[Haskell-cafe] I love purity, but it's killing me.

[Sittampalam, Ganesh]

Sebastiaan Visser wrote:
> On May 27, 2009, at 1:49 AM, Conal Elliott wrote:
>> Hi Tom,
>> 
>> I've been working on another code-generating graphics compiler,
>> generating GPU code.  As always, I run into the problem of efficient
>> common subexpression elimination.  In Pan, Vertigo & Pajama, I used
>> lazy memoization, using stable pointers and weak references, to avoid
>> the worst-case-exponential behavior you mention below.  I'm now using
>> a bottom-up CSE method that's slower and more complicated than I'm
>> going for.
> 
> What do you mean with `exponential behavior'? Exponential related to
> what? 
> 
> For my FRP EDSL to JavaScript (toy) compiler[1] I've been
> implementing CSE as well. I traverses the expression tree recursively
> and creates an small intermediate language containing id's (pointers)
> to expressions instead of real sub-expressions.   
> 
> Maybe (probably) I am very naive, but I think this trick takes time
> linear to the amount of sub-expressions in my script. When using a
> trie instead of a binary tree for the comparisons there should be no
> more character (or atomic expression) comparisons that the amount of
> characters in the script.    
> 
> So the problem seems not to be CSE algorithm, but the fact that EDSL
> itself tends to blow up because it is hosted in Haskell. Like Tom's 
> example:
> 
>  > let d = Add c c
>  >     e = Add d d    -- "e" now as 16 leaf nodes.
> 
> But again, I might be missing some important point here.

That's exactly right. But it's pretty inconvenient to have your
expression tree to blow up exponentially in relation to the code the
user actually wrote! You can indeed construct an intermediate language
that collapses this blowup, but the pass to create it must take
exponential time if written completely purely, since it has to visit
everything at least once.

In my experience [1], observable sharing using GHC's stable names is a
pretty effective solution to this problem.

Ganesh

[1] http://www.earth.li/~ganesh/research/paradise-icfp08/

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