[Haskell-cafe] memorize function with number parameterized types in GHC

[oleg at okmij.org]

Bin Jin wrote:

> Here is a function that will be called everytime by `(*)` in `Num` typeclass
> > montgKeys :: (PostiveN p, Integral a, Bits a) => p -> a
>
> as you can imagine, I always pass (undefined :: p) as parameter to
> `montgKeys`, so if it's handled well, it should be memorized for
> future usage. But tracing shows that both `p2num` and `montgKeys` are
> evaluated every time being called.

First of all, let us get rid of the argument p. Let's define

> newtype W p a = W{unW:: a}

then we can easily re-write montgKeys to give it the following signature:

> > montgKeys :: (PostiveN p, Integral a, Bits a) => W p a

You can use ScopedTypevariables to set the needed 'p' from the context. 

So, montgKeys becomes a polymorphic constant, quite like minBound.
Now, the hope is that when the types p and a are determined, GHC could
specialize montgKeys and turn it into a real constant. Perhaps some
RULE or specialize pragmas may help...