[Haskell-cafe] Properties of optimizer rule application?

[Henning Thielemann]

Reading various papers and the Wiki about GHC optimizer rules I got the
impression that there are not much properties I can rely on and I wonder
how I can write a reliable fusion framework with this constraint.
 I read about the strategy to replace functions early by fusable
implementations and replace them back to fast low-level implementation if
fusion was not possible. However, can I rely on the back-translation if I
have no warranty that the corresponding rule is applied? Is there some
warranty that rules are applied as long as applicable rules are available
or is the optimizer free to decide that it worked enough for today?
 I see several phases with a fixed number of iterations in the output of
-ddump-simpl-iterations. Is there some idea behind these phases or is the
structure and number rather arbitrary? If there is only a fixed number of
simplifier runs, how can I rely on complete fusion of arbitrary large
expressions?
 At some place I read that the order of application of rules is arbitrary.
I like to have some warranty that more special rules are applied before
more general rules. That is, if rule X is applicable whereever Y is
applicable then Y shall be tried before X. This is currently not assured,
right?
 Another text passage tells that the simplification is inside-out
expressions. Such a direction would make the design of rules definitely
easier. Having both directions, maybe alternating in the runs of the
simplifier, would be also nice. I could then design transforms of the
kind:
   toFastStructure . slowA . slowB . slowC . slowWithNoFastCounterpart
   fastA . toFastStructure . slowB . slowC . slowWithNoFastCounterpart
   fastA . fastB . toFastStructure . slowC . slowWithNoFastCounterpart
   fastA . fastB . fastC . toFastStructure . slowWithNoFastCounterpart
   fastA . fastBC . toFastStructure . slowWithNoFastCounterpart
   fastABC . toFastStructure . slowWithNoFastCounterpart

 On the one hand the inner of functions may not be available to fusion, if
the INLINE pragma is omitted. As far as I know inlining may take place
also without the INLINE pragma, but I have no warranty. Can I rely on
functions being inlined with INLINE pragma? Somewhere I read that
functions are not inlined if there is still an applicable rule that uses
the function on the left-hand side. Altogether I'm uncertain how inlining
is interleaved with rule application. It was said, that rules are just
alternative function definitions. In this sense a function definition with
INLINE is a more aggressively used simplifier rule, right?
 On the other hand if I set the INLINE pragma then the inner of the
function is not fused. If this would be the case, I could guide the
optimizer to fuse several sub-expressions before others. Say,
  doubleMap f g = map f . map g
 could be fused to
  doubleMap f g = map (f . g)
 and then this fused version can be fused further in the context of the
caller. The current situation seems to be that {-# INLINE doubleMap #-}
switches off local fusion and allows global fusion, whereas omitting the
INLINE pragma switches on local fusion and disallows global fusion. How
can I have both of them?