Eugene Kirpichov wrote:
In the last couple of days I completed my quest of making my graphing
utility timeplot ( http://jkff.info/software/timeplotters ) not load the
whole input dataset into memory and consequently be able to deal with
datasets of any size, provided however that the amount of data to *draw* is
not so large. On the go it also got a huge speedup - previously visualizing
a cluster activity dataset with a million events took around 15 minutes and
a gig of memory, now it takes 20 seconds and 6 Mb max residence.
(I haven't yet uploaded to hackage as I have to give it a bit more testing)
The refactoring involved a number of interesting programming patterns that
I'd like to share with you and ask for feedback - perhaps something can be
simplified.
The source is at http://github.com/jkff/timeplot
The datatype of incremental computations is at
https://github.com/jkff/timeplot/blob/master/Tools/TimePlot/Incremental.hs .
Strictness is extremely important here - the last memory leak I eliminated
was lack of bang patterns in teeSummary.
Your StreamSummary type has a really nice interpretation: it's a
reification of case expressions.
For instance, consider the following simple function from lists to integers
length :: [a] -> Int
length xs = case xs of
[] -> 0
(y:ys) -> 1 + length ys
We want to reify the case expression as constructor of a data type. What
type should it have? Well, a case expression maps a list xs to a
result, here of type Int, via two cases: the first case gives a result
and the other maps a value of type a to a function from lists to
results again. This explanation was probably confusing, so I'll just go
ahead and define a data type that represents functions from lists [a]
to some result of type r
data ListTo a r = CaseOf r (a -> ListTo a r)
interpret :: ListTo a r -> ([a] -> r)
interpret (CaseOf nil cons) xs =
case xs of
[] -> nil
(y:ys) -> interpret (cons y) ys
As you can see, we are just mapping each CaseOf constructor back to a
built-in case expression.
Likewise, each function from lists can be represented in terms of our
new data type: simply replace all built-in case expressions with the new
constructor
length' :: ListTo a Int
length' = CaseOf
(0)
(\x -> fmap (1+) length')
length = interpret length'
The CaseOf may look a bit weird, but it's really just a straightforward
translation of the case expression you would use to define the function
go instead.
Ok, this length function is really inefficient because it builds a huge
expression of the form (1+(1+...)). Let's implement a strict variant
instead
lengthL :: ListTo a Int
lengthL = go 0
where
go !n = CaseOf (n) (\x -> go (n+1))
While we're at it, let's translate two more list functions
foldL' :: (b -> a -> b) -> b -> ListTo a b
foldL' f b = Case b (\a -> foldL' f $! f b a)
sumL :: ListTo Int Int
sumL = foldL' (\b a -> a+b) 0
And now we can go for the point of this message: unlike ordinary
functions from lists, we can compose these in lock-step! In particular,
the following applicative instance
instance Applicative (ListTo a) where
pure b = CaseOf b (const $ pure b)
(CaseOf f fs) <*> (CaseOf x xs) =
CaseOf (f x) (\a -> fs a <*> xs a)
allows us to write a function
average :: ListTo Int Double
average = divide <$> sumL <*> lengthL
where
divide a b = fromIntegral a / fromIntegral b
that runs in constant space! Why does this work? Well, since we can now
inspect case expressions, we can choose to evaluate them in lock-step,
essentially computing sum and length with just one pass over the
input list. Remember that the original definition
average xs = sum xs / length xs
has a space leak because the input list xs is being shared.
Remarks:
1. Reified case expressions are, of course, the same thing as Iteratees,
modulo chunking and weird naming.
2. My point is topped by scathing irony: if Haskell had a form of
*partial evaluation*, we could write applicative combinators for
*ordinary* functions [a] -> r and express average in constant space.
In other words, partial evaluation would make it unnecessary to reify
case expressions for the purpose of controlling performance / space leaks.
Best regards,
Heinrich Apfelmus
--
http://apfelmus.nfshost.com
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