[m-dev.] Thinking about mode analysis and uniqueness
Nancy Mazur
Nancy.Mazur at cs.kuleuven.ac.be
Tue Jan 7 19:11:18 AEDT 2003
* Ralph Becket <rafe at cs.mu.OZ.AU> [2003-01-06 14:42]:
> Hi Nancy,
>
> Nancy Mazur, Monday, 6 January 2003:
> >
> > Hi Ralph,
> >
> > You might have a look at the reuse branch.
>
> You're right - I'll look into it. Does your analysis handle partial
> instantiation? I wasn't (and aren't) interested in that option; also,
> I'm primarily interested in working with mode declarations supplied by
> the programmer, both of which should make the analysis simpler.
Hmmm, okay, I'm starting to see the point... The main difference is that
you want to propagate the declared uniqueness information into the
procedure, and try to derive from this information as much valuable
reuse information as possible. Am I correct to say that you're only
interested in unique terms which are related to arguments that were
declared as such?
Within CTGC we go further by also considering a priori non uniquely
declared arguments as potential candidates for reuse. And that is why we
need more detailed aliasing and liveness information.
> > * Ralph Becket <rafe at cs.mu.OZ.AU> [2003-01-06 04:08]:
> > > Inference:
> > >
> > > (sX, X ~ Y) => sY
> > > (dX, X ~ Y) => dY
> > >
> > > (X < Y, sY) => sX
> > > (dX, X < Y) => dY
> >
> > I'm not sure this is correct...
> >
> > Your definition X < Y:
> > || X < Y X is possibly used in the construction bound to Y. < is a
> > || partial order.
> >
> > So this reflects situations like: Y = f(X, ... )
> > If so, then the 'deadness' of X doesn't tell anything about the deadness
> > of Y...
>
> The rule (dX, X < Y) => dY says that live values cannot include dead
> components.
I'm still confused about your terminology. Further on you make clear
that uX means that the outermost constructor of X is unique.
But the statement dY, resp. lY, means that the whole structure of Y is dead,
resp. alive? Including its components?
Am I right?
> The rule (dX, X ~ Y) => dY says that we must assume that a possible
> alias of a dead variable is also dead (since we may have updated the
> value bound to that variable.)
>
> Both of these rules seem reasonable to me. I agree that I am placing
> stronger constraints on bindings than are required by the language
> definition, but I would argue that this is a conservative approximation
> and is hence safe.
>
> > The other way around;
> > X = f(Y,...)
> > If X is dead, this indeed implies all the Y's being dead...
>
> I don't agree at all. X being dead simply means that there can be no
> further references to X (and, if X is unique, that we may destructively
> update the value bound to X.) Put another way, X being dead only
> affects the top-level functor, not the arguments of that functor.
Hmmm, I guess I'm still wrong...
Sorry of being so blunt ;-)
But the meanings of uX, dX, and lX are still not fully clear to me as
with respect to the components of X...
dX = outermost functor of X is dead (= not used in the further
computation of the program)
dY = outermost functor of Y is dead
Y = f(X,Z,..) => X < Y
So, outermost functor of X is dead, ie. not used.. but for
example, Z may still be used? and is perhaps not dead. Oh, I see, but if
Y would have still been in use, then so would X...
Okay, okay.. I got it.. sorry... You're right.. ;-)
> > but I don't see
> > how this rule will ever get applied. Because in most situations, you are
> > interested in proving that all the arguments are dead, in order to
> > conclude that X is fully dead. And even then, you have to be sure that
> > the outermost constructor is not shared.
>
> My analysis hopefully allows us to detect when a particular cell may be
> reused. I don't see why that requires showing that the arguments to the
> functor in question are also dead: if they're boxed then overwriting the
> parent functor cell can do no harm; if they're not boxed then there
> shouldn't be any references to those addresses.
this remark was because of my bad understanding of what you meant by
dX, only the outermost functor being dead...
> > I don't know if I'm making myself clear here, but the thing is, I don't
> > understand the point of this rule ;-)
>
> I don't think I understand your point. Can you give me an example where
> you think my analysis gets it wrong?
no ;-)
not for the moment...
> > > Aliasing, X = Y
> > >
> > > lX, fX, lY, bY | X = Y | bX, X ~ Y
> > >
> > > Test for equality, X = Y
> > >
> > > lX, bX, lY, bY | X = Y |
> > >
> > > Construction, X = f(Y, ...)
> > >
> > > lX, fX, lY, bY, ... | X = f(Y, ...) | bX, Y < X
> > >
> > > Deconstruction, X = f(Y, ...)
> > >
> > > lX, bX, lY, fY, ... | X = f(Y, ...) | bY, Y < X, ...
> > >
> > > We may also have postcondition uY for some uY depending upon the
> > > inst of X at this point.
> >
> > I don't know how finegrained you are planning to go (and I'm not sure
> > anymore what the goal of this mode-analysis was in the first place),
>
> The point is to identify safe cells for reuse in the context of nested
> unique values.
... based on the uniqueness declarations provided by the programmer.
> > but
> > uY will only be the case if X is fully unique.
>
> No, I can have a uniquely referenced value f(Y, Z) which has the unique
> reference for Y and a shared reference for Z.
Again my confusion of what you mean by uY, i.e. the outermost functor of
Y is unique.
> > Are you planning to make
> > a difference between uX, and the uniqueness of the outermost functor of
> > X?
>
> Yes, uniqueness only refers to the top-level functor of a variable in
> this analysis. Thanks for pointing out an omission in my description!
>
> > Anyway, I have the feeling that you really ought to check the
> > reuse-branch I've been working on. If the only difference is the degree
> > of detail of the analysis, then it's not difficult to modify the level
> > op detail by simplifying the domains we use.
>
> Given that I've been thinking about this far less than you have, I'd be
> surprised if that wasn't the case!
>
> > I wonder how the precision of the overall process will be. I have a
> > strong feeling that everything will be shared at some point.
>
> Why? I've tried to come up with reasonably precise definitions of when
> a variable is the unique reference to a particular functor and when that
> variable dies (and hence whether or not that functor's cell may be
> safely overwritten.)
>
> I can't see how the analysis would go wrong; tomorrow morning I'll try
> going through some examples and see what happens. I'll post the
> results.
The point was that I didn't fully understand that you are planning to
infer local uniqueness purely based on the declared unique modes.
So if I'm right, it's not your primer intention to try to reuse parts and bits
of structures that are only declared as input for example, hence being
considered as 'shared' ?
> > > Disjunction, (P ; Q), starting with state S
> > >
> > > If PrecondP | P then S must entail PrecondP.
> > > If PrecondQ | Q then S must entail PrecondQ.
> > > If X is a nonlocal and P | bX then we must also have Q | bX
> > > and vice versa.
> > > For any nonlocals X and Y we must have
> > > if P | dX then (P ; Q) | dX (and similarly for Q),
> >
> > I disagree. It's not because P leaves a variable dead, that the whole
> > disjunction makes it dead. What if Q contains some non-deterministic
> > call depending on X. In that case, even if X is not used 'after' (P; Q),
> > it is unsafe to call it dead, as it still may be used upon backtracking.
>
> You've caught me out - I haven't addressed mostly deadness and so forth.
> The analysis presented here is an approximation to the real thing, which
> I haven't fully worked out; I'm hoping the audience will allow me a
> little leeway for now while the basic idea is discussed. However, I
> will say that since unique values can't be passed out of
> non-deterministic contexts, it's not obvious to me that there's a
> problem.
>
> > > if P | sX then (P ; Q) | sX (and similarly for Q),
> > > if P | X < Y then (P ; Q) | s < Y (and similarly for Q),
> > > if P | X ~ Y then (P ; Q) | s ~ Y (and similarly for Q).
> >
> > Hmmm. What if P | sX and Q | X < Y ? What is the result?
> > (P ; Q) | sX sY ? How does the information get lost here?
>
> Yes. The analysis isn't 100% accurate, but I don't think that's an
> issue. I think this analysis will work for 90+% of the key cases and is
> simple enough to be efficiently implementable.
>
> > I think you should be more specific on how the 'least upper bound' of
> > the different elements in your domain is... because it is the least
> > upper bound that you are computing here...
>
> I'm sorry - it may be because I've had a couple of beers, but I'm not
> clear what you mean here! Can you rephrase the suggestion?
Well, my terminology was a bit too technical perhaps. What I meant is
that typically you combine the information collected for each branch of
a disjunction, and approximate the result by one single value which is a
correct and safe description of what happens in each of the branches.
In your scheme above, you say that X < Y in one branch results in X < Y
for the whole disjunction (hmm, I now see that you wrote s < Y, was that
the purpose?). In the next line you say that if one branch gices X ~ Y,
then the whole disjunction will be X ~ Y.
And therefore my natural question: if one branch yields X < Y, and the
other X ~ Y, what is the result? What is the final approximation you
take for correct?
> > > Variable Death
> > >
> > > If at any point we have uX and for all Y s.t. X ~ Y we have that
> > > Y does not appear anywhere in the subsequent computation, then
> > > we infer that X is dead, hence dX.
> >
> > "anywhere in the subsequent computation" may be a bit harder then you
> > think if you want to take non-deterministic procedure calls into
> > account...
>
> But I don't, really. I'm pretty much only concerned with explicitly
> declared unique values, which rules out non-deterministic contexts.
Okido
>
> > > Reuse criterion
> > >
> > > A variable X's cell may be destructively updated (reused) if we
> > > have (uX, dX).
> > >
> > > I'll hold off posting thoughts on efficient implementation until I see
> > > what holes people can find in the above.
> >
> > I'll repeat myself ;-) But this analysis is the goal of the liveness
> > analysis we're doing in the context of CTGC. The precision of this
> > analysis is finer-grained then what you specify here.
>
> How much more complex is your analysis?
The analysis is not focused on declared unique terms, but is able to
derive for itself which (parts of) input arguments become dead in the
context of the procedure. This requires interprocedural analysis as you
need detailed aliasing information between terms.
> How much more effective is it?
If you give me an exmample of a procedure for which you plan to derive
some kind of local uniqueness, then I can try it out with our analysis..
> I really don't want to reinvent the wheel, but I was under the
> impression that your analysis was far more general and costly than what
> I have in mind.
It is indeed.
> > So, my questions would be:
> > - what is the exact purpose of all these inferences?
>
> To provide "cheap" local analysis for nested unique values in order to
> support destructive update thereof. I'm primarily interested in cases
> where the uniqueness of the headvars is known.
I see.
> > - can't the liveness information we collect be simply used for your
> > purposes? Or is the analysis too complex/time consuming?
>
> For the first part, I'll have to go look at your code.
> For the second part, I don't know - how costly is your analysis?
It's a full interprocedural analysis, with fixpoints and the whole lot.
> > The thing is, that the analysis we've implemented infers for each
> > variable that is ever deconstructed whether it becomes dead or not. If
> > it's not dead, the analysis will still say to what it is aliased. And if
> > the aliases die, then at some point the whole structure may die.
>
> Agreed. I belive I cover this case.
>
> > Other, a finer grained question...
> > I guess you don't need a fixpoint computation, because every argument
> > of a procedure call that is bound is automatically set to shared?
>
> Yes, I'm not particularly interested in inter-procedural inference.
ok.
> > For the moment I have no further remarks... but I think we should talk
> > ;-) Or else one of us will do some work in double here...
>
> Definitely! I should go and re-read your papers. Or have you a
> disseration I could look at?
Not yet, writing it as we speak ;-)
> The plus-side of my analysis is that it should be relatively cheap
> (there's an equivalence class and a partial order involved, but I reckon
> the average equivalence class will have but two or three members and the
> average depth of any tree in the partial order will similarly be two or
> three.)
Nancy
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