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> As I said, HVM spawns threads on to-be-evaluated redexes closes to the root of the program's normal form. So, either there is a significant speedup, or the program is sequential (or too small), and there is no speedup, but the overhead is minuscule, since a bounded, small amount of spawn() occurs.

To me that sounds like overhead. Rather than just computing 1 + 1 as a single assembly language instruction you’re sending the 1 + 1 expression tree to a thread’s work queue or something? If I’m misunderstanding can you clarify?

> Compiling a function in isolation is fine, why wouldn't it be? Not sure I get it.

It seems like optimal evaluation is a whole program optimization - you need the whole program available in order to do it, you can’t just compile one function to assembly language in isolation, and then link that against other precompiled functions. Do I have the wrong idea here?

> Just because I used integers as an example, which happens to be optimized, it means an entire optimization technique isn't interesting? This applies to every data structure that can be defined algebraically.

I do think it sounds cool as I said, but I want to see it on an example I care about, not Peano arithmetic. Especially since deforestation is already an optimization that is used by languages that don’t do optimal evaluation. So I want to see how HVM does it better, if that’s the case. And not just you telling me how it’s theoretically better. :)

Lastly, a while ago I remember you mentioning that you couldn’t compile arbitrary lambda calculus terms. Is that still the case and if so can you better describe what can’t be compiled?

I think I very much agree with your points and approach to parallelism.

> This applies to every data structure that can be defined algebraically.

Is this a mutually true? I’d expect this to hold for inductive algebraic data types but not co-inductive types?

> You can just run HVM in a single thread, though.

How easy would it be to share data structures between different threads? Say I have a large binary tree in one thread, can I send it to another thread without much cost? How about lambdas?

That isn't how it works. HVM threads work transparently, you don't need to think about them. The same data structure *can* be visible to multiple threads under some conditions, through cloning; for example, consider the following program:

    (Sum Nil        )  = 0
    (Sum (Cons x xs))  = (+ x (Sum xs))
    (Head (Cons x xs)) = x

    (Main x) =
      let xs = (Cons 1 (Cons 2 (Cons 3 Nil)))
      (Pair (Sum xs) (Head xs))

The result of this program is `(Pair 6 1)`. Since `Pair` is the topmost (root) node of the normal form, each of its elements will be computed in a separate thread. Because of that, the same `[1,2,3]` list will be accessed by each thread. But that's not actually a shared reference, because values only exist in one place; instead, the lazy cloner makes copies of the list, layer-by-layer, and sends these copies to the thread that will handle them.

Note that if the same expression was written in a deeper position of the normal form, it would be evaluated sequentially. This is what avoids the fine-grained parallelism issue. It also means that in many cases HVM will not be as parallel as it could, though! But when the parallelism kicks in, it is always productive.

Ok. I'd be interested in the following benchmark: A program that reads in a large map of key-value pairs; it then reads in a list of keys, and produces a list of values (order of the output is not important). The map can be modeled by e.g. a red/black tree.

I'd be interested in the performance in Haskell, if it was implemented using a number of worker threads (each with their own reference to the map), versus the best implementation you can think of in HVM.

Looks good. I'll keep that in mind and let you know if we write such a benchmark. Opening an issue would be helpful to remind us!