Fusing loops by specializing on functions with SpecConstr?

[Sebastian Graf]

 Hi Alexis,

I've been wondering the same things and have worked on it on and off. See
my progress in https://gitlab.haskell.org/ghc/ghc/issues/855#note_149482
and https://gitlab.haskell.org/ghc/ghc/issues/915#note_241520.

The big problem with solving the higher-order specialisation problem
through SpecConstr (which is what I did in my reports in #855) is indeed
that it's hard to

   1. Anticipate what the rewritten program looks like without doing a
   Simplifier pass after each specialisation, so that we can see and exploit
   new specialisation opportunities. SpecConstr does use the simple Core
   optimiser but, that often is not enough IIRC (think of ArgOccs from
   recursive calls). In particular, it will not do RULE rewrites. Interleaving
   SpecConstr with the Simplifier, apart from nigh impossible conceptually, is
   computationally intractable and would quickly drift off into Partial
   Evaluation swamp.
   2. Make the RULE engine match and rewrite call sites in all call
   patterns they can apply.
   I.e., `f (\x -> Just (x +1))` calls its argument with one argument and
   scrutinises the resulting Maybe (that's what is described by the argument's
   `ArgOcc`), so that we want to specialise to a call pattern `f (\x -> Just
   <some expression using x>)`, giving rise to the specialisation `$sf ctx`,
   where `ctx x` describes the `<some expression using x>` part. In an ideal
   world, we want a (higher-order pattern unification) RULE for `forall f ctx.
   f (\x -> Just (ctx x)) ==> $sf ctx`. But from what I remember, GHC's RULE
   engine works quite different from that and isn't even concerned with
   finding unifiers (rather than just matching concrete call sites without
   meta variables against RULEs with meta variables) at all.

Note that matching on specific Ids binding functions is just an
approximation using representional equality (on the Id's Unique) rather
than some sort of more semantic equality. My latest endeavour into the
matter in #915 from December was using types as the representational entity
and type class specialisation. I think I got ultimately blocked on thttps://
gitlab.haskell.org/ghc/ghc/issues/17548, but apparently I didn't document
the problematic program.

Maybe my failure so far is that I want it to apply and optimise all cases
and for more complex stream pipelines, rather than just doing a better best
effort job.

Hope that helps. Anyway, I'm also really keen on nailing this! It's one of
my high-risk, high-reward research topics. So if you need someone to
collaborate/exchange ideas with, I'm happy to help!

All the best,
Sebastian

Am So., 29. März 2020 um 10:39 Uhr schrieb Alexis King <
lexi.lambda at gmail.com>:

> Hi all,
>
> I have recently been toying with FRP, and I’ve noticed that
> traditional formulations generate a lot of tiny loops that GHC does
> a very poor job optimizing. Here’s a simplified example:
>
>     newtype SF a b = SF { runSF :: a -> (b, SF a b) }
>
>     add1_snd :: SF (String, Int) (String, Int)
>     add1_snd = second add1 where
>       add1 = SF $ \a -> let !b = a + 1 in (b, add1)
>       second f = SF $ \(a, b) ->
>         let !(c, f') = runSF f b
>         in ((a, c), second f')
>
> Here, `add1_snd` is defined in terms of two recursive bindings,
> `add1` and `second`. Because they’re both recursive, GHC doesn’t
> know what to do with them, and the optimized program still has two
> separate recursive knots. But this is a missed optimization, as
> `add1_snd` is equivalent to the following definition, which fuses
> the two loops together and consequently has just one recursive knot:
>
>     add1_snd_fused :: SF (String, Int) (String, Int)
>     add1_snd_fused = SF $ \(a, b) ->
>       let !c = b + 1
>       in ((a, c), add1_snd_fused)
>
> How could GHC get from `add1_snd` to `add1_snd_fused`? In theory,
> SpecConstr could do it! Suppose we specialize `second` at the call
> pattern `second add1`:
>
>     {-# RULE "second/add1" second add1 = second_add1 #-}
>
>     second_add1 = SF $ \(a, b) ->
>       let !(c, f') = runSF add1 b
>       in ((a, c), second f')
>
> This doesn’t immediately look like an improvement, but we’re
> actually almost there. If we unroll `add1` once on the RHS of
> `second_add1`, the simplifier will get us the rest of the way. We’ll
> end up with
>
>     let !b1 = b + 1
>         !(c, f') = (b1, add1)
>     in ((a, c), second f')
>
> and after substituting f' to get `second add1`, the RULE will tie
> the knot for us.
>
> This may look like small potatoes in isolation, but real programs
> can generate hundreds of these tiny, tiny loops, and fusing them
> together would be a big win. The only problem is SpecConstr doesn’t
> currently specialize on functions! The original paper, “Call-pattern
> Specialisation for Haskell Programs,” mentions this as a possibility
> in Section 6.2, but it points out that actually doing this in
> practice would be pretty tricky:
>
> > Specialising for function arguments is more slippery than for
> > constructor arguments. In the example above the argument was a
> > simple variable, but what if it was instead a lambda term? [...]
> >
> > The trouble is that lambda abstractions are much more fragile than
> > constructor applications, in the sense that simple transformations
> > may make two abstractions look different although they have the
> > same value.
>
> Still, the difference this could make in a program of mine is so
> large that I am interested in exploring it anyway. I am wondering if
> anyone has investigated this possibility any further since the paper
> was published, or if anyone knows of other use cases that would
> benefit from this capability.
>
> Thanks,
> Alexis
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