> Yipes! Ok, so I'm missing some typing subtlety. Why does this end up with a 
> single polymorphic type:
> 
> # let map_2 m g f x = m g (m f x);;
> val map_2 : ('a -> 'b -> 'b) -> 'a -> 'a -> 'b -> 'b = <fun>

You want it to have type

(forall 'a 'b 'f. ('a -> 'b) -> ('a 'f -> 'b 'f))
   -> ('b -> 'c) 
   -> ('a -> 'b) 
   -> 'a 'f 
   -> 'b 'f

but OCaml doesn't allow nested quantifiers (i.e., higher-rank
polymorphism).

It actually wouldn't be very hard to support, if you're prepared to
accept the need for the occasional type annotation - see
http://research.microsoft.com/~simonpj/papers/putting/index.htm.

--KW 8-)

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