[Haskell-cafe] Is fusion overrated?

Roman Cheplyaka roma at ro-che.info
Wed May 18 07:55:21 CEST 2011

If one thinks about Haskell data structures as of ordinary data
structures, fusion seems a great deal -- instead of producing
intermediate lists and possibly running out of memory, we just run a
loop and use constant amount of space.

But Haskell data structures are quite different -- they are produced as
demanded. Consider the example from the Stream Fusion paper[1]:

    f :: Int → Int
    f n = sum [ k ∗ m | k ← [1..n], m ← [1..k ] ]

Assuming the sum is a strict left fold, it consumes elements of lists
one-by-one and runs in constant space.

The list part can be transformed to

    foldr (++) [] $ map (\k -> map (\m -> k*m) [1..k]) [1..n]

which is capable of producing elements one-by-one. So the whole thing
probably should run in constant space as well.

Of course I don't claim that fusion is useless -- just trying to
understand the problem it solves. Are we saving a few closures and cons
cells here?

[1] Stream Fusion. From Lists to Streams to Nothing at All.
    Duncan Coutts, Roman Leshchinskiy, Don Stewart.

Roman I. Cheplyaka :: http://ro-che.info/
Don't worry what people think, they don't do it very often.

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