Jon Harrop <jon@ffconsultancy.com> wrote:
> Would someone be so kind as to enlighten me (and probably a few other people!) 
> as to what these intruiging GADT things are and what they're good for? :-)

They are a (conservative) extension to Algebraic Data Types (and G=Guarded or Generalized, depending on the author). 
 The basic idea is that instead of giving names to the various constructors in a Sum type, you give explicit functions 
which become the constructors.  Furthermore, you then make type inference context-dependent: the type of each 
constructor is inferred independently, and can have different 'guards'.  

Or at least that's my quick-and-dirty impression, which definitely contains technical inaccuracies, but is roughly 
right.  To get a good introduction, why not turn to 
http://pauillac.inria.fr/~fpottier/slides/slides-msr-11-2004.pdf
for a pleasant and informative read.  The slides give references as well as example applications.

For more information:
http://research.microsoft.com/Users/simonpj/papers/gadt/gadt.ps.gz
http://citeseer.ist.psu.edu/669510.html (and several more at http://cristal.inria.fr/~simonet/publis/)
http://www.cs.bu.edu/~hwxi/academic/drafts/ATS.pdf   [tougher read...]

For interesting but serious discussions:
http://lambda-the-ultimate.org/node/view/552
http://lambda-the-ultimate.org/node/view/116
http://lambda-the-ultimate.org/node/view/290

The most convincing example I have seen is that an eval function for a statically-typed language
let rec eval e = 
   match e with 
     | Lit n -> n
     | Plus(a,b) -> (eval a) + (eval b)
     | True -> true
     | False -> false
     | And(a,b) -> (eval a) && (eval b)
     | If(t,c,a) -> if eval t then eval c else eval a
     | IfZero e' -> (eval e') = 0
is currently rejected in ML languages, but with GADTs the above can be accepted, as it can't "go wrong".

Jacques