unfair, however, because really I needed both answers to understand this to the point that `forall` doesn&#39;t leave me with a faint sense of dread when I see it in a type signature.

All Forall Solutions on Gang of Coders

Total of 1 Forall Solutions

What does the `forall` keyword in Haskell/GHC do?