Nested constructed product results?

[Alexis King]

Hi all,

I spent some time today looking into the performance of a program
involving a parser type that looks something like this:

    data AnnotatedParser a = AnnotatedParser
      { annotation :: Annotation
      , parser :: String -> (Maybe a, String)
      }

The `Annotation` records metadata about the structure of an
`AnnotatedParser` that can be accessed statically (that is, without
having to run the parser on some input). `AnnotatedParser`s are built
from various primitive constructors and composed using various
combinators. These combinators end up looking something like this:

    (<+>) :: AnnotatedParser a -> AnnotatedParser b -> AnnotatedParser (a, b)
    AnnotatedParser ann1 f <+> AnnotatedParser ann2 g = AnnotatedParser
      { annotation = Seq ann1 ann2
      , parser = \s1 ->
          let !(a, s2) = f s1
              !(b, s3) = g s2
          in ((,) <$> a <*> b, s3)
      }

Use of these combinators leads to the construction and subsequent case
analysis of numerous `AnnotatedParser` closures. Happily, constructed
product result[1] analysis kicks in and rewrites such combinators to cut
down on the needless boxing, leading to worker/wrapper splits like this:

    $w<+> :: Annotation
          -> (String -> (Maybe a, String))
          -> Annotation
          -> (String -> (Maybe b, String))
          -> (# Annotation, String -> (Maybe (a, b), String) #)
    $w<+> ann1 f ann2 g =
      (# Seq ann1 ann2
       , \s1 -> let !(a, s2) = f s1
                    !(b, s3) = g s2
                in ((,) <$> a <*> b, s3) #)

    <+> :: AnnotatedParser a -> AnnotatedParser b -> AnnotatedParser (a, b)
    <+> (AnnotatedParser ann1 f) (AnnotatedParser ann2 g) =
      case $w<+> ann1 f ann2 g of
        (# a, b #) -> AnnotatedParser a b
    {-# INLINE <+> #-}

This is great, and it cuts down on allocation significantly, but there
is still something unsatisfying about it: the `parser` function inside
the record is not affected by CPR! This is a shame, because
essentially all use sites immediately deconstruct the pair, making it
a prime candidate for unboxing. Ideally, we’d like to get this, instead:

    $w<+> :: Annotation
          -> (String -> (Maybe a, String))
          -> Annotation
          -> (String -> (Maybe b, String))
          -> (# Annotation, String -> (# Maybe (a, b), String #) #)
    $w<+> ann1 f ann2 g =
      (# Seq ann1 ann2
       , \s1 -> let !(a, s2) = f s1
                    !(b, s3) = g s2
                in (# (,) <$> a <*> b, s3 #) #)

In practice, little combinators like `$w<+>` are marked INLINE, so `f`
and `g` are usually known rather than unknown calls. This nested CPR
transformation would allow the tuple construction to fuse with the
tuple deconstruction, eliminating quite a lot of unnecessary
boxing/unboxing.

Unfortunately, it seems as though GHC’s implementation of CPR is
entirely first-order: although function arguments are given rich
demand signatures, results are only described one level deep. But as
the above example hopefully illustrates, that’s leaving significant
optimization opportunities on the table! Hence, my questions:

    1. Has this notion of “nested CPR” been explored at all before?
    2. Does such an extension to CPR sound worth its weight?

I peeked a little at GHC.Types.Cpr and GHC.Core.Opt.CprAnal, and it
seems quite manageable to me, but I haven’t actually looked into an
implementation attempt just yet. I’m mostly interested in whether
others have thought about something like this and/or run into similar
issues in the past, or if this is really an unusual construction.

Thanks,
Alexis

[1]: https://www.microsoft.com/en-us/research/wp-content/uploads/2016/07/cpr.pdf