[Haskell-cafe] library on common sub-expression elimination?

wren ng thornton wren at freegeek.org
Sat Aug 13 04:59:58 CEST 2011

On 8/12/11 12:52 PM, Anton Kholomiov wrote:
> Just to make it explicit, is it
>       \a i ->
>           let t = a ! i in
>           if i>= 0 then
>              t
>           else if i>  0 then
>              t + a ! (i-1)
>           else ....
> bad idea, because of last else-case? Can it be mended with
> one another pass  for if-expressions?

Lifting the computation out of the guards preserves the semantics of the 
original program only if:

     (a) you can guarantee that it has no observable effects
         (i) this clearly precludes nontermination
         (ii) this also precludes it taking any non-zero measurable 
length of time to compute (or memory, or any other observable resource)


     (b) you can guarantee that the computation is executed in every 
possible execution path from the point to which the computation is 
lifted (including all exceptional paths); moreover, you can guarantee 
that all observable effects generated prior to the original sites of the 
computation are identical along all paths.

The reason for including (a)(ii) is that, if the computation takes a 
non-zero measurable length of time, then we can detect a difference 
between the original and the modified program whenever the computation 
does not adhere to condition (b). This is notable for performance 
reasons, but, more importantly, it's critical for the semantics of 
security. The relative time taken by different branches of a computation 
is an observable effect which could allow the informational content of 
"secret" variables[1] to leak out and be discovered.

It is only valid to ignore (a)(ii) when the semantics you're preserving 
explicitly exclude concerns with program execution time, memory, 
security, etc., by assuming/pretending that these things aren't observable.

[1] In this case, information about the value of i, and possibly 
additional things in the trailing else case.

Live well,

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