[Haskell-cafe] Runtime strictness analysis for polymorphic HOFs?

Paul Chiusano paul.chiusano at gmail.com
Mon Jun 15 15:22:01 EDT 2009

Thanks for replies everyone. :) I had not heard of Rice's theorem but it's
not too surprising.
A couple thoughts I had:
1. In general determining whether a function is strict is undecideable. But
a conservative approximation can certainly be guaranteed to terminate. And
what is stopping us from having our conservative analysis continue at
runtime, as terms are evaluated by the running program? I think I could
formulate some notion of having the running program incorporate all
available information from terms that have already been evaluated into its
analysis. This could be considered the best possible analysis that doesn't
affect the termination properties of the program. (Since it does not affect
evaluation order of the program or what terms are evaluated.) Of course,
like Claus says there are tradeoffs here since a more accurate analysis
might not be efficient enough timewise to be useful. But like I said, we
already have a "budget" for doing some analysis at runtime since unnecessary
memory allocation of thunks also incurs a runtime cost.

2. Having to rewrite higher-order functions so they can be inlined and
specialized isn't really a general solution, IMO. It's too fragile, can't be
counted on to apply in 100% of all relevant cases, and places additional
conceptual burden on the programmer. You have to explicitly unpack the
concept and reason about it in each case. I'd rather be able to write the
most natural, idiomatic code, and have the compiler/runtime be a bit
smarter! Of course, if you are just looking to eek out performance from your
available tools, ad hoc solutions like this are fine. But I am asking if we
could do better!

So, right now it sounds like I should maybe explore this problem a bit more
to see what I find out, but tread carefully...


On Mon, Jun 15, 2009 at 1:39 PM, Claus Reinke <claus.reinke at talk21.com>wrote:

> I was recently trying to figure out if there was a way, at runtime, to do
>> better strictness analysis for polymorphic HOFs, for which the strictness
>> of
>> some arguments might depend on the strictness of the strictness of
>> function
>> types that are passed as arguments [1]. As an example, consider foldl. The
>> 'seed' parameter of foldl can be made strict as long as the binary
>> function
>> used for the fold is strict in its arguments. Unfortunately, because
>> strictness analysis is done statically, Haskell can't assume anything
>> about
>> the strictness of the binary function - assuming we only compile one
>> instance of foldl, it must be the most conservative version possible, and
>> that means making the seed parameter lazy. :-(
> As has been pointed out, strictness analysis is not decidable. That doesn't
> mean it is undecidable - running the code and seeing what it does gives a
> naive semi-decision procedure. So strictness analysis can be made more
> precise by using more and more runtime information; unfortunately it also
> becomes less and less useful as a static analysis in the process (in
> practice,
> not just termination is important, but also efficiency of the analyses, so
> an
> analysis would tend to become unusable before it became possibly non-
> terminating - there are trade-offs between precision and efficiency).
> For typical higher-order functions, there's a simple workaround, already
> employed in the libraries, namely to split the definition into a simple
> front
> that may be inlined, and a recursive back where the parameter function is
> no longer a parameter. Then, after inlining the front at the call site, the
> back can be compiled and analysed with knowledge of the parameter
> function. See the comment above foldl:
> http://www.haskell.org/ghc/docs/latest/html/libraries/base/src/GHC-List.html#foldl
> Claus
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