For someone who couldn't make head of tail of it, you are spot on.
That's just the way it works.
You ask why not have a rule for
map f (map g xs) = map (f.g) xs
Because then we'd need one for
map f (filter g xs)
and one for
map f (take n xs)
and so on and so on and so on.
The way it is now, ONE rule, the fold/build rule
deals with fusion. The others are all there to express things
in terms of fold and build, AND THEN to return certain common
patterns of usage for foldr to their familiar mapList and filterList
forms.
Does that help?
Simon
> -----Original Message-----
> From: Kevin Atkinson
> Sent: Tuesday, June 29, 1999 8:34 PM
> To: [EMAIL PROTECTED]
> Subject: Another rule guestion.
>
>
> I was looking through PrelBase.lhs and I can not make head or
> tails out
> of the point in all the run around with build, mapFB, etc. is.
>
> As I see it the simplification of "(map f. map g) l" would go as
> follows:
>
> (map f . map g) xs
>
> map f (map g xs)
>
> build$ \c n -> foldr (mapFB c f) n (map g xs)
>
> build$ \c n -> foldr (mapFB c f) n
> (build$ \c n -> foldr (mapFB c g) n xs)
>
> --with rule: foldr k z (build g) = g k z
>
> build$ \c n ->
> (\c n -> foldr (mapFB c g) n xs) (mapFB c f) n
>
> build$ \c n -> foldr (mapFB (mapFB c f) g) n xs
>
> -- with rule: mapFB (mapFB c f) g = mapFB c (f.g)
>
> build$ \c n -> foldr (mapFB c (f.g)) n xs
>
> (\c n -> foldr (mapFB c (f.g)) n xs) (:) []
>
> foldr (mapFB (:) (f.g)) [] xs
>
> -- with rule: foldr (mapFB (:) f) [] = mapList f
>
> mapList (f.g) xs
>
> which seams like a hell of a lot of work when the rule "map f
> (map g xs)
> = map (f.g) xs" should do the trick.
>
> I am sure all this run-around is here for a good reason, but
> what is it?
> I am also sure that understanding what all this run-around does is the
> key to understanding why the rule "replaceMany (map f l) a =
> replaceManyMap f l" is not behaving as expected.
>
> Thanks in advance for any help with this. I can see how the rule
> rewriting mechanism can be very powerful; however, it is not
> very useful
> if I can't figure out how it works...
> --
> Kevin Atkinson
> [EMAIL PROTECTED]
> http://metalab.unc.edu/kevina/
>
