[Haskell-cafe] Memoization-question

[Bulat Ziganshin]

Hello Daniel,

Thursday, December 11, 2008, 11:49:40 PM, you wrote:

sorry fo r noise, it seems that i know ghc worse than you

> Am Donnerstag, 11. Dezember 2008 21:11 schrieb Bulat Ziganshin:
>> Hello Daniel,
>>
>> Thursday, December 11, 2008, 11:09:46 PM, you wrote:
>>
>> you is almost right. but ghc don't share results of function calls
>> despite their type. it just assumes that value of any type may use a
>> lot of memory even if this type is trivial :)

> I may misunderstand you here. But if you give a type signature specifying a
> nice known type, I'm pretty sure ghc _does_ sharing (tried with Int -> Int
and Integer ->> Integer, g 200 instantaneous), at least with -O2. Without 
> sharing, it would require 2^(n+1) - 1 calls to evaluate g n, that wouldn't be
> nearly as fast. Without the type signature, it must assume the worst, so it
> doesn't share.

>>
>> example when automatic sharing is very bad idea is:
>>
>> main = print (sum[1..10^10] + sum[1..10^10])

> Depends on what is shared. Sharing the list would be a very bad idea, sharing
> sum [1 .. 10^10] would probably be a good idea.

>>
>> > Am Donnerstag, 11. Dezember 2008 16:18 schrieb Mattias Bengtsson:
>> >> The program below computes (f 27) almost instantly but if i replace the
>> >> definition of (f n) below with (f n = f (n - 1) * f (n -1)) then it
>> >> takes around 12s to terminate. I realize this is because the original
>> >> version caches results and only has to calculate, for example, (f 25)
>> >> once instead of (i guess) four times.
>> >> There is probably a good reason why this isn't caught by the compiler.
>> >> But I'm interested in why. Anyone care to explain?
>> >>
>> >> > main = print (f 27)
>> >> >
>> >> > f 0 = 1
>> >> > f n = let f' = f (n-1)
>> >> >       in f' * f'
>> >>
>> >> (compiled with ghc --make -O2)
>> >>
>> >> Mattias
>> >
>> > Not an expert, so I may be wrong.
>> > The way you wrote your function, you made it clear to the compiler that
>> > you want sharing, so it shares.
>> > With
>> >
>> > g 0 = 1
>> > g n = g (n-1)*g (n-1)
>> >
>> > it doesn't, because the type of g is Num t => t -> t, and you might call
>> > it with whatever weird Num type, for which sharing might be a bad idea
>> > (okay, for this specific function I don't see how I would define a Num
>> > type where sharing would be bad).
>> > If you give g a signature like
>>
>> g :: Int ->> Int,
>>
>> > the compiler knows that sharing is a good idea and does it (cool thing
>> > aside: with
>> > module Main where
>> >
>> > f 0 = 1
>> > f n = let a = f (n-1) in a*a
>> >
>> > main = do
>> >     print (f 27)
>> >     print (g 30)
>> >
>> > g 0 = 1
>> > g n = g (n-1)*g (n-1)
>> >
>> > main still runs instantaneously, but g n takes exponential time at the
>> > ghci prompt. That's because in main the argument of g is defaulted to
>> > Integer, so it's shared.)
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-- 
Best regards,
 Bulat                            mailto:Bulat.Ziganshin at gmail.com