After doing some pragmatic tests, it seems that neither the arrow preprocessor nor GHC's builtin one generate / optimize to the (***) combinator.

For example,

p = proc (x,y) -> do
  x' <- f <- x
  y' <- g <- y
  return (x',y')

is equivalent to

p = f *** g

But I have the impression this kind of rewrites is not being done? Is it possible to provide rewrite rules for arrows?

Since *** is a method of the arrow type class, it might have a more optimal implementation.

I haven't looked at the arrow preprocessor or GHC's code  yet, but comments are welcome, I might see things wrongly.

Cheers,
Peter