[klipt]

So if I put (x1, x2...) through pipes f and g, instead of calculating all the f(x)s first followed by all the g(f(x))s, it calculates g(f(x1)), then g(f(x2)), etc.

How is that order of operations different to stream fusion? Why does stream fusion require more purity than Unix pipes?

[newen]

Let's say there's a global mutable variable M (doesn't have to global, can be x1.M = M, x2.M = M, for example, but easier to think with global) which is used by and modified when f(x) or g(y) runs. Then, the order of operations would matter and so you get different results with and without stream fusion.

[klipt]

Right, but couldn't the same thing happen with Unix pipes if the components write to a global file?

You can do the same optimization Unix pipes does without language enforced purity, just with a caveat that functions sharing state might behave weirdly when fused.

[newen]

You could... I guess language designers generally avoid those types of optimizations since it can bring about unexpected results. As in, if syntactically the code is using one order of operations and semantically the code is using another order of operations, even if it's documented, lots of programmers would stumble into difficult to find bugs and be surprised by this behavior. Or worse, just get wrong results and never even find out it's wrong.