Henning Thielemann wrote:
To give a precise example: If I have a sequence of 'map's
map f0 . map f1 . ... . map fn
then there is some length where this is no longer collapsed to a single
'map'?
No. After applying a rule, the simplifier optimises the result of the
rewriting. This means that with (map f (map g x) = map (f . g) x),
map f (map g (map h xs))
is first rewritten to
map (f . g) (map h xs)
and the immediately to
map (f . g . h) xs
Rewriting does not shift the "focus" of the simplifier.
project . project . foo
with the rules
project (project x) = project x
project (foo x) = projectFoo x
Both rules can be applied to the expression, but you get one fusion more,
if you use the first one first. Let me guess, in order to solve that, I
should restrict the first rule to an earlier phase than the second rule.
That's one possibility. It would be vastly preferable, however, to add
the rule
project (projectFoo x) = projectFoo x
In general, you want your rewrite system to be confluent. I suspect that
non-confluence always indicates a design problem. This is within one
set of rules, of course - explicitly staged things like "rewriting back"
of stuff which didn't fuse are different.
Roman
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