Sorry I screwed up. The following is indeed memoizing:
fib5 :: Int -> Integer
fib5 = \ x -> fibs !! x
where fibs = map fib [0 ..]
fib 0 = 0
fib 1 = 1
fib n = fib5 (n-2) + fib5 (n-1)
Here, the eta-expansion does not matter. But as you say, memoized_fib
below is not memoizing, since x is in scope in the where clauses, even
though they do not mention it. Thus, for each x we get "new"
definitions of fibs and fib. Yet, this is only true for -O0.
For -O1 and greater, ghc seems to see that x is not mentioned in the
where clauses and apparently lifts them out. Thus, for -O1..
memoized_fib is also memoizing. (I ran it, this time ;-) !)
Cheers,
Andreas
On 22.07.13 11:43 PM, Tom Ellis wrote:
On Mon, Jul 22, 2013 at 04:16:19PM +0200, Andreas Abel wrote:
In general, I would not trust such compiler magic, but just let-bind
anything I want memoized myself:
memoized_fib :: Int -> Integer
memoized_fib x = fibs !! x
where fibs = map fib [0..] -- lazily computed infinite list
fib 0 = 0
fib 1 = 1
fib n = memoized_fib (n-2) + memoized_fib (n-1)
The eta-expansions do not matter.
I meant to write
"Then, eta-expansions do not matter."
(In general, they do matter.)
But this is *not* memoized (run it and see!). The "eta-expansions" do
indeed matter (although I don't think they are truly eta-expasions because
of the desugaring of the where to a let).
What matters is not the let binding, but where the let binding occurs in
relation to the lambda. There's no compiler magic here, just operational
semantics.
Tom
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Andreas Abel <>< Du bist der geliebte Mensch.
Theoretical Computer Science, University of Munich
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http://www2.tcs.ifi.lmu.de/~abel/
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